Overview

This is the last big push to bring everyone in the class up to speed on solar resource topics, so stick with it, folks! We will be learning a lot more about measuring light directly in the field relative to estimated light calculations based on empirical (data-driven) correlations.

Why do our eyes create so much bias in determining solar decision making? Is there something better than vision to compare the solar resource? Is the human eye really designed to be a solar detector of intensity? It's time to come eye to eye with our embedded ethics of measurement in society. More on that soon!

We use the concept of components to break the sky dome and the ground into digestible chunks of surfaces with common emission/absorption/ scattering characteristics (e.g., direct, G_b, diffuse, G_d, circumsolar diffuse, ground reflected diffuse, G_g). Components of global irradiance relate to the sources of light within the sky dome. A component is a term for the groups of physical orientations and scattering of light (e.g., diffuse component, beam component). The characteristic measures are assessed within temporal blocks as statistical summations of irradiation on a horizontal surface (e.g. G / I / H / H-bar / annual) and the degree of light scattering found on a horizontal surface via the clearness indices (e.g., k_T, K_T, K-bar_T ).

Figure 4.0: Diagram of the multiple components of a clear sky

Credit: Jeffrey R. S. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0 [1]

We shall see that when it is challenging or costly to measure multiple components of light (scattered and unscattered), we have old and somewhat dated tools to attempt broad estimations on the contributions of each component to the total irradiation incident on the aperture of interest. You will see how we often rely on historical observations and empirical correlations by solar scientists and engineers for hourly, daily, and monthly average day data. The main tools used for these older equations are both measured hourly Global Horizontal Irradiation (GHI, or I) gathered from a horizontally mounted pyranometer, and daily extraterrestrial irradiance (Air Mass Zero = AM0, or Top Of Atmosphere = TOA, or just I₀), which you learned about in the last chapter. We shall also find that one can infer more than just the components of light from the ratios of measured irradiation to AM0 calculated irradiation--however, there can be significant errors included in the process. We can also describe the fractions of days in a given month where lighting conditions will be clear or overcast/cloudy.

You will also see reference to the Typical Meteorological Year. Keep an eye out for that...it will be a major part of SAM simulation software.

By the end of this lesson, you should be able to:

• explain why the human eye is a poor solar detector and creates bias in decision making;
• describe the equipment used to measure irradiance and irradiation in the field and from space;
• contrast collecting data for horizontal irradiance and DNI with (Plane of Array) POA measurements;
• describe the meaning of a component of light, and list the components for anisotropic skies on a tilted surface;
• explain scenarios where direct POA (Plane of Array) measurement is not available and one must use empirical correlations (via clearness indices) to estimate irradiation on a horizontal surface;
• understand and be able to apply typical meteorologic year (tmy) data to energy system simulations.

What is due for Lesson 4?

This lesson will take us one week to complete. Please refer to the Course Calendar in Canvas for specific time frames and due dates. Specific directions for the assignments below can be found within the lesson.

Questions?

If you have any questions, please post them to the Lesson 4 General Questions thread in Yellowdig. I will check the forum regularly to respond. While you are in a discussion, feel free to post your own responses if you, too, are able to help out a classmate.

Consider: I have personally heard people tell me that solar technology is not viable in Pennsylvania, North Dakota, and Minnesota. The news media have erroneously stated solar is too diffuse for all of the United States (old Fox News report: because Germany was supposed to be brighter?). Additionally, my colleagues have been told stories that solar is not viable in places such as Santa Barbara and San Francisco, as well.

None of these armchair philosophy assessments is correct. First, speculation on the solar resource using visual cues is not appropriate; our eyes do not actually measure the solar resource in a meaningful way for SECSs. Second, speculative resource arguments (even measured data) must ultimately be tied to economic arguments. Here, we lack the financial argument (the economics) associated with the avoided cost of fuels from incorporating solar energy technologies in a given locale for a client of interest. We will cover the financial and economic discussion in the next lessons to come, but let's go back to vision for a moment.

Sight Perception is a funny thing

Sight perception works to our advantage as individuals when we wish to minimize risk, such as avoiding that lion prowling through the forest in the evening. It also adapts with weak or intense signals, trying to feed the brain a useful stream of information. As such, sight also has limitations, in that our sensory systems are combined with a cognitive system to extrapolate small signals into big information or really intense signals into reasonable information. The goal of sight is information about the world around us, not the amount of light delivering that information to us.

How does the eye work?

Figure 4.1: Distribution of rods and cones in the human retina.

Credit: Modified by Brownson from Osertberg, G. "Topography of the Layer of Rod and Cones in the Human Retina", Acta Opthalmologica, Supplement, Vol. 6, 1-103, 1935.

