2.1.1.1 Fluid-bound properties

In CSP systems, the absorbed concentrated solar radiation is typically transferred to a specific medium, the so called heat transfer fluid (HTF) and thus made available for the final conversion into the desired form of energy. Consequently, the characteristics and thermophysical properties of this HTF play an important role in most performance analyses and energy balances.

2.1.1.2 Temperature

Beyond describing the process and observing its operational limits, temperature measurements are essential in performance assessment of CSP systems. While temperatures of components characterize their operating conditions, the temperature of the HTF mainly serves in determining the useful enthalpy provided by a system.

HTF temperature

Resistance temperature measurement devices (RTD) have gained great acceptance in performance testing due to their general qualities in view of accuracy and stability. They can be connected using two, three, or four wires, as shown in Fig. 2.1.

In the four-wire measurement setup, two wires are connected to a constant current source while the other two are connected to a volt meter with high impedance. The voltage drop across the wire and connection resistance is thus negligible, which makes the four-wire connection the favorable setup in terms of measurement uncertainty. Pt100 sensors with a platinium coil resistance of 100 Ω at 0°C and a specific resistance increasing almost linearly with temperature are the most commonly used RTDs in industrial applications. Pt100 sensors are classified as A or B [1] with lower temperature deviations and thus lower systematic uncertainty effects for type A sensors. Further differentiations are 1/3 and 1/10 B, referring to allowable deviations of 1/3 or 1/10 of those defined in class B, thus they are more accurate sensors than class A. Additionally, typical sensor characteristics such as hysteresis and drift are to be included in the uncertainty budgets of temperature measurements.

Depending on the process and safety requirements of a system, the fluid temperature can be measured either with sensors in direct contact with the medium or by mounting them in thermowells. In either case, sufficient immersion depths need to be ensured in order to prevent unwanted heat loss via the sheath [2]. Accuracy of 1% requires an immersion depth of five times the sensor diameter (industrial use); with increasing immersion depth, the accuracy increases (0.01% accuracy for 10 times the sensor diameter in good laboratory practice).

For temperature sensor installations with thermowells, the estimation of the required immersion depth should be based on the outer diameter of the thermowell. In case dynamic operation is included in the test program, the increased signal response time due to the thermal inertia of the thermowell wall material must be accounted for.

Temperature sensors are commonly calibrated for absolute temperature and classified relative to references in block calibrators. The requirements for accuracy and precision of HTF temperature measurements in performance testing strongly depend on the test application, in particular expected temperature differences. Measurement of small temperature differences generally requires lower uncertainty of inlet and outlet temperatures than large temperature differences. In order to obtain meaningful results even for small temperature differences, it is advisable to use relative calibration in order to rule out potential systematic deviations of temperature sensors. Accurate measurements of small temperature differences can often be achieved at lower costs using relative calibrated sensors with an adequate signal connection and conversion than would arise if using high-precision absolute calibrated sensors.

2.1.1.3 Flow rate

In the majority of performance tests, the HTF mass flow rates required for the enthalpy balance are calculated from volumetric flow rate measurement data and HTF density information. The only instruments directly measuring the mass flow rate are Coriolis meters, which are typically limited to maximum operating temperatures of 350°C or 400°C and which cause comparatively high pressure drops. An overview of the functioning principles of the flow meters most commonly used in CSP applications is given in (Fig. 2.2).

For small-scale test setups, almost any measurement principle may be applied according to individual needs in terms of operation conditions during testing. If applicable for the HTF in question, magnetic flow meters often offer relatively small measurement uncertainty. In large-scale or even utility-scale systems involving higher mass/volumetric flow rates vortex meters, orifice/nozzles or inline ultrasonic flow meters are typically used. They are chosen due to their low pressure loss and robustness, and may vary considerably in measurement uncertainty.

Available calibration facilities for flow meters are in general operated at temperatures below 100°C and are mostly limited to water and very few common fluids in industrial application. Therefore, calibration of flow rate sensors under field operating conditions is rare. Instead users have to rely on manufacturers' assumption of linearity, temperature corrections, and extrapolation to some extent. Where possible, cross-checking of flow rate measurement data using different type instruments is strongly advisable.

2.1.1.4 Pressure

The main objectives of pressure measurements in performance testing usually lie in a general characterization and monitoring of the operation of a system, and/or pressure drops caused by particular components. Furthermore, they serve to determine whether the HTF is in liquid or gaseous state in order to use the corresponding thermophysical properties for the evaluation of the performance. Differential pressure measurements can serve for liquid level monitoring of sealed tanks or volumetric flow measurements with orifices and nozzles.

The best measurement approach and setup needs to be selected according to the individual requirements of a particular pressure measurement application in terms of pressure itself, operating temperature at the point of interest, type, and state of the HTF and uncertainty:

• High operating temperatures may require thermal decoupling of the hot fluid and the pressure sensor.

• Short and straight pressure lines are preferable for differential pressure measurements.

• The vertical alignment of pressure lines should be ensured, avoiding accumulation of gas in systems with liquid HTF.

2.1.1.5 Thermophysical properties of HTFs

State-of-the-art concentrating solar systems operate with various HTFs such as (pressurized) water, water/steam, air, thermal oil, and molten salt. While water and air have a long track record for a wide variety of applications and standardized fluid property data, the thermophysical properties of thermal oils (typical eutectic mixture of diphenyl oxide and biphenyl or silicone oil) and molten salt mixtures are typically less well understood and analyzed, and thus usually associated with higher uncertainty.

In the course of long-term operation, degradation of HTFs such as thermal oils and molten salt mixtures has been observed. This effect is mainly influenced by elevated operation temperatures but also by the system and its operation modes. As a consequence of degradation effects and potential fluid conditioning measures (e.g., separation of low boiler and sediments in the case of thermal oil), the chemical composition of the fluid changes individually in the course of its service life. Therefore, its thermophysical properties are likely to change and thus monitoring or repeated analysis is required to ensure long-term high-quality of test results.

2.1.1.6 Steam quality

The steam quality characterizes the mass fraction in a saturated mixture that is vapor. The steam quality is particularly relevant when determining the useful enthalpy provided by direct steam generation systems, since the enthalpy of steam (gaseous state) is at least one order of magnitude higher than the enthalpy of water (liquid state) of the same temperature and pressure.

Performance evaluation of direct steam generating systems typically requires information on steam quality with a high time resolution to characterize and rate a system fully. However, to date there are no robust, commercial instruments for inline steam quality characterization nor inline separate measurement of steam and water flow rates in saturated steam. Instead, probing ones such as throttling calorimeters are used. As a substitute, the enthalpy balance is often based on separate flow rate measurements of water and steam downstream of the separator including the water level and retention capacity of the separator vessel. Due to the inertia of the separator, this workaround approach can only be applied successfully and with moderate uncertainty when considering longer stable test sequences and evaluating them as a whole.

Alternative approaches under development constitute wire mesh sensors providing three-dimensional information imaging phase distributions in flows [6]. While their use is currently too costly and laborious for commercial power plants, they might soon become available for research and development purposes.

2.1.2.1 Availability and focusing

The tracking of a concentrating solar power system determines its availability in terms of readiness to convert incident solar power to useful power. This way, it delimits valid test periods and characterizes the systems useful inputs for efficiency calculation. The system orientation can be measured by inclinometers and rotary position transduces or derived from signals of sun sensors. The difference between actual and ideal concentrator orientation can be calculated and the focusing state evaluated considering characteristic acceptance function of the system under investigation. This approach implies the need for precise absolute calibration of angular sensors or additional measures dealing with potential sensor offsets and common drift with time and ambient temperature.

2.1.2.2 Cleanliness

The cleanliness of the concentrator and receiver characterizes the state of a system. This is particularly relevant for those systems that cannot be thoroughly cleaned before a test due to their dimensions or other restrictions. Soiling or cleanliness can be expressed in terms of actual reflectance or transmittance of surfaces relative to their clean values.

Concentrator or reflector cleanliness is thus commonly measured with (field) reflectometers relating measurement values to those for clean surfaces. Especially for large fields, however, efficient methods and representative sampling approaches including soiling rates are required and not standardized yet [7]. Due to a lack of both accessibility and adequate field instruments measuring reflectivity or transmissivity of curved surfaces, receiver cleanliness is not usually measured during performance testing of large systems. Instead, the receivers are washed with the regular collector procedures and their reflectivity is assumed to correspond to that of the reflectors.

Generally speaking, cleanliness information needs to be individually and critically reviewed for overall quality and representativeness.

2.2.1.1 Solar irradiance—introduction

Solar radiation is the electromagnetic radiation that is emitted by the sun. Solar radiation can refer to solar exposure and/or to several physical quantities such as solar energy, solar irradiance, or solar radiance [12]. The irradiance is the radiant power incident on a surface per unit area. It has the units W/m² and is also called radiative flux density or radiative flux. Irradiance can be obtained by integration of the perpendicularly incoming component of the radiance over the solid angle. Radiance has the units W/m²/sr. It describes how much radiation is coming from a certain direction. Irradiation is the incident energy per unit area received during a specified time interval (units J/m²).

The electromagnetic radiation that reaches the top of the terrestrial atmosphere is called extraterrestrial solar radiation. Approximately 97% of the extraterrestrial solar irradiance is confined to wavelengths between 290 and 3000 nm.

Seen from outside the atmosphere of the earth, the sun appears basically as a disk whose size can be quantified by the angular distance α_disk between the visible edge of the disk and its center. This angle can be calculated from the sun's mean visible radius and the distance between the sun and the earth, r_s. Because of the ellipticity of the earth's orbit, r_s and α_disk vary during the year.

Due to interactions between the radiation and the atmosphere (scattering and absorption) the terrestrial solar radiation is divided into two components (Fig. 2.3). Direct normal radiation refers to solar photons that reach the surface without being scattered or absorbed. Diffuse radiation refers to such photons that reach the observer after one or more interactions with the atmosphere. These definitions and their usage for solar energy will be discussed in detail in the following.

In the strict sense of the definition, DNI is the irradiance on a surface perpendicular (called also normal) to the vector from the observer to the center of the sun consisting of radiation that did not interact with the atmosphere.

The mathematical formulation of this strict definition makes use of the broadband transmittance of the atmosphere T and the extraterrestrial normal irradiance DNI₀ for the actual sun-earth distance:

$DN{I}_{\mathrm{strict}}=DN{I}_{0}T$

[12]. These quantities are broadband values and therefore refer to the full range of the extraterrestrial solar spectrum. T is determined as the spectrally weighted average of the spectral transmittance T_λ,

$T_{\lambda }=exp\left(-{\tau }_{\mathrm{tot},\mathrm{s}}\left(\lambda \right)\right)\text{,}$

with τ_tot,s being the total optical thickness along the slant path depending on wavelength λ. The optical thickness of a given material between the points s₀ and s₁ is defined as

$\tau \left(s_0,s_1\right)={\displaystyle {\int }_{s_0}^{s_1}{k}_{\mathrm{e}\mathrm{x}\mathrm{t}}{\rho }_{\mathrm{mat}}ds\prime }\text{,}$

with mass extinction cross section k_ext and volumetric mass density ρ_mat of the material [13]. In the case of vertical paths, the optical thickness is also called optical depth. The optical thickness of the atmosphere can be derived as the product of the air mass and the atmosphere's optical depth from the top of the atmosphere to sea level under standard conditions (in particular at pressure of 1013 hPa). The air mass describes the optical path length through the atmosphere to the observer relative to the optical path length to sea level for the sun in the zenith and standard conditions. Please note that optical thickness and optical depth are often not distinguished correctly in the existing literature.

This strict definition is useful for atmospheric physics and used in some radiative transfer models, but brings along a complication for ground observations: It is not possible to measure whether or not a photon was scattered if it reaches the observer from the direction in which we see the solar disk. Therefore, DNI is interpreted differently in the world of measurements and also in solar energy applications.

Direct solar radiation is understood as the “radiation received from a small solid angle centered on the sun's disk” [14]. Please note that this definition from ISO-9060 does not distinguish between direct radiation on the horizontal or the normal plane. For CSP resource analysis, mostly the DNI is discussed, while in meteorology, direct radiation is often reported referring to the horizontal plane. The size of the above-mentioned small solid angle for DNI measurements is recommended to be 5·10⁻³ srad¹ (corresponding to 2.5 degree half angle) [12]. This recommendation is approximately 10 times larger than the radius of the solar disk itself (yearly average 0.2665 degrees). This is due to the fact that instruments for DNI measurements (pyrheliometers) have to be tracked to follow the path of the sun, and small tracking errors must be allowed. The large field of view (FOV) of pyrheliometers reduces the effect of such tracking errors.

In this work, we use DNI as the experimental DNI measured with a pyrheliometer according to the typical usage in solar energy applications.

Corresponding to this understanding of DNI, the diffuse horizontal irradiance (DHI) is the irradiance caused by solar radiation from a solid angle of 2π srad above a horizontally leveled surface excluding the radiation that is interpreted as DNI. Global horizontal irradiance (GHI) is the irradiance caused by solar radiation from a solid angle of 2π srad above a horizontally leveled surface. In accordance with this definition, the GHI can be calculated from DNI and DHI using the solar elevation angle, determined by a sufficiently accurate algorithm (e.g., [15]).

2.2.1.2 Irradiance measurements

There are different options for solar irradiance measurements. One option for DNI measurements uses a solar tracker with a pyrheliometer (Fig. 2.4). A pyrheliometer consists of a sensor element that is positioned at a well-defined distance behind an aperture. Thus, only radiation from a small angular region around the optical axis reaches the sensor element. For the often harsh conditions faced in solar resource assessment and at CSP test sites, mostly field pyrheliometers are used. Such instruments have entrance windows in the aperture in order to protect the instrument from e.g., dust and rain.

Field pyrheliometers usually use blackened thermopile sensors. Thermopiles generate a voltage that is proportional to the irradiance absorbed by the sensor surface. The voltages are in the order of 10 μV/(W/m²) and a calibration constant is required to convert the output voltage into a DNI signal. The calibration constants change with time and instrument utilization, and once every 1–2 years, a recalibration is required. International standards for the calibration of thermopile sensors exist (e.g., [16–18]).

Thermopile sensors allow a broad spectral response of the instrument, e.g., 300–4000 nm. This interval corresponds well to the energy-rich part of the terrestrial solar spectrum and to the spectral range of widely used pyrheliometers.

Absolute cavity pyrheliometers consist of a radiometer head with a blackened cavity and a control unit. Absolute cavity pyrheliometers are operated on the principle of adjusting an electrical power source to the same power as the incoming radiative power. The electrical power can be measured and with the cavity geometry, the DNI is obtained in absolute units of W/m². Absolute cavity pyrheliometers are used to calibrate other radiometers.

The tracking errors of solar trackers for pyrheliometers should be well below 0.7°. Solar trackers with sun sensors reach much better accuracies of 0.05–0.1° when operated according to manufacturer manuals and best practices [19]. Automated trackers with sun sensors are recommended and care has to be taken during the adjustment of the tracker.

DHI and GHI can be measured with horizontally leveled pyranometers (see Fig. 2.4). Field pyranometers usually use blackened thermopiles as sensor elements that can receive short-wave radiation from the complete hemisphere above the sensor. The thermopile is usually placed under one or two glass domes, but diffusor disks are also used in some cases.

There are also photoelectric pyranometers making use of photodiodes instead of thermopiles. Photodiode sensors are commonly placed below a diffusor disk. Photoelectric pyranometers usually do not provide the spectral selectivity required in the ISO 9060 definition of the pyranometer classes [14].

As with pyrheliometers, pyranometers also use calibration constants, and periodic re-calibration is required.

The most accurate way to determine the GHI is by deriving it from accurate measurements of the DHI and the DNI [14], because good-quality pyrheliometers have a lower uncertainty than the best available pyranometers. In the ideal case, the GHI measurement with the unshaded pyranometer is only used as a quality check by comparing this measurement to the calculated GHI.

For DHI measurements, a shading structure is required, e.g., a tracked shading ball as shown in Fig. 2.4. The combination of a pyranometer and a shading structure that blocks the direct radiation on its way to the sensor is also called a diffusometer. Shading objects in the shape of balls, disks, or rings are used. Shading balls and shading disks must be tracked to the sun and cover only the part of the sky corresponding to the angular region defined for measuring DNI (see above). Shading rings cover the complete solar path during a day as seen from the pyranometer. Shading rings are even designed so that they cover the sun's path on consecutive days, so that readjustment of the shading ring position is only required every two days. Hence, shading rings also block a considerable part of the diffuse radiation. Therefore, correction functions are necessary to determine the DHI from the shading ring setup, and the accuracy of such a DHI determination is lower than for a DHI measurement with a shading disk or a shading ball.

Preferably, the instruments used for solar resource assessment and CSP testing should be well maintained ISO 9060 “First Class” pyrheliometers and “Secondary Standard” pyranometers. The expected accuracy of DNI measurements with well-maintained and thoroughly calibrated pyrheliometers is 1%–2% (1σ) depending on the other meteorological parameters, the logger and the cabling. For well calibrated and well-maintained pyranometers lower accuracies are reached (~2%). Please note, that these uncertainties are only valid for well-maintained instruments (including daily cleaning). If no daily maintenance can be provided, the uncertainty of such measurement systems can be worse than that of less expensive radiometers as, e.g., Rotating Shadowband Irradiometers (RSIs), discussed in the following.

RSIs consist of a pyranometer and a shadowband that rotates, e.g., once per minute around the pyranometer such that the sensor is shaded for some time independent of the solar positions (Fig. 2.5). When the shadowband is in its resting position, the GHI is measured. DHI is measured during the rotation when the shadow falls on the sensor. DNI is then calculated using GHI, DHI, and the solar zenith angle.

RSIs are often called RSRs or RSPs, depending on the instrument manufacturer (in these abbreviations, irradiometer is replaced by radiometer or pyranometer, respectively). The notation RSI refers to all such instruments measuring irradiance by use of a rotating shadowband. There are two types of RSIs: those with either continuous or discontinuous rotation of the shadowband.

The operational principle of RSIs with continuous rotation is explained in the following. At the beginning of the rotation, the shadowband is below the pyranometer in its resting position, and GHI is measured. The rotation is performed with constant angular velocity and takes approximately 1–2 s. During the rotation, the irradiance is measured with a high and constant sampling rate (e.g., 1 kHz). This measurement is called burst or sweep. In the moment when the center of the shadow falls on the center of the sensor, it detects DHI approximately. However, the shadowband covers some portion of the sky so that the minimum of the observed burst is less than the DHI. Thus, so-called shoulder values are determined by curve analysis algorithms as an input for an internal calculation of the DHI. The shoulder values correspond to the measurement obtained when the shadowband's shadow falls directly next to the pyranometer, but not on it. Currently, all RSIs with continuous rotation use photodiode pyranometers. This is necessary because the sensors need a sufficiently short response time in order to measure the irradiance signal during the rotation of the shadowband.

RSIs with discontinuous rotation do not measure the complete burst, but only four points of it [20]. First, the GHI is measured while the shadowband is in the resting position. The shadowband then rotates from the resting position towards the position where it nearly shades the pyranometer and stops, and a measurement is taken (e.g., during 1 s). Then it continues the rotation towards the position in which the shadow lies centered on the pyranometer and another measurement is taken. The last point is measured in a position in which the shadow just passed the pyranometer. The measurement with the completely shaded sensor is used equivalently to the minimum of the burst. The two measurements for which the shadow is close to the sensor are used equivalently to the shoulder values. The disadvantages of RSIs with discontinuous rotation are that a more exact azimuth and time alignment are required, and that one DHI measurement takes much longer than in the case of a continuous rotation.

DHI is typically determined only once or twice a minute, as it requires a shadowband movement. On the other hand, GHI measurements can be sampled in a higher frequency, e.g., every second. The variation of the GHI also contains some information on the change of DNI, and different algorithms are used to determine the averages of DHI and DNI between two rotations using the more frequent GHI measurement [21,22].

RSIs experience systematic errors due to cosine and temperature effects and the non-uniform spectral responsivity of the RSIs photodiode pyranometer. Correction functions can be employed to reduce these errors significantly. Several sets of correction functions exist which use the ambient temperature, solar zenith angle, air mass, GHI, and DHI as input parameters as summarized in Wilbert et al. [21,22].

Calibration constants that are multiplied with the photodiode output to obtain irradiance and recalibration are also required for RSIs as in the case of thermopile sensors. The calibration of RSIs can currently not be performed following existing international standards. The reasons for this are the non-uniform spectral responsivity of the photodiode pyranometer and the variation of the solar spectrum with the atmospheric conditions and the solar position. Several methods for calibration are used; most rely on long-term calibration campaigns (approximately 2 months) [23].

Typical standard uncertainties for corrected 10 min data are 2% for GHI and 2–3% for DNI when considering conditions that are relevant for CSP (simplified as cases with GHI and DNI over 300 W/m²) [22].

The accuracies of well-maintained RSIs are lower compared to well-maintained ISO 9060 first class pyrheliometers and secondary standard pyranometers. Nevertheless, in field measurements these initially lower accuracies of RSIs are often overcompensated for by advantages of RSIs [21,22], including their low soiling susceptibility [24,25], high robustness, and comparatively lower cost (instrumentation and operation and maintenance). Therefore, RSIs are frequently used in solar resource assessment.

2.2.1.3 Circumsolar radiation

For the correct use of DNI measurements in CSP modeling, circumsolar radiation plays an important role. Due to forward scattering of direct sunlight in the atmosphere, the circumsolar region closely surrounding the solar disk looks very bright. The radiation coming from this region is called circumsolar radiation.

For the typical FOV of modern pyrheliometers (2.5 degree half angle), circumsolar radiation contributes to the DNI measurement. This contribution can be quantified if the radiance distribution within the solar disk angle and the circumsolar region and the so called penumbra function [26] of the pyrheliometer are known. Such quantification is of particular interest for CSP, since the optics of most concentrating plants accept only a fraction of the available circumsolar radiation. The usable radiation in the plant is thus lower than the one measured with a pyrheliometer. This effect has to be considered in order to avoid an overestimation of the intercepted irradiance of a system.

Circumsolar radiation can be described by the radiance emanating from the circumsolar region and the sun as a function of the angular position relative to the center of the sun. The radiance distribution usually shows approximately radial symmetry around the center of the sun. Hence, such an azimuthal average radiance profile is a good approximation of the radiance distribution in most cases. The term “sunshape” refers to normalized broadband radiance profiles as a function of the angular distance from the center of the sun, normalized with the radiance at the center of the sun. Broadband refers to the spectral range of 300–4000 nm which corresponds to the spectral range of common pyrheliometers (see above).

The sunshape observed on the ground is highly variable and often differs strongly from the extraterrestrial radiance profile. This is basically due to forward scattering of the light by aerosol particles or ice crystals in cirrus clouds.

Fig. 2.6 shows sunshapes derived from the Lawrence Berkeley Laboratory (LBL) circumsolar telescope [27], the former DLR sunshape camera [28], and the SFERA sunshape measurement system [29]. Averages over several measurements are shown. The average sunshape named “avg. sunshape, filled” is considered the most accurate average sunshape for PSA. The “standard solar scan” was determined by Rabl and Bendt [30] as a normalized average from LBL's broadband absolute radiance profiles. The term “standard” should not be misunderstood. It refers to an average of many sunshapes that mostly deviate strongly from the “standard solar scan.” “DLRMean” shows an average sunshape and is presented under this name in Neumann et al. [28]. DLR0 shows another sunshape from this publication with relatively low circumsolar irradiance. The DNI and frequency weighted average of the profiles from Neumann et al. [28] is shown as “DLR, 2002, DNI weighted avg” and has been determined in Wilbert [31]. As sunshapes are normalized to 1 at the center of the sun, the DNI and frequency weighting are of importance.

The average sunshape named “avg. sunshape, filled” is derived with the DNI weighting method from a gap-filled continuous sunshape series for 2012 in 1-min resolution. A total of 24% of all sunshapes for DNI≥200 W/m² come from the gap-filling. The unweighted average calculated from the continuous 1-min time series for 2012 is shown as “avg. sunshape (unweighted), filled.” The sunshape called “avg. sunshape, unfilled” was derived with the weighting using all original sunshape measurements before the temporal gap-filling. The gap-filling has a noticeable effect, as measurement failures often occur during the system startup and more data with high air masses is lost. The data from LBL and Neumann et al. [28] are not gap-filled. The SFERA system was also deployed at Masdar, UAE and Odeillo, France, and further averages are available for these sites [31,32]. Other measurement methods exist that use RSIs [31] and pyrheliometers with different fields of view [33]. In addition, the modeling of circumsolar radiation based on satellite data is possible [34].

In the legend of Fig. 2.6, the circumsolar ratio (CSR) of the sunshapes is also given. The CSR characterizes the sunshape to some extent. It is defined as

$\mathrm{C}\mathrm{S}\mathrm{R}\left({\alpha }_{\mathrm{in}},{\alpha }_{\mathrm{out}}\right)=\mathrm{CSNI}\left({\alpha }_{\mathrm{in}},{\alpha }_{\mathrm{out}}\right)/{\mathrm{D}\mathrm{N}\mathrm{I}}_{\mathrm{circ}}\left({\alpha }_{\mathrm{out}}\right)\text{,}$

where α_in is the innermost angular distance from the center of the sun that is considered to be part of the circumsolar region (half angle). Typically α_in is the solar disk angle. α_out is the greatest angular distance from the sun's center that is considered to be part of the circumsolar region.

DNI_circ(α_out) is defined as the normal irradiance caused by the radiation observed within α_out around the sun's center (half angle), independent of whether or not the photons were scattered. It is related to the broadband radiance L_BB by

${\mathrm{D}\mathrm{N}\mathrm{I}}_{\mathrm{circ}}\left({\alpha }_{\mathrm{out}}\right)={\displaystyle \underset{\phi =0}{\overset{\phi =2\pi }{\int }}}{\displaystyle \underset{\alpha =0}{\overset{\alpha ={\alpha }_{\mathrm{out}}}{\int }}}{L}_{\mathrm{B}\mathrm{B}}\left(\alpha \right)cos\left(\alpha \right)sin\left(\alpha \right)\mathrm{d}\alpha \mathrm{d}\phi \text{.}$

CSNI(α_in, α_out) is the circumsolar normal irradiance observed in the circumsolar region between the angular distances α_in and α_out from the center of the sun.

The extent of the circumsolar region α_out cannot be defined in a universally valid way. This is due to the fact that different pyrheliometers and different concentrating collectors use radiation up to individual angular distances α_out from the center of the sun. Hence, α_out has to be selected depending on the investigated technology.

For the most accurate CSP modeling, the sunshape and the DNI are required. If the sunshape can be entered to the CSP model, this sunshape must be complemented by providing the corresponding DNI_circ(α_out). DNI_circ(α_out) can also be calculated from the experimental DNI and the sunshape in the CSP model, but to our knowledge, this option is currently not used. α_out usually has to be the greatest angle for which the sunshape information provides the radiance.

After the detailed discussion of the circumsolar radiation, we emphasize again that the experimental DNI obtained with a pyrheliometer is abbreviated as DNI in this work.

2.2.1.4 Clouds and aerosols—basics

Modeled DNI data are usually based on several atmospheric properties and radiative transfer calculations or parameterizations. The main parameters involved in radiative transfer calculations are optical depths of atmospheric components.

The total optical depth is the sum of the optical depths caused by clouds, aerosols, water vapor, Rayleigh scatterers, ozone, and other absorbing gases:

${\tau }_{\mathrm{tot}}={\tau }_{\mathrm{clouds}}+{\tau }_{\mathrm{Aeros}}+{\tau }_{\mathrm{H}2\mathrm{O}}+{\tau }_{\mathrm{Rayl}}+{\tau }_{\mathrm{O}3}+{\tau }_{\mathrm{MolAbs}}$

For CSP applications, the aerosol optical depth (AOD, τ_Aeros) and the cloud optical depth (τ_clouds) are of particular relevance due to their temporal and spatial variability, while the others are either well known (Rayleigh scatters) or less influencing (gaseous absorption). Clouds can attenuate the DNI completely, so that no direct solar radiation reaches the CSP plant, or does so only partially. The AOD is strongly wavelength dependent and its spectral dependence has to be known. Aerosol optical parameters as AOD, its spectral dependence, and scattering properties vary strongly as a function of the aerosol's chemical composition and the aerosol particle size.

2.2.1.5 Additional meteorological parameters

In addition to DNI, other meteorological parameters and effects must be included in plant yield assessment. In the following, we discuss the:

• wind speed, gust and direction;

• air temperature;

• relative humidity;

• atmospheric pressure;

• beam attenuation inside solar tower plants between a heliostat and the receiver; and

• the soiling of CSP plant components.

The importance of the first four of these parameters is investigated in Chhatbar and Meyer [35]. Although their effect on the plant yield is much less than that of DNI, it cannot be neglected.

Wind speed, wind gust, and wind direction are important parameters for the CSP plant yield. The wind gust is also called peak gust and defined as the maximum wind speed in a given time interval. Intervals of about 3 s are useful for most applications [12]. If the wind speed and/or wind gust exceeds a certain upper limit, the collectors must be moved to a stow position and the plant must be switched off. Plant components such as mirrors might also break due to the wind. Furthermore, wind speed, gust, and direction are important for the evaluation of both the optical efficiency of the collector (deformation) and the receiver efficiency (convection). Wind speed, gust, and direction are often understood as the horizontal component of the wind velocity. For some applications in CSP testing, the three-dimensional wind velocities are also of importance.

Wind speed and gust are measured with anemometers. The most common designs are cup anemometers and propeller anemometers. These instruments consist of a rotor that moves corresponding to the wind velocity and a signal generator that is connected to the rotor. Care has to be taken especially for gust measurements, as the dynamic response of the system must be considered. In addition, a relatively high sampling rate of 4 Hz is desirable [12]. There are several other anemometer types, with one of the most common being an ultrasonic sensor. Ultrasonic anemometers measure the time that an ultrasonic signal needs to cross a constant measurement distance that is exposed to the wind. Combination of several measurement paths can be used to derive the wind direction and the wind vector. For the measurement of the convective losses of tower receivers, LIDAR (light detection and ranging), RADAR (radio detection and ranging), and SODAR (sonic detection and ranging) techniques may also be of interest. For further details on these measurement options, see Emeis [36].

Wind direction can also be measured with wind vanes. Wind vanes change their direction corresponding to that of the horizontal component of the wind vector. The position of the vane can be read by, e.g., a potentiometer setup.

Air temperature and relative humidity influence the cooling and the receiver efficiency. Relative humidity is measured with hygrometers and dry bulb temperature with thermometers. Electrical temperature measurement with temperature dependent resistors or band gap sensors and capacitive or resistive humidity measurements are common for solar resource assessment. These sensors rely on the systematic change of the electric properties of the sensor material with the temperature or the relative humidity. Temperature and relative humidity sensors can be acquired as combined sensor (hygro-thermometers) including radiation shield and optional ventilation.

The atmospheric pressure is of importance for the receiver and power block efficiency (depending on the technology) and for cooling. For CSP applications, electronic barometers are of interest due to the availability of automated data logging. Electronic barometers consist of a transducer that creates an electronic signal depending on the state of a sensor element. The sensor element can be a piezoelectric material, an aneroid capsule that changes its shape or position due to the pressure, or a resonator that changes its mode of vibration with the pressure.

For solar tower technologies, the fraction of the AOD in the lowest part of the atmosphere up to the height of the tower needs to be separated from the total AOD. The extinction on the optical path between the heliostat and the receiver at the top of the tower has significant impact on the power output. For 1 km slant range between a heliostat and the receiver, around 10% of the energy is lost already for rather clear conditions, while for more turbid conditions, more than 30% can be lost. Such losses are highly relevant for the selection of the appropriate CSP technology for a given site, the plant design optimization, and the efficiency evaluation. The larger the plant, the more important this issue becomes. Recently methods to determine the beam attenuation have been developed [37,38]. The recommended measurement methods use selected transmissiometers or visibility sensors and dedicated data post-processing techniques to derive the broadband transmittance as a function of the slant range.

Site-specific soiling of CSP plant components is a result of particles settling down on the mirrors, receivers, entrance windows, or envelope tubes. It may drastically reduce the optical efficiency of power plants (e.g., as reviewed by ref. [39]).

Most studies on mirror soiling use handheld reflectometers to measure soiled mirrors before and after a cleaning. The ratio of the soiled reflectance and the clean reflectance is called cleanliness. Its change over time is called soiling rate and depends on the site of a CSP plant and the actual weather conditions during the measurement. Recently, measurement methods to determine the cleanliness with less personnel effort and higher time resolution have been developed [40]. The Tracking Cleanliness Sensor compares the DNI to a pyrheliometer measurement of DNI after reflection by an exposed mirror probe. The effect of soiling on entrance windows and receiver tubes is less relevant than that on mirrors, but it should be considered, too. Soiling and cleaning procedures are also discussed in chapters 3 and 8.

2.2.3.1 Satellite-derived data sets

Satellite-derived solar radiation data sets are based mainly on the monitoring of clouds by geostationary satellites. Polar orbiting satellite orbits are also used, but for the determination information on aerosols and other atmospheric constituents.

The geostationary orbit is a circular orbit approximately 36,000 km above the Equator. The satellite's angular velocity is chosen so, that geostationary satellites are placed above a fixed point on the Equator, the sub-satellite, or nadir point. Each satellite family has a nominal position related to a specific longitude and covers approximately 60 degrees from the sub-satellite point. Combining satellites with various sub-satellite points allows generating data sets covering the whole Earth up to a latitude of 60 degrees North and South. Satellite families have changed along the years, and when a change of the on-board technology takes place, they are referred to as a new satellite generation.

Satellite observations capture the radiation that has been reflected and/or scattered by the Earth's surface and its atmosphere. Each pixel value of a satellite image represents a specific area, depending on the characteristics of the satellite spatial resolution, the data processing and of each pixel position over the Earth's surface. At the sub-satellite pixel, the usual spatial resolution is 1–3 km. Towards larger satellite zenith angles, the pixel size increases, e.g., to 5×6 km in Southern Europe. The observations are taken with a typical temporal repetition rate of 15–30 min; this is also called temporal resolution. Depending on the geographical region, a reduced data set may be transmitted to the satellite ground segment (e.g., reducing the available observations to 3-hourly over South America). The observation of all pixels is done in a consecutive and scanning manner, resulting in different observation times for each pixel.

Satellite retrieval methods to derive solar radiation at the surface can be divided mainly into statistical and physical methods. In the first case, relationships between the digital count of a pixel of the satellite and global radiation measured at the Earth's surface are established (e.g., [44]), and tested/validated at several locations. Later these relationships are applied to the whole image. Due to the sparse ground measurement network for DNI, the number of stations both for the tuning and the validation is restricted and often those two data sets have not been kept separated strictly during the method development. Finally, GHI is converted to DNI using empirical “GHI2DNI” models (see e.g., Perez et al. [45] for a summary description).

In the second case, models are based on physical considerations taking into account the absorption and scattering behavior of the atmospheric components, the cloud reflectance and absorption, and the ground albedo, as well as other parameters. Although these models do not need ground measurements as the basis for tuning, they need detailed atmospheric information and fast radiative transfer approximations in order to process the large amount of 15-min resolved satellite observations.

Most recent models have a mixed nature (Perez et al. [45]). For the treatment of clouds, statistical approaches are used. In the physical part of the approaches, clear-sky models are used. Please note that a cloudless sky is called clear sky, which should not be confused with a clear atmosphere, because a cloudless sky can also occur if the atmospheric turbidity due to aerosols and water vapor is high. The problem of estimating DNI in such cloudless conditions is transferred to the problem of AOD and water vapor estimation. Typically, these “clear sky models” are used based on auxiliary data sets, e.g., from chemical transport modeling or NWP, but not being obtained from the satellite observations itself. These inputs have to be available worldwide and for many years only monthly mean data sets from the climatology research field have been available. Recently, some databases and services try to cover this lack of information, as e.g., MODIS (evaluated e.g., in refs. [46,47]) or the Copernicus aerosol service in the context of Copernicus Atmospheric Monitoring Service (CAMS, e.g., [48,49]). To describe the effect of clouds, a so-called cloud index can be used instead of radiative transfer theory and the cloud optical depth. The cloud index is derived from a set of satellite images including the current image and images with and without clouds, respectively. From the cloud index, the calculation of GHI using the Heliosat-2 method is possible. In this case, “GHI2DNI” models are used to determine DNI.

Satellite-derived solar radiation databases are often available as commercial products; some of them provide useful meta-data and validation reports. Few satellite-derived solar radiation data sets are free and available to public access.

2.2.3.2 Historical databases from NWP—the re-analysis option

NWP models are developed for weather forecasting purposes (e.g., [50] and see Chapter 8). For given initial conditions, the differential equations describing the evolution of the atmosphere are resolved to predict the weather. These models can also be used for “analyzing and predicting the past.” In the re-analysis mode, the NWP model is run using all available initialization input data (e.g., also that have become only available after a while and had not used in the original operational forecast run) and the most recent model physics. Available re-analysis products cover different periods in different temporal and spatial resolutions. Re-analysis products are operated by institutional bodies, but their results may not be free.

Re-analysis data sets are made with respect to climatological purposes and therefore cover more than 30 years. Satellite-derived data is available at a maximum of 20 years. For long-term purposes they need to be harmonized as the underlying observations have been made with a series of instruments, while the re-analysis is per definition using a single NWP physics and data assimilation scheme.

In recent years, some comparison of solar radiation data from re-analysis products has demonstrated that in general, their results are still far less accurate than satellite-derived solar radiation data [51]. Even so, there are specific developments that show a relevant improvement when using new parametrizations [52] and post-processing treatments [53]. These types of post-processing treatments are also commonly applied in the case of satellite-derived models and are shown below in the post-processing section.

While satellite-derived models have been developed focused on solar radiation variables, NWP models were focused on meteorological variables such as temperature, precipitation, and humidity. Radiation is typically implemented in order to describe the thermodynamics in the upper atmosphere, while the irradiance at the ground has not been in the focus.

Re-analysis data sets are typically the only option to obtain reliable long-term information about some other meteorological parameters needed for CSP simulations such as wind, temperature, humidity, and pressure. Hence, even if NWP data are not used for the creation of the long-term DNI data set, NWP data are almost always included in solar resource assessments.

2.2.4.1 Post-processing techniques definition and classification

All the post-processors try to improve the model behavior using the long-term direct model output and simultaneous, additional data, e.g., from a shorter period, or from a lower spatial resolution, and look for a relationship. After that, the relationship is applied to a longer period or a higher spatial resolution of the model output.

We distinguish between two main post-processing cases: regional-adaptation and local-adaptation.

• Regional adaptation is performed by model developers using available related modeled variables, as well as all available ground measurements in the geographical area covered by the specific product data set. Examples of regional post-processing are reported frequently by model developers (e.g., [55]).

• Local adaptations are performed by experts using the outcome from a data set (usually including already regional adaptations) and local ground measurements. These local ground measurements are commonly not available for the product development and must be collected for a specific CSP project. This assessment is focused on the specific location, and manages as much data bases as possible as well as at least nearly 1 year of valid local measurements [56].

An overview of different methods for site adaptation is given in Polo et al. [57]. Some cases deal with only one explicit variable, being the output from satellite-derived or re-analysis data sets adjusted to ground measurements, or the re-analysis data is adjusted to the satellite-derived data set. Other cases are examples of multivariate approaches and are called “data fusion” because two or more input data sets are actually fused applying linear models or non-linear models.

2.2.5.1 Typical meteorological years

It is generally accepted that a data set of meteorological measurements with true sequences and real interdependencies between meteorological variables is needed for the power plant energy yield assessment. Although there were proposals based on the use of only one week at each month [58], most of the proposals are focused on the use of a whole year, using real months selected from a long-term hourly database. Then, the objective is to derive the mean energy output of the CSP plant through the years, from the simulation of the solar system with this condensed annual series.

The first meteorological data sets for simulations were proposed by Benseman and Cook [59]. This study was the starting point of the so-called TMY methodology [60] or reference meteorological years (RMY) in the case of the Danish methodology [61]. The methodology from Hall et al. [60] was applied to 26 sites in the United States, and the output was available for comparisons of output technologies and systems. About 20 and 30 years later, new TMYs were calculated including new data and locations with slightly modified methods, and the products were called TMY2 [62] and TMY3 [63] in order to avoid misunderstandings with these different versions. However, the term TMY is also used to refer to TMYs created with methods that deviate from Hall et al. [60]. In addition to the methods from the original TMY, the TMY2 and the TMY3 with several modifications of the TMY methodology have been developed around the world, as summarized in Cebecauer and Suri [64].

The method to derive TMYs is summarized in the following. Data from 12 individual months are chosen from a period of several years of hourly meteorological data. The selection of the months is made based on the Finkelstein and Schafer method for arbitrary (non-Gaussian) cumulative distributions, and taking into account one or typically more meteorological variables. The months are selected in a two-step process. The first step is the selection of five candidates for 1 month of the TMY based on the cumulative distribution functions (CDFs) of each month and the average CDFs of all meteorological measurands that are considered relevant for the selection. The Finkelstein-Schafer (FS) parameters [65] for each considered measurand are determined for this purpose. Then a weighted sum of the FS for each measurand is calculated. The weighting factors for the FS of different measurands vary in the literature. For CSP, a high weighting should be given to DNI. The 5 months with the smallest weighted average of the FS are then selected as candidates. In the second step, 1 month is selected from the 5 candidate months. One option is to select the month whose mean DNI is closest to the long-term mean for the considered month of the calendar year. Other methods use the mean of other measurands and the persistence structure associated with mean and median daily dry-bulb temperature and the daily GHI sum for the final selection.

In recent years, solar thermal electricity projects have pushed researchers to look for specific solutions for CSP. From a methodological point of view, main differences presented in the TMY provided by different experts are related to the following:

(1) The variables needed to build the final series and their weighting factors: One extreme option is the use of DNI as unique relevant input. Otherwise additional related meteorological variables such as GHI, wind speed, or temperature have to be considered with nonzero weighting factors for the selection procedure.

(2) The use of measured and/or modeled data: some research lines propose the use of satellite-derived solar radiation data during long-term periods, as the main input for the TMY construction. The option of using an annual ground measurement campaign at the project's specific location is also much extended.

(3) The application of one, two or several criteria in the final selection of the month from the candidate months.

Some of the methodologies to derive TMYs exclude years affected by aerosols from volcano eruptions. This is only correct if the plant project's financing scheme does not include the risk of volcano eruptions separately. Such extreme cases must be included in the project evaluation, but it is important that they are included only once and not twice. As stated above, the TMY is not the only information required for CSP yield analysis. There is the need to provide probabilistic information for profitability assessments and annual payback. In addition to the TMY annual series, information related to the project annual payback in a bad year is needed for the promoters. A common approach for this evaluation is, as in the case of the TMY, to try to obtain a single annual meteorological data set, for the solar energy simulation.

2.2.5.2 Stochastic assessment and probability of exceedance

As mentioned in the last section, there is a need to provide information related to the energy yield during bad years. The best and most obvious option for this is to simulate the energy output of a power plant for many years of meteorological data. However, often the available data set is not sufficiently long, and at times a simplified method is required.

In order to have a reference, the most common studies try to obtain information about a CSP plant's annual energy output that is exceeded by 90% of the years during the power plant's lifetime. This annual output is called the P90 value of the annual energy output (unit: MWh_el). In addition to P90 values, P75, P10, and other Pxx exceedance values are also used. Although the objective is to provide a P90 energy output, P90 values of the DNI sum are also often used (unit: kWh/m²). However, there is no linear relation between the annual DNI value and the annual energy output, as is derived from the well-known need to simulate the plant's energy output from sub-hourly values. Because of this non-linear relation, it is not sufficient to determine only the P90 DNI value; a P90 meteorological year is required.

A debate related to adequate methodologies to generate meteorological P90 year series is still ongoing [64,66,67]. There is now consensus that P90 solar radiation series have to be related to the P90 annual DNI value, and not to P90 monthly DNI values concatenation. A P90 year must then be an annual series that has the P90 annual value of DNI. Due to internal monthly and daily solar radiation variability, an infinite number of different annual data sets can have the same annual DNI value, and the methodology for choosing one of them has to be consistent with the objective of trying to obtain a P90 annual energy output exceedance value. Most of the proposals have a methodological path not far from the TMY methodology, using months as candidates among the worsts available months instead from the available near to mean months. The main differences between the currently discussed approaches are related to the way of selecting the bad months for building the bad year.

There are clear future research needs related to the multi-year data set generation. In this case, multi-annual data sets are used for simulation instead of the TMY and P90 annual series. The mean and P90 annual values are evaluated from the empirical cumulated density function of the multi-year data set. The simplest multi-year data set is the to simulate the energy output with long-term gridded data sets locally corrected during the whole available period of years (typically around 20 years in the case of satellite and 40 years in the case of NWP re-analysis models). The output will cover most of the possible annual values permitting to assess long-term mean values as well as characteristic percentiles. But even when using data from gridded data sets of 20- or 40-year length, longer data sets are needed for an adequate stochastic approach where Monte Carlo simulations can be applied. Therefore, methods are being developed to derive an arbitrary number of realistic yearly data sets for multi-year analysis (e.g., [68]).