Overview

Welcome to Lesson 1! Here we start talking about solar energy and the value that societies derive from solar energy options, both past and present. Many of us who are extremely interested in solar energy have yet to learn about the deep, deep roots that the solar field has established over and over again in societies across the world. Additionally, we hear about amazing new developments in solar in the media, events that seem to be happening weekly (and sometimes daily)! We would like to generate a sense for why solar energy applications are growing now, why they did grow and sometimes bust in the past, and what we might expect in the future.

We will use examples from reading, images, and your own experience to explore the differences between:

1. Solar Resource (light from the sun),
2. Solar Energy Conversion Systems as designed technologies, and
3. Solar Goods and Services delivered by the combination of 1 and 2 (for example, electricity as 'solar good' and shade as 'solar service').

This lesson will also explore some historical aspects of the solar field, where societies have found fuels (geofuels such as coal, petroleum products, natural gas, and the biofuels such as wood and manure) more challenging to access due to various constraints. We will see that, in fact, an inability to access fuels is often the driving force for solar development. In contrast, when access to fuels is unconstrained, we find that solar development tends to slow or cease in society. In this lesson, we will also see how emerging solar industries correlate with global shifts in perspective regarding anthropogenic global warming, sustainability, and energy security. Frameworks will be explored for policy and entrepreneurial responses to these new perspectives.

Learning Outcomes

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

• Discriminate between (1) Solar Resource, (2) Solar Energy Conversion Systems, and (3) Solar Goods and Services;
• Explain the goal of solar design in terms of locale, stakeholders/clients, and solar utility
• Connect the historical and modern contexts for solar energy growth/recession to stakeholder preference, fuel constraints, and solar rights/access.

What is due for Lesson 1?

This lesson will take us one week to complete. Please refer to the Course Calendar in Canvas for specific timeframes and due dates - those can vary from semester to semester. Specific directions for the assignments below can be found further within this lesson.

Questions?

If you have any questions, please post them to the Questions thread in Yellowdig. I will check that forum regularly to respond. Feel free to go through the comments and post your own responses if you are able to help out a classmate.

Energy Demand in USA Society

We believe the global demand for energy in its various forms will keep rising, spurred on by an expected increase in population and industrialization of many developing countries. Policymakers, entrepreneurs, and scientists will be faced with serious questions on how to produce and deliver required energy to consumers. But focusing in on the USA, how does a country use energy where local population growth is smaller, and energy use has been outsourced to other developing nations?

Figure 1.1:Historical energy demand (consumption) within the USA, separated in terms of resource. The chart begins at 1775 and ends near 2010. In this chart, renewables from wind and solar are not presented--only hydropower is seen in yellow. This changed as of 2010, as we will see below.

Click for text alternative to Figure 1.1.

Bottom of chart displays dates from approximately 1775 to nearly 2010, marked in increments of 10 years. The left side of chart displays Energy consumed in Quadrillion BTUs, marked in increments of 5 Quadrillion BTUs. Six types of fuel are displayed on the chart: Wood, Coal, Petroleum, Natural Gas, Nuclear, and Hydro.

Wood begins at a little above 0 Quadrillion BTUs in 1775 and stays low, rising to only about 4 at its peak in about 1870.

Coal begins at a little above 0 Quadrillion BTUs in about 1850, becomes the primary fuel source from about 1883 -1950, rising to a height of about 17 Quadrillion BTUs in the 1920s and 1940s (with a dip in the 1930s), suffers another dip from about 1950-1960 (during which time petroleum and natural gas were gaining great ascendency), then rises again to about 22 Quadrillion BTUs by the early 2000s. Coal begins dipping again as the chart ends near 2010.

Petroleum begins at about 1 Quadrillion BTUs in about 1900 and starts to rise sharply by about 1917. By 1950, it equals coal at about 12 -13 Quadrillion BTUs. Petroleum continues to rise sharply, reaching a peak of close to 40 Quadrillion BTUs in the early 2000s. Petroleum begins dipping again before the chart ends near 2010.

Natural gas is close to 1 Quadrillion BTUs in about 1920. Its usage rises to about 23 Quadrillion BTUs by about 1970 before dipping in the 1970s, then rising again to about 23 Quadrillion BTUs by the end of the chart.