The eye has two main conversion molecules: rods and cones, located in the retina. The two systems have adapted for dim lighting (rods) and full daylight. Rods absorb only certain wavelengths of light that are longer and lower energy, while the system of cones (actually multiple kinds of cones) absorbs the wavelengths of light that we interpret as color. In both systems of absorption, the maximum range of wavelengths is limited and does not include the ultraviolet and infrared regions that comprise about 50 percent of the shortwave band of solar irradiance. So, our eyes do not detect a large range of solar wavelengths, and the response factor of those receptors is not linear either. This is a detraction to using the eye as a quantitative solar detector.

Notice in the figure that the rods and cones are distributed across the back of the eye, but the two systems are not distributed in the same fashion. Rods are distributed broadly across the retina, with the exception of the fovea centralis. In complement, cones are distributed tightly within the fovea centralis. The two distributions are linked to the lens system of the eye.

• Cones: found mainly at the focal point of our lenses, the fovea centralis
• Rods: found distributed everywhere except at the fovea centralis

The implications of this property of concentrating optics is that cones will only detect light in the direction that the eyes are pointing. So, our color detection system is relatively poor at sensing diffuse or scattered light from areas of the sky or ground at which the eye is not pointing. Mark one more detraction for the eye as a solar detector.

Going back to the rods...they are distributed everywhere except the focal point, and so will detect diffuse light entering the eye from all angles. Recall that rods are not color sensitive; they just detect long wavelength photons, such as those at night or during the twilight. If you want to see more at night while riding a bike or running, you are encouraged to defocus your vision to allow peripheral light to be detected. The optical implications are that your rods are not part of a concentrating system and will detect diffuse light better at the expense of color discrimination, but only at low levels of light. Mark yet another detraction for the eye as a quantitative solar detector.

And now, your additional macroscopic feedback system to control light acceptance, the iris. As the object of your eye is to provide your brain with the best information, not power, the iris is a feedback system meant to open wide when the light is dim, and squeeze up small when the light is intense. No matter what your rods and cones are doing, your iris is constantly adapting to maximize the signal of visual information to the brain. In a power detection system, we do not want an adaptive iris system, because it again detracts from our goal of linear detection of irradiance changes across the day.

We can also add the eyelids and eyebrows to your optical system, as they block or shade much of the bright light to your eyes. We can add behavior to our eye system, in that very few people actually look up to sense the light in the sky, and tend to look to the horizon instead, meaning our lenses are not trained vertically upward, but more along a horizontal plane (we mount solar detectors flat, to point up to receive the entire sky dome of light). All in all, we can come to the conclusion that the eye is not the ideal constant solar detector to inform us quantitatively of the amount and changes in irradiance during the day.

Power vs. Information

When a device takes one form of energy as an input and transforms it into different new forms of energy as outputs, the process is called energy conversion. The source of that input energy is called a resource. Now, if we were to draw upon the resource of the Sun from the point of a dude on Earth's surface, the energy form is electromagnetic radiation. We will call this light, bearing in mind that light from the Sun can be visible or invisible (ultraviolet and infrared) to the eye.

If one wished to transform the light into an electronic, or electrochemical signal, the resulting device (an energy conversion system) could be tailored to provide lots of power (more energy, less information) or to provide lots of information (less energy, more information). Let's use two examples: a photovoltaic cell (solar-electronic transducer), and the human eye (solar-electrochemical transducer).

• The photovoltaic cell is designed to respond in a linear fashion to the intensity of solar irradiance, thus delivering the maximum amount of power, but not functioning well at all in the night or during twilight. The device will provide changing levels of voltage and current (voltage times current is power) in a direct linear response to the intensity of irradiance.
• The human eye is designed with an iris, rods and cones, and lenses to respond in an adaptive, logarithmic fashion to the intensity of solar irradiance. The eye will detect the tiniest of solar signals on a starry night, and will adapt to the brightest of desert suns during the day, while always providing very similar levels of electrochemical voltage and current to the brain, but with a high degree of information content that can separate the light reflecting from a "lion" vs. a "tiger" vs. a "bear." A device that can sense a signal over many orders of magnitude is a logarithmic detector.

Summary

The eye is designed to provide you with the information sufficient to avoid bumping into bad things in extreme lighting conditions. This is called information, but it is not the useful information for assessing the solar resource quantitatively. A linear detector like a photovoltaic device is required to accurately measure the power of the solar irradiance.

Why Measure?

Measurement is an important aspect of all scientific endeavors. It is especially important in the proper and efficient design of solar energy collection systems. Proper solar assessment involves metrological and climate data, and correct measurement of global (beam and diffuse) radiation is essential to any solar design effort. Without adequate and precise measurement of the solar resources, system designers and engineers would essentially be "flying blind." In this section, we will discuss the equipment used to perform the required measurements.

Video: Measuring sunlight - Edited version for World Meteorological Day 2019 (4:36)

Pyranometers and Pyrheliometers

The Pyranometer: Global Irradiation Measurements

Pyranometers act as solar energy transducers, in that they collect irradiance signals and transform them into electrical information signals. That information is passed on to a data logger and computer, and then we either present the data in short bursts (1 second) or integrate and average the data over longer periods of 1 minute to 1 hour.

Research grade pyranometers use a film of opaque material to collect thermal energy. The thermal energy diffuses into a thermal transducer called a thermopile (a stack of thermal devices) that produces a small current proportional to the temperature. We should note that metals (in general) are very good reflectors, making them also very poor absorbers. So, how do we get a material that functions on thermal gradients to make use of the radiation from the sun?

The key is in the absorber material: Parson's black is a paint with very low reflectance across shortwave and longwave bands of light (~300-50,000 nm; making it an effective blackbody). However, if covered by glass (a selective surface), the "window" of light acceptance from the Sun is about 300-2800 nm. This system assembly forms a shortwave (band) global (component) pyranometer. Now imagine, if we develop a thermopile with a thin coating of a black absorber, but replace the glass with a material that is transparent in the longwave band (many organopolymers/plastics), we will have created a longwave (band) global (component) pyranometer.

On the other hand, inexpensive pyranometers can use photodiodes. Photodiodes are photovoltaics (just small). They are semiconductor films that directly convert shortwave band radiation into electrical signals (no thermal conversion step necessary). While the cutoff for a silicon photodiode is <1100nm, the integrated power response is fairly comparable to that of a Parson's black-coated thermopile detector. However, they do not perform as well (relative to thermopile detectors) near sunrise and sunset due to a cosine response error.

Review of a pyranometer in operation:

For standard research, technicians mount pyranometers in a horizontal orientation. Pyranometers produce a voltage in response to incident solar radiation. Provided that a pyranometer uses a thermopile (thermoelectric detector), the device acts as an "integrator" of all components and bands of light. In the case of a glass enclosure, even a thermopile detector will operate only in the shortwave band. Pyranometers based on photodiodes are used only for shortwave global radiation measurements. The following two images are explained in detail at the University of Oregon's Solar Radiation Monitoring Laboratory [12] (maintained by Dr. Frank Vignola). The left image is a LI-COR pyranometer [13], which uses a silicon photodiode to measure irradiance (a little PV cell). The right image, which looks like a flying saucer from the 1950s, is an Eppley Precision Spectral Pyranometer (PSP) [14]. The Eppley is a First Class Radiometer, and uses a thermopile to measure irradiance. The white ring is to reflect stray light away, such that the system does not heat up and so that the influence of the ground reflectance (the albedo) is minimal.

Figure 4.2: LI-COR pyranometer (left), Eppley Precision Spectral Pyranometer (PSP) (right)

Credit: UO SRML [12]

Standard pyranometers are designed to be mounted horizontally in shadow-free areas, with the normal vector relative to the surface of the collector (which is horizontal) pointing vertically. Measurements of downwelling shortwave band irradiance from a horizontal pyranometer collect Global Horizontal Irradiance, or GHI. However, through a simple modification, a pyranometer may also be used to measure diffuse irradiance. By using an occulting disk or band, beam radiation can be blocked from the sensor surface of the pyranometer, leaving only diffuse radiation to be measured.

The Pyrheliometer: Beam Component Measurements

If we wished to measure only the direct component of downwelling irradiation, we would use a pyrheliometer. The device is a combination of a long tube with a thermopile at the base of the tube and a two-axis tracking system to always point the aperture of the device directly normal to the surface of the Sun. A measure of irradiance from a pyrheliometer is therefore called Direct Normal Irradiance (DNI) (G_b,n) data. An Eppley Normal Incidence Pyrheliometer [14] is displayed below on the left, while an Eppley Solar Tracker [14] is displayed on the right.

Figure 4.3: Left: Eppley Normal Pyrheliometer (tracking system not displayed). Right: Eppley Solar Tracker system (2-axis tracking ability). The Eppley Normal Incidence Pyrheliometer is to be mounted on the Solar Tracker.

Credit: UO SRML [12]

Curious side note: The World Meteorological Organization (WMO) has a definition for "sunshine." Sunshine means irradiance conditions of >120 W/m² from the direct component of solar radiation. Really, sunshine has a definition!

Satellite-Based Methods

Until now, we have assumed that measurements of GHI or DNI will come from surface-based measurement methods. By reading Ch. 4 of the CSP Best Practices, we also see that satellites can be used to retrieve GHI (not typically DNI). Geostationary Satellites are used to collect GHI data.

In the United States, the National Oceanic and Atmospheric Administration's [15] geostationary satellites go by the name of "GOES," which is an acronym for "Geostationary Operational Environmental Satellite." Two operational geostationary satellites, GOES-13 and GOES-11, currently orbit over the equator at 75 and 135 degrees longitude West, respectively. As an aside, GOES-12 is currently drifting east toward $\varphi =-60°$, where it will provide images of South America.

To access images from GOES or geostationary weather satellites operated by other countries visit:

• University of Wisconsin's Website [16].
• NOAA's GOES Satellite Server [17]. This is operated by the National Environmental Satellite, Data and Information Service (NESDIS).

Geostationary satellites are far from perfect. Consider that images of clouds at high latitudes will become highly distorted due to the cosine projection effect, or from viewing the Earth at increasingly oblique angles. For latitudes poleward of approximately 70 degrees, geostationary satellites become essentially useless. But, this is also where the solar resource becomes quite limited. Polar-orbiting satellites can therefore collect at high latitudes where geostationary satellites are not efficient. Each polar orbiter has its cycle effectively fixed in space, completing 14 orbits per day while the Earth rotates.

Which is better, direct measurements or making do with estimations from less data?

Now that we have our measurements, how do we make use of them to estimate irradiance on any given tilted surface? In the following section, we want to sort out the way that we measure light in comparison to the way that we use solar data for simulations of SECS in software like SAM (System Advisor Model). The SAM model will only have hourly Global Horizontal Irradiation metrics to use (I), but we will want to estimate the hourly irradiation for an oriented surface (POA, I_t).

As you move through this lesson, think about the Plane of Array (POA) for a Solar Energy Conversion System, and think about how we often measure irradiance using a horizontal pyranometer (and ONLY a horizontal pyranometer, unfortunately). What is the value of DNI in estimating the solar resource components for any given tilted (and maybe even moving) surface?

Estimating Light from Less Data (only GHI available)

As you have learned from reading Chapter 8, the main way that meteorologists have measured irradiation is from a horizontal surface. However, most of our SECSs are mounted on non-horizontal surfaces. This presents a challenge.

• A component is a term for the groups of physical orientations and scattering of light (e.g., diffuse component, beam component).
• We use the concept of components to break the sky dome and the ground into digestible chunks for receiving or reflective surfaces with common emission/absorption/scattering characteristics (e.g., direct, diffuse, circumsolar diffuse, ground reflected diffuse).
• A solar collector with a non-horizontal orientation (tilt: $\beta \ne 0$)will receive solar irradiance from a multitude of reflecting and scattering surfaces, including the beam of the Sun, the refracted solar light from the broad sky, and the reflected light from the ground.

When measuring the solar irradiation incident on a surface of interest, we measure the total or Global solar irradiance, which is a sum of the two components: Beam and Diffuse. Here, we present an equation for components of irradiance, G (we could have shown components of hourly irradiation in the same way) incident upon a horizontal surface.

$$G=G_b+G_d$$

Solar radiation that reaches the earth from the sun is generally not constant. A number of factors can affect the amount of radiation we receive. These factors include time of day and year, state of the atmosphere, and presence of aerosols. As stated earlier, the total solar radiation incident on a surface comprises of different components, and there is a simple reason for this. Not all the light emitted by the sun reaches the surface of the earth without any interference. As the emitted light passes through the atmosphere, a number of things generally happen. Some of the light may be absorbed, scattered, or reflected by the air molecules, water vapor, and aerosols. This portion eventually reaches the earth but not with the full intensity it had when originally emitted by the sun. We call this diffuse irradiance (G_d).

$$G_t=G_{b,t}+G_{d,t}+G_{g,t}$$

Air chemistry in the path of the beam will scatter the energy into a small cone of light, called the circumsolar component of the sky dome. Next, the scattering events that occur during the day produce a blue or white hue across the hemispherical surface. This is referred to as the sky diffuse component of irradiance. A horizon diffuse component is observed as the path length increases for scattering in the sky. Finally, the reflectance of the ground surfaces will contribute an extra component as long as the collection system is not mounted horizontally. Some light will be reflected from the ground back to the tilted surface. This component is appropriately called ground reflected component.

$$G_{d,t}=G_{circ,t}+G_{sky,t}+G_{hor,t}$$

There also exist portions of the emitted light that reach the earth directly with no interference from the atmosphere. This is called the direct or beam irradiance (G_b). If we have a measurement of DNI (Direct Normal Irradiance), then we can quickly estimate beam irradiance for the horizontal surface via the cosine relation to the zenith angle (${\theta }_z$). Atmospheric conditions, however, have a strong influence on the amount of beam radiation we receive. On clear, dry days, atmospheric condition can attenuate beam radiation by around 10% and by nearly 100% on very dark cloudy days.

Figure 4.4: Diagram of the multiple components of the clear sky.

Credit: Jeffrey R. S. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0 [1]

The Flow of Data from GHI to components to POA

In the following flow chart of data processing, we see that measured irradiance (shortwave, from the Sun) is measured in four typical manners:

Figure 4.5: Flow chart of data processing

Credit: Jeffrey R. S. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0 [1]

In the figure, we have integrated the time step to 1 hour of irradiation on a horizontal and tilted surface, respectively: I and I_t.

Measurement 1 (GHI) is the most common for a local site assessment in SECS design. Equipment for measuring DNI and DHI are atypical in an application site where the initial site assessment is beginning, and are absent from our satellite maps of the solar resource. Measurement 4 (POA) is becoming more and more popular, as it can potentially remove several steps of error propagation from empirical correlation on site.

Looking across the top line (Measurement 1), we see that we must perform "empirical correlations" using a metric called an "hourly clearness index" (k_T) to arrive at "calculated horizontal components of I_b and I_d (beam and diffuse hourly irradiation). Then, we must apply an "anisotropic diffuse sky/ground model" and sum the tilted components of irradiation, to finally arrive at a calculated POA irradiation estimate.

Paths 2 and 3 add to the level of precision by stepping past the clearness index correlations (which is error-prone) before applying an anisotropic diffuse sky/ground model and summing to a new calculated POA estimate.

Path 4 skips all of the empirical models and directly measures and integrates the irradiation on a POA surface. The one additional benefit would be to have a DNI measure along with a POA measure, for component decomposition if necessary (required for windows, for example).

The availability of solar data is very important when calculating the amount of radiation incident on a collector. Engineers and designers commonly make use of average hourly, daily, and monthly local data. However, the most common measurement available is the Global Horizontal Irradiance (GHI), which is then integrated through a data logger into hourly irradiation, or minute irradiation.

Estimation is an effective tool that involves the use of empirical models that were developed over the last 4-5 decades. The only tools we need are the equations for calculating hourly and daily extraterrestrial irradiance (Air Mass Zero, or AM0) and the integrated energy density (J/m²) gathered from a horizontally mounted pyranometer. These empirical methods to decouple beam and diffuse horizontal components are termed Liu and Jordan transformations, after the initial paper in 1960.

The Clearness Index

The linkage between the two data for horizontal orientation are the clearness indices (k_T, K_T, and ${\overline{K}}_T$). This index is simply a measure of the ratio of measured irradiation in a locale relative to the extraterrestrial irradiation calculated (AMo) at the given locale.

• $k_T=\frac{I}{I_0}$: the hourly clearness index for Total or global irradiation (that's what the "T" is for). This is a ratio of measured energy density against energy density for extraterrestrial solar in one hour.
• $K_T=\frac{H}{H_0}$: the daily clearness index for Total irradiation. This is a ratio of measured energy density against energy density for extraterrestrial solar in one day.
• ${\overline{K}}_T=\frac{\overline{H}}{\overline{H_0}}$: the monthly average daily clearness index for Total irradiation. This is a ratio of measured energy density averaged over the month as one day, against the energy density for extraterrestrial solar for an average day.

For K_T →1: atmosphere is clear. For K_T →0: atmosphere is cloudy. However, this measure incorporates both light scattering and light absorption. Keep in mind that a fraction is not a percentage, and in our case for a cumulative distribution, it is a decimal value between 0--1.

The Clear Sky Index

There is also an alternate indicator for the way that the atmosphere attenuates light on an hour to hour or day to day basis. This is the "clear sky index" (k_c). Mathematically, the clear sky index is defined as

$$kc=\frac{\text{measured}}{\text{calculated clear sky}}$$

and it has been proposed that 1-k_c is a very good indicator of the degree of "cloudiness" in the sky.

So, why do we use either the clearness index or the clear sky index? The answer at the moment is persistence. While it is likely that the clear sky index is more useful than the older clearness index in the long term, all the core research for the empirical calculations used in softwares like TRNSYS, Energy+, and SAM was based on k_T.

The Historical Backdrop: the Clearness Index

In the 1960s, Liu and Jordan found that for different US locations with the same value of ${\overline{K}}_T$ , the cumulative distribution curves of K_T were identical, almost irrespective of latitude and elevation.\marginnote{A cumulative distribution describes the frequency or fraction of occurrence of days in the month below a given daily clearness index, K_T}. This work was expanded into equations by Bendt et al.,\cite{Bendt81} using 20 years of real measurements in 90 locations in the USA. However, it was determined that the data sets were not so similar from region to region (e.g., the tropics had different correlations than the temperate USA, India was different from Africa, etc.) This work was followed by Hawas and Muneer for India and Lloyd for the UK, among others.\cite{Hawas85,Lloyd82}

Remember this! K_T distributions are not universal---they are regional and empirically derived. For all of our future work, we will only rely on hourly k_T values, and the manner in which k_T is used to back out a value of I_b, the hourly beam irradiation component on a horizontal surface.

Estimating the Plane of Array (tilted surfaces)

We shall see that we do not need to measure every component of light (scattered and unscattered) to make estimations on the contributions of each component to the total irradiation incident on the aperture of interest. We can rely somewhat on decades of historical observation and empirical correlation by solar scientists and engineers for hourly, daily, and monthly average day data.

The main tools we need are the equations for hourly and daily extraterrestrial irradiance (Air Mass Zero, or AM0) and the integrated energy density (irradiation: $MJ/m^2$) gathered from a horizontally mounted pyranometer, which you learned of in the last section. We shall also find that we can infer more than just the components of light from the ratios of measured irradiation to AM0 calculated irradiation--we can describe the fractions of days in a given month where lighting conditions will be clear or overcast/cloudy.

Following our step to break apart the beam horizontal component from the diffuse horizontal components, we then estimate the components on a tilted surface.

Procedure for Components

For a tilted plane of array,

Total Radiation = beam + diffuse, sky + diffuse, ground

$$G_t=G_{b,t}+G_{b,d}+G_{g,t}$$

A simple calculation of the beam component can be achieved using

$$G_{b,t}=G_{b,n}.cos\theta$$

Radiation on a sloped surface can be calculated for the beam component of irradiation by the geometric scaling factor of

$$R_b=\frac{cos(\theta )}{cos({\theta }_z)}$$

In order to estimate the diffuse component, we use alternate models that become increasingly better fits with the empirical data. We can integrate any of these equations over an hour or a day (irradiation). I prefer to offer the irradiance version as a bit easier to read. Note: all of these estimation models use irradiation values that were measured from a pyranometer mounted along the horizontal plane, and then estimated for beam and diffuse components from data correlation or directly measured using a shadow band measurement and energy balance equations.

Isotropic Diffuse Model: Liu & Jordan (1960)

The isotropic sky model was developed in the 1960s to estimate the diffuse sky on a tilted surface, complemented by an estimate for diffuse light from the ground. This model assumes that the sky is uniform in composition across the sky dome.

The following expression gives the total solar irradiance incident on a tilted surface as

$$G= {\text{beam+diffuse}}_{\text{sky}}{\text{+diffuse}}_{\text{ground}}$$ $$G_{total}=G_b{R}_b+G_d(F_{surface-sky})+G\rho (F_{surface-ground})$$

where,

$$F_{surface-sky}= \frac{1+cos\beta }{2}$$ $$F_{surface-ground}= \frac{1-cos\beta }{2}$$ $$G_{d,t} =G_d. \frac{1+cos\beta }{2}$$ $$G_{g,t}={\rho }_g(G_b+G_d). \frac{1-cos\beta }{2}$$

The fraction proportional to the collector tilt is called the diffuse sky irradiance tilt factor for an isotropic sky model, and the reflectance of the ground is called the albedo (a fraction between 0 and 1), and is multiplied by the GHI and the diffuse ground irradiance tilt factor for an isotropic sky model.

Note: "Surface": the aperture. $\rho$ : is the collective reflectivity of the ground (the albedo). $\rho$ reduces the irradiance G by a value between 0--1. On an inclined surface, G_d,ground increases, relative to a horizontal collector.

HDKR Model:

This model incorporates isotropic diffuse, circumsolar radiation and horizontal brightening. It also employs an anisotropic index A defined mathematically as

$$A=\frac{G_{N,I}}{G}$$

The total irradiance on a tilted surface is then calculated by using

$$G_T=(G_b+G_{d}A)R_B+G_d(1-A)\frac{1+\cos \beta }{2}\times \left[1+\sqrt{\frac{G_b}{G}}{\sin }^3\frac{\beta }{2}\right]+G\rho \frac{1-\cos \beta }{2}$$

Go to Kalogirou (Solar Energy Engineering) Ch 2 (pdf from Library) this will be labeled the "Reindl model"

Perez Diffuse Model: Richard Perez (1990)

This is an anisotropic diffuse sky model that takes into consideration the real observations of subcomponents of diffuse light. The Perez model adds the circumsolar diffuse component and the horizon diffuse component to the diffuse$_{sky}$ component of the isotropic model. Notice how the beam component is not mentioned here--it doesn't change.

Sidenote: Richard Perez is a Senior Research Associate in the Atmospheric Sciences Research Center in SUNY Albany. He has a great website [18].
$$G_d=G_{iso}+G_{cir}+G_{hor} +diffus{e}_{ground}$$ $$G_d=\left[G_d(1-F_1)\frac{1+cos\beta }{2}\right]+\left[G_d(F_1)\frac{cos\theta }{cos{\theta }_z}\right]+\left[Gd(F_2)sin\beta \right]+\left[G_d\rho \frac{1-cos\beta }{2}\right]$$ The shape factors (F) in this model can be reviewed in the original article by Perez et. al (1990). However, we can inspect the equations and observe in the equation that $F_{surface-sky}$ is reduced by a proportion of $F_1$ (circumsolar radiance), and $F_2$ can either increase or decrease the contribution of horizon radiance.

References:

Liu, B.Y.H., Jordan, R.C., 1960. The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation. Solar Energy 4(3),1-19

Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990. Modeling daylight and Irradiance components from direct and global irradiance. Solar Energy 44(5), 271-289

The data that you will find in your SAM simulation software, and the data that is all over the web in resources like the NREL Dynamic Maps of the USA solar resource [20], come from a single database, called the NSRDB, or the National Solar Radiation Database. There are currently three generations of TMY.

What is a Typical Meteorological Year? Why would we use a synthesized year of data for solar resource simulations?

A typical meteorological year (TMY) data set provides designers and other users with a reasonably sized annual data set that holds hourly meteorological values that typify conditions at a specific location over a longer period of time, such as 30 years. TMY data sets are widely used by building designers and others for modeling renewable energy conversion systems. Although not designed to provide meteorological extremes, TMY data have natural diurnal and seasonal variations and represent a year of typical climatic conditions for a location. The TMY should not be used to predict weather for a particular period of time, nor is it an appropriate basis for evaluating real-time energy production or efficiencies for building design applications or solar conversion systems.

...The TMY data set is composed of 12 typical meteorological months (January through December) that are concatenated essentially without modification to form a single year with a serially complete data record for primary measurements. These monthly data sets contain actual time-series meteorological measurements and modeled solar values, although some hourly records may contain filled or interpolated data for periods when original observations are missing from the data archive.

Wilcox and Marion (2008) NREL/TP-581-43156

Estimation can often be evaluated relative to 30 year averages of weather conditions at specific locations, termed the Typical Meteorological Year (TMY). These data are not reasonable estimates of extreme conditions (e.g., hurricanes, tornadoes) and may also be inaccurate for evaluating site or time-specific data. The most common database is TMY3, now collected from the period of 1991 to 2010.

TMY data was initially developed to aid in building simulation, for modeling the energy demands in counterpoint with the solar/meteorological gains. As in your software SAM (and the source code, TRNSYS), TMY is also used by SECS design teams for initial estimates of energy and financial returns on investment. We can use SAM's TMY data set to evaluate PV, solar hot water, and CSP systems.

The source data for the TMY set in the USA comes from the NSRDB, or the National Solar Radiation Database.

Lesson 4 Discussion in Yellowdig!

We have just read about Typical Meteorological Years (TMY) as simulation inputs in beginning project assessment. I want you to consider the positive and negative attributes of TMY data sets in terms of project design and then in terms of project operation and management. Post your answers to the following questions, and then let's have a discussion about them.

Tagging

When you create a post in the Yellowdig discussion space, you are required to choose a topic tag. For Lesson 4 discussions, please use these tags:

You can tag your post with one or several topics at the same time. All posts and contributions you create are added up to one score at the end of the week.

Importance of interaction

Yellowdig tip: remember to check in the Yellowdig site often - it is much easier to aborb the posted information in bits rather than reading multiple posts and comments in a bulk. Click to "Home" icon - you will be able to see all the unread posts in one place.

Grading

Yellowdig points you earn over the weekly point earning period (from Saturday to next Friday) will count towards 1000 pts. weekly target. But you can go above it (to 1350 pts. max). Yellowdig discussions will account for 15% of the total grade in the course. Check back the Orientation Yellowdig page in Canvas for more details on the points earning rules.

Deadline

There is no hard deadline for participating in these discussions, but I encourage you to create your posts in the middle of the study week (Sunday) to allow others to engage and respond while we are learning specific topics in the lesson. Also, remember that each weekly point earning cycle ends Friday night, and a new period starts on Saturday.

I want you to think about the need for estimation in preparing a new project design using a software like SAM. When does the estimation process give way to more detailed measurements in a SECS project?

Think about where estimated data sets like TMY fit in the process of applying solar resource data detailed below.

1. Pre-feasibility
2. Feasibility
3. Due Diligence
4. Project Acceptance and Systems Operation

When do we need to work as a larger design team with solar resource specialists who can monitor a site actively and maintain the equipment? When is the investment in measurement equipment appropriate for the planned project? For solar incorporations on the facade of a building (roof, windows, walls), do we need to measure the solar resource at the site?

As the world looks for low-carbon sources of energy, solar power stands out as the most abundant energy resource. Harnessing this energy is the challenge for this century. Photovoltaics and concentrating solar power (CSP) are two primary forms of electricity generation using sunlight. These use different technologies, collect different fractions of the solar resource, and have different siting and production capabilities. Although PV systems are most often deployed as distributed generation sources, CSP systems favor large, centrally located systems. Accordingly, large CSP systems require a substantial investment, sometimes exceeding $1 billion in construction costs. Before such a project is undertaken, the best possible information about the quality and reliability of the fuel source must be made available. That is, project developers need to have reliable data about the solar resource available at specific locations to predict the daily and annual performance of a proposed CSP plant. Without these data, no financial analysis is possible. This handbook presents detailed information about solar resource data and the resulting data products needed for each stage of the project."

--Tom Stoffel, Dave Renné, Daryl Myers, Steve Wilcox, Manajit Sengupta, Ray George, Craig Turchi; NREL/TP-550-47465

The purpose of this activity is to learn how the clearness index ($k_T$ ) can be determined for a specific day and time based on collected meteorological data and knowledge of the extraterrestrial solar irradiance. By definition, $k_T$ is essentially the attenuation factor of the atmosphere, showing the ratio between the solar radiation incoming into the Earth atmosphere and that reaching the ground:

where $I$ is the energy density measured at the horizontal surface at a locale, and $Io$ is the energy density just outside the Earth’s atmosphere at AM0. Of course, there are multiple natural phenomena that are responsible for scattering and reflection losses.

The clearness index was developed by the researchers Liu and Jordan at the University of Minnesota in the 1960s, and to this day this metric is still used by various models and empirical correlations for quantifying components of solar light.

In this activity, you will need to calculate the hourly $k_T$ values for two different hours on July 31^st, 2007 at Penn State SURFRAD location (Rock Springs). This activity builds upon irradiance data you were treating in Lesson 3, so you will use the same SURFRAD file for the clearness index calculations.

Part 1. Calculation of hourly irradiation (I) from SURFRAD data

Extract GHI data from the SURFRAD file (Penn State location) for July 31^st, 2007 for two different hours: (a) 8-9 am and (b) 1-2 pm.

Convert GHI data (measured in $W/m^2=J/s.m^2$ ) to energy density values (in $J/m^2$ ) by multiplying them by time. Note: SURFRAD data are recorded at 3 min step.

Find the total solar energy density (irradiation) delivered per square meter over each hour period. This is the measured $I$ value. Present your results in $MJ/m^2$ .

Part 2. Calculation of the extraterrestrial irradiation (I_o)

1. Calculate the hourly extraterrestrial GHI (AM0) for each of the hours of 8-9 am and 1-2 pm hours on July 31, 2007 using the equation below:
   \[{I_o} = \frac{{12 \cdot 3600}}{\pi } \cdot {G_{0,n}} \cdot \left[ {\frac{\pi }{{180}}({\omega _2} - {\omega _1})\sin \phi \sin \delta + \cos \phi \cos \delta (\sin {\omega _2} - \sin {\omega _1})} \right]\]
   In this equation: ${\omega }_i$ is hour angle for hourly endpoints 1 (beginning) and 2 (end); $\varphi$ is latitude, $\delta$ is declination for the day of interest, and $G_{0,n}$ is normal irradiance at AM0. All these parameters can be taken from the Bird model for State College location you used in Lesson 3. You only need data for day #212 in this calculation.
2. Present your $I_o$ value in $MJ/m^2$ . The results for $I_0$ are expected to be on the order of 0.5-5 $MJ/m^2$ . This will provide you with the denominator value in the $k_T$ expression.

Part 3. Calculation of $k_T$

Plug in your $I$ and $I_o$ values into the $k_T$ ratio and obtain values for both 8-9 am and 1-2 pm hours. Your result should be a number between 0 and 1.

Provide a brief discussion of results. What are the reasons for clearness index to change during the day?

Submitting Your Work

Your report should include the following: (a) Data tables with GHI for specific hours (8-9 am and 1-2 pm on 7/31/07) and corresponding irradiation values; (b) hourly energy density $I$ in $MJ/m^2$ ; (c) calculation of extraterrestrial irradiation shown; (d) hourly extraterrestrial energy density $I_o$ in $MJ/m^2$ ; (e) $k_T$ values for each of two hours; (f) brief discussion of the obtained values.

Upload your report file to Canvas (Lesson 4 Learning Activity DropBox) in PDF or docx format.

Grading Criteria

This activity is graded out of 30 points. 

Deadline

See the Calendar tab in Canvas for specific due dates.

This was the last of four lessons wrapping up the arc of core solar resource assessment content. In Lesson 4, you were introduced to the key elements of the solar resource and the ways we measure or estimate the resource in a given locale. We built upon our knowledge from Lessons 2 and 3, and also drew some content in a Lesson 3 activity to be applied in a Lesson 4 activity.

You went through a detailed reading on Best Practices for Solar Collection and Use to start, which provided us with a good amount of information for both CSP and non-CSP practices too. There were elements in the reading that stressed the importance in finding the appropriate data set for a SECS development plan. Solar resources are important to residential and commercial buildings, as well as to PV arrays, as well as to utility scale CSP and solar hot water or steam applications. Your job is to be aware of the type of data you use, to know the transformations that are done to the data to turn it into a useful input (for simulation), and to develop levels of confidence in using various qualities of data as a practitioner.

Now that you have completed the lesson, you should be able to:

• explain why the human eye is a poor solar detector and creates bias in decision making;
• describe the equipment used to measure irradiance and irradiation in the field and from space;
• contrast collecting data for horizontal irradiance and DNI with (Plane of Array) POA measurements;
• describe the meaning of a component of light, and list the components for anisotropic skies on a tilted surface;
• explain scenarios where direct POA (Plane of Array) measurement is not available and one must use empirical correlations (via clearness indices) to estimate irradiation on a horizontal surface;
• understand and be able to apply typical meteorologic year (TMY) data to energy system simulations.

You can always go back to these readings and dig into the references. There is now extensive documentation to guide you in your practical development; you just need to reach out and read it!