Nuclear begins at just above 0 Quadrillion BTUs a little before 1950, stays steady until close to 1970, then begins rising slowly to a peak of about 7 Quadrillion BTUs by the end of the chart.

Hydro begins at just above 0 Quadrillion BTUs in 1775 and stays low, rising to about 4 Quadrillion BTUs at its peak in the late 1990s.

Credit: U.S. Energy Information Administration, Annual Energy Review 2011, published September 2012.

Trends and milestones in the past few centuries

1880 to 1920:

• Farming work displaced by machines (industry).
• USA urban population grows from 28% to 50%.

1883:

• Fossil fuel combustion (coal) equal to biofuel combustion (wood).

1950-1980 (Post WWII):

• US urban population growth slows.
• Cars and highways lead people to the suburbs.
• Manufacturing decreases (outsourcing energy).

2010:

• Renewable energy surpasses nuclear power: exponential growth of the renewable industry kicks in hard!
• Wind surfaces as a large renewable energy player.
• Solar emerging: Decentralized solar power is rapidly expanding on rooftops ("behind the meter")

2010-2020:

• Emergence of 100% renewable cities and communities – USA: Rock Port, MO (2008); Greensburg, KS (2013); Burlington, VT (2014); Kodiak Island, AS (2014); Aspen, CO (2015); Georgetown, TX (2018). More than 40 cities globally (CleanChoice Energy, 2024).

2019:

• Solar energy system costs hit historic lows, falling ~70% over the 2010-2020 decade, to become economically competitive with other energy sources.
• Significant growth of solar installed capacity: total new electric capacity increased from 4% in 2010 to 40% in 2018 in the USA.

Figure 1.2: Levelized Cost of Electricity (LCOE) progression for solar energy without investment tax credits or state/local incentives.

Credit: US DOE – energy.gov/solar-office

2020:

• Globally, renewable sources demonstrated the fastest growth over the past two decades, reaching over 11% contribution to the global energy mix.

  Year	Fossil fuels	Wood biomass	nuclear	renewables
  2000	77.3%	10.2%	5.9%	6.6%
  2020	78.0%	6.7%	4.0%	11.2%

  Source: World Economic Forum, 2022

The Big Picture

Figure 1.3: Energy supply and demand by sectors in the USA in 2022.
A larger version of this chart.

Credit: Lawrence Livermore National Laboratory / US DOE (2022)

This annual energy flow chart shows the total energy generated by different sources and consumed by different sectors. The units used here are quadrillions of Btu’s (“quads” for short) indicate massive amounts of energy used at the national scale.

The total estimated energy consumption in the US in 2022 is around 100 Quads, and this number is on the upper end of the typical consumption bracket:

Total Annual Energy Consumption in the US over the Past Decade

Credit: based on data from Laurence Livermore National Lab

The contribution of solar energy has not yet approached the magnitude of traditional fossil fuel sources in the US, however its contribution to the renewable share of the electricity generation is actually substantial.

Let’s crunch some numbers:

National Electricity Mix

Total renewable energy share (including solar, wind, hydro, biomass, and geothermal) in the electricity sector sums up to 7.9 Quads (21%), which is comparable to 8 Quads (22%) for nuclear energy, 8.9 Quads (24%) for coal, and 12.5 Quads (33%) for natural gas. That is about 1/5 of the entire national electricity mix. If we look back at similar data for the year of 2012, renewables only accounted for 12% at that time.

What sources are fastest growing?

Comparing the data from the historical energy data from a decade ago (2012) and the most recent (2022), the fastest growing generation capacities are solar, wind, and natural gas. Nuclear remained steady, hydropower and geothermal showed small decline, biomass – small increase, and coal was on significant decline over these ten years.

Summarizing the trends:

By a big margin, solar has been the fastest growing source (almost 7-times growth!) in the national energy industry. The impacts were primarily seen in the residential and commercial sectors, which in addition to the grid may benefit from the distributed generation options (small-scale and off-grid installations).

Projections

Figure 1.4: Energy consumption by fuel source (Quads): three decade history and projections.

Source: US Energy Information Administration (AEO2022)

Projections shown in this plot are based on the analysis of energy markets by EIA: “we project that renewable energy will be the fastest-growing U.S. energy source through 2050. Policies at the state and federal levels continue to provide incentives for significant investment in renewable resources for electricity generation and transportation fuels. New technologies continue to lower the cost to install wind and solar generation, further increasing their competitiveness in the electricity market, even as the policy effects we assume level out over time.”

“We project that consumption of natural gas will keep growing as well, maintaining the second-largest market share overall. The expected growth in natural gas consumption is driven by expectations that natural gas prices will remain low compared with historical levels.” (EIA, AEO2022)

Major Players

In the past century, society has been dependent on combustible products such as coal, natural gas, and petroleum products as the fuels of choice. While these energy sources are relatively cheap, they are not always available or located where we most need them, and they are non-renewable. In addition to this, there are real concerns about the effects burning these products could have on human health and safety as well as large impacts on the environment in general. The following are geofuels (resources from the Earth that are non-renewable).

• Coal (fossil fuel)
• Petroleum derivatives (fossil fuel)
• Natural Gas (fossil fuel)
• Nuclear (fissile fuel)

Nuclear energy is an additional geofuel that does not have a major CO₂ impact and is a major resource in countries like France. However, it has a strong "yuck factor" for the majority of society in Germany and the USA. It has the additional challenge of undesirable proliferation of fissile material for arms use. Again, there are numerous countries including the USA that make use of nuclear power for low-CO₂ energy, but infrequent, high-visibility events such as Three Mile Island, Chernobyl, and Fukushima Daiichi continue to influence popular will to invest and develop the resource.

Renewable energy sources provide a suitable alternative to using fossil fuel combustion (which generates CO₂) to meet our energy needs. The well-planned use of renewable energy sources such as solar energy must form a part of the portfolio of energy sources. There are numerous real challenges for renewables like solar, such as intermittency and diurnal cycles (night-day), as well as the ability to identify economic opportunities, which is why we are putting a lot of effort into understanding the solar resource and the related economics in this course.

Energy production and CO₂ production—link to population

The following link uses Gapminder World to show the increases in cumulative CO₂ production through time associated with population growth. Click on the link and press "Play" in the bottom left of the diagram:

• Cumulative CO₂ production (logarithmic y-axis) vs. Population

You can explore this tool later and create your own plots with respect to time. For example, if you were to plot energy production (Supply) or use (Demand) you would see the same trend, or if you were to plot cumulative CO₂ (log) vs. total energy production (log), they would show a rough linear correlation. But, for now, I want you to see where there are links between population, energy production, and CO₂ production. Why is the USA more or less stable in its CO₂ production?

Yellowdig!

This semester we are adopting a new platform for class discussions – Yellowdig! If you have only participated in the Canvas discussions so far, this may feel a little different. My hope is that this tool will help us make the discussions more engaging while maintaining the breadth and depth of learning we hope for. Please refer to the course orientation page that explains the steps to establish your Yellowdig account and set yourself up for participation.

Already have the Yellowdig account? – Then go to Canvas course menu, and click on “Yellowdig” link on the left to enter the conversation space.

Lesson 1 Discussion: History of Energy Resources

Tagging

Yellowdig Tip: When you create a post in the Yellowdig discussion space, you are required to choose a topic tag. For Lesson 1 discussions, use either (or both) of these tags:

You can create a single post or split it into two different topics – whatever feels best for you!

Importance of interaction

When it comes to Yellowdig, your posts, comments, replies, questions and answers – all these may add points to your yellowdig score, so don’t hold back! In order for these activities to work best for your learning, you need to participate frequently, keep up with conversations going and take opportunities to interact with your peers. Sometimes spontaneous conversations sparkled over a single fact mentioned bring more value than initial content.

Grading

Yellowdig discussions will account for 15% of the total grade in the course. Your posting and interactions will contribute to your weekly participation score (1000 pts.). After each week, all the Yellowdig points you earned will be transferred to Canvas and added to the your cumulative participation grade. Check the Orientation Yellowdig page for more details on the points earning rules – how many you get for starting a conversation, posting a comment, or attracting traffic on your post.

Notifications

Be sure to set notification preferences in Yellowdig if you’d like to receive emails about someone posting or replying to your post. That will allow you not to miss important action as you go through the week.

Deadline

I encourage you to create your posts in the middle of the study week (Sunday) and not to wait until the end of the lesson. That will allow others to respond in a timely manner. Each conversation will stay open after the lesson is done, but it will be harder to earn a high score with your work once everyone moved on to the next lesson. Note that point earning window for each lesson is limited to one week.

Energy Constraint Response

We can observe that popular perception of solar energy is strongly influenced by access to inexpensive fuels. In periods when fuels were effectively accessible, inexpensive, and unconstrained, a light-induced energy transfer (for sensible or latent heat change or for electricity generation) is usually perceived as diffuse and insufficient for performing work. However, for periods in history where fuels have become constrained (e.g., inaccessible due to high cost or high risk), innovation has turned to solar technology solutions. In such cases, the use of light-induced energy transfer is perceived as ubiquitous, and ample for performing work.

Evidence of such fuel constraints is observed as far back as the fifth century BC. During this period, the Greeks faced severe shortages of wood fuel. Archeological remains demonstrate that home designs evolved such that all houses could draw maximal utility from the Sun's warmth in winter months. It is interesting that famous Greek individuals commented on this solar design of homes. Aristotle has commented that home builders would shelter the north side of a home to keep out the cold winter winds. Socrates also lived in a home heated by the sun, and observed, "In houses that look toward the south, the sun penetrates the portico in winter" keeping the space warm (Note: a portico is just an older term for a porch). The Greek playwright Aeschylus further noted that only primitive cultures "lacked knowledge of houses turned to face the winter sun, dwelling beneath the ground like swarming ants in sunless caves." How primitive have we been these years without solar designed homes?

The Sun as a large stock for Renewable Energy Resources

A renewable resource has a rate of withdrawal (a flow) from the stock that does not exceed the rate of resource replenishment.

Sun: pretty big stock for wind and solar.

The sun provides energy in the form of radiation. Solar radiation is the most important natural energy resource available to us because it drives all environmental processes acting at the earth's surface. It drives the earth's rain cycle, which powers modern hydroelectric generators, and large-scale atmospheric circulations which provide the winds that have powered windmills for centuries. The sun doesn't warm the air, because the sky is largely transparent. The sun warms the ground which then warms the air. We will show how solar energy conversion devices often take advantage of the solar-thermal connection. In fact, we can often take advantage of air masses contained by walls, trees, or hills to trap and store thermal energy from the sun.

Solar energy technologies convert solar irradiance (sunlight) into forms of energy found useful to society. Historical and current developments in solar technology often coincide with specific economic or fuel constraints. As we observe from our reading assignment, technologies using solar energy conversion have been developing for a long time. Solar and wind power are among the options providing a low or non-CO² associated energy source for electricity production. Solar energy is also a natural part of heat production in buildings or solar thermal plants. This section will review the value of solar energy from a historical context while also discussing the origins of using solar energy and the present-day development of the solar energy industry.

Controlling Home Heating: Passive Solar

Below is a link to a video of the Ryoan-ji Zen temple in Japan. Look to the left of the marker at the white field just to the south of the brown roof (you will need to zoom in a few times first). This is the famous rock garden of the temple. The white field reflects light into the adjoining room to the north, and the walls surrounding the field keeps cool air inside the area. As a side note, the icon you see on the building is a map symbol for a Buddhist temple.

If solar energy is this important, and the Greeks in the fifth century B.C already recognized this, you may ask why solar energy applications are not more prevalent than they are at the moment? While there is no simple answer to this, there are still many obstacles that lie in the way of its widespread adoption. The future of solar power development will depend on how we deal with constraints such as scientific and technological problems, marketing and financial limitations, and political actions and agreements that favor other energy sources.

Hot Air and Water

Horace de Saussure was a Swiss naturalist of note to the history of solar development in the 18th century. He began to explore the role of a glass cover on a confined space like a box or a room. In the 1760s, de Saussure observed the following: "It is a known fact and a fact that has probably been known for a long time, that a room, a carriage, or any other place is hotter when the rays of the sun pass through glass." To find out how effectively a glass cover works to trap solar gains, de Saussure constructed a large flat pine box that was insulated inside, with a glass cover on top. Inside the box, he placed smaller boxes. When the flat cavity-cover absorber was exposed to the sun (no concentration), the internal box heated to 109 °C (228 °F), which is 9 degrees higher than the boiling point of water.

Figure 1.4: Langley's hot box. A Cross-section of Langley's hot box, which was similar to de Saussure's later models. A thermometer penetrating the walls at right was used to measure the air temperature inside the inner box.

Credit: The Solar Cooking Archive

Functionally, the clear glass allows shortwave irradiance to transmit through and be absorbed by the dark interior of the box. In addition, the glass cover prevents the warm air from escaping. This is a classic flat plate cover-absorber system. The hot box that de Saussure began with later became a prototype for flat plate solar hot water panels, providing hot water to millions since 1892. The hot box also led to the development of modern solar cookers. For more information on solar thermal design, visit the following links:

• Solar Thermal Energy for Homes
• How Solar Cooking Works

Photovoltaics

Figure 1.5: Photovoltaic shading structure: an autonomous and mobile station that replenishes energy for electric vehicles using solar energy

Credit: Tatmouss from Wikimedia (CC BY-SA 3.0)

While photovoltaic materials were explored in the 1860s, tied to research in transatlantic telegraph cables (using selenium; by electrician Willoughby Smith), they did not emerge into the larger market until nearly 100 years later. Photovoltaics using silicon material were introduced to the commercial world during the early 1950s by three lead scientists at Bell Laboratories: Calvin Fuller (a chemist), Gerald Pearson (a physicist and materials experimentalist), and Darryl Chapin (a device engineer). The development of a silicon-based PV cell led to applications in space and telecommunications first, followed by applications for the petroleum industry (for anti-corrosion in wells).

PV has proved itself as a standard technology for decades. All of today's satellite communications are powered by photovoltaics, starting with the Vanguard 1 (which had no "off" switch, and so continued to transmit long after it needed to). So, be thankful, we would not even have a modern society without the advent of PV!

Review

Constraints have included wood shortages in Greece and Rome in early centuries BCE, shortages of trees and fuel in the Chaco civilizations of the Anasazi peoples of North America, coal reserve constraints in 19th century France, and fuel access constraints in rural California before the 1920s. We have recently (the past decades) entered into a new period of constrained fuel consumption due to climate forcing effects from anthropogenic greenhouse gases (associated with fuel combustion, agriculture, and high energy demand), as well as increased risk in supply chains for fuels (the quest for energy independence).

An important context of the approach to solar energy is understanding what a system is. We define a system as a collection of elements that are connected together via weak or strong network relations and that have a pattern or structure that yields an emergent set of behaviors. We are concerned, in this course, with environmental systems, each with boundaries that describe the system and its surroundings.

A Solar Energy Conversion System (SECS), as the name implies, is a system that converts the energy from the solar resource into work found useful by society. This system has the potential to be deployed as an ecosystems technology or an environmental technology, meaning the energy system interacts in a constructive way with the patterns of nature. As a process, solar energy conversion calls upon designers and engineers to include all the elements essential for the proper functioning of a conversion system. These include the Sun, the Earth and the applied technological system (for example solar thermal or solar photovoltaic) in question. These systems call upon researchers to simultaneously assess scales of solar resource supply and use, systems design, distribution needs, predictive economic models for the fluctuating solar resource, and storage plans to address transient cycles.

Collector Basics

We have reviewed the basic system concept that can be used to design solar energy conversion applications, and more detailed and thorough information will be presented in a future lesson. At this point, we move on to the nature and composition of SECS on the Earth side (incident surfaces).

A Solar Energy Conversion System consists of the following elements:

• Aperture (the opening to allow light in, and at the same time constrain the solar flux into the system);
• Receiver (the opaque absorber that converts the sun to other forms of energy, the active element that is responsible for energy conversion);
• Storage (sometimes there will be a designed or naturally present storage mechanism, as sunlight is intermittent);
• Distribution Mechanism (internal to the system, responsible for energy delivery);
• Control Mechanisms (which helps adapt the conversion process to the intermittent/seasonal changes and user needs).

The next section of this lesson provides you with an exercise to identify these elements in several different solar energy conversion systems functioning in diverse settings.

Activity: Identifying the Components of Solar Energy Conversion Systems

Based on the reading in the previous page of the lesson, we understand that almost everything exposed on the Earth's surface can be described in terms of a solar energy conversion system. Some systems are capable of producing more useful work than others, and there are both technologically designed and natural systems. We will use this activity to explore this concept and to identify various SECSs embedded in society. Some will be obvious in the context of this class, while others will require a more nuanced view or a creative perspective.

Take a look at each of the following five images, and thoughtfully locate as many SECSs as you can in each one. Now, try to identify and list the functional components (aperture, receiver, storage, distribution, mechanism, and control mechanism) for each of these SECSs and think about how they work. Please write a short paragraph for each image that identifies all of the SECS’s as well as an explanation of how each one serves as a component. It may even be possible that some of the systems are themselves components of a larger system, in which case you will need to dial out your perspective to a larger system.

Do your best to explore and be creative rather than looking for all the "right" answers.

Submission

Please fill in the "matrix" (Excel spreadsheet template provided) based on the results of your analysis. You are also welcome to provide any additional discussion on the systems you observe in the images. Submit your work into “Lesson 1 Learning Activity Dropbox” in Canvas.

Grading Criteria

This activity is graded out of 20 points. Each image is worth 4 points, 2 points for identification of the components and 2 points for your explanation.

Deadline

See the Canvas calendar for specific due dates.

The last activity emphasized the way that SECS can "work" as a functional system. Now, I would like you to read and reflect on the broader concept of "design" as pattern with a purpose in society and the environment. As you are reading, look into the ways that society has established frameworks for integrating solar goods and services into local solutions (which we will expand upon as "locale"). The following points are highlighted in the text.

• Solar as Lighting Aid
• Solar Rights and Access
• Solar Power Entrepreneurs
• Solar Ecosystems Services

In this section, we are going to be looking at some of the same pictures we saw in the Learning Activity, but from a different perspective. We will call the following case studies "frameworks," and investigate the value of solar energy conversion systems in different contexts. Consider the following frameworks as interpretations of valuing the solar resource and the resulting solar goods and services by society (in economic and sustainability terms): the same resource can be applied to different client needs, the way that we have set up legal ramifications to protect access and rights to the resource, the entrepreneurial/ecopreneurial spirit that is a part of SECS design and implementation, and the ecosystems services that surround our SECSs.

Solar as Lighting Aid

Figure 1.7: Liter of Light demonstration for solar light tube.
NPR Audio Article (Transcript available on the website)

Credit: Jay Directo/AFP via Getty Images

Many of us will come into the field of solar energy with a slightly biased view that the solar resource is useful for making electricity (a preferred solar good by many stakeholders) using photovoltaic technologies (the Solar Energy Conversion System of note in current society) or for making hot air or water (like a solar hot water panel, another SECS technology). However, we must be also aware of the use for daylighting. Daylight is as essential to human health as clean water and air. The variable intensity of daylight has been found to increase alertness within the office space (as opposed to constant light conditions with artificial lighting).

In the case of a Liter of Light (see link to NPR article, above), the ecopreneurial venture by this non-profit means using appropriate technology to deliver a high solar utility (again, meaning a preference to the set of goods and services from solar energy conversion systems) to their clients at accessible costs. The bottles are discarded 1 L plastic soda bottles, filled with water and a drop of bleach (to minimize algal growth or other microbes). The technology is the same as a "light pipe," or a fiber optic, using different indices of refraction between air, water, and plastic to create a phenomenon called total internal reflection. On boats, this type of light direction uses a centuries-old SECS technology called a deck prism.

Not only do these warm climate homes benefit from better lighting, they also avoid fuel costs for electricity (if available) and combustible fuels such as kerosene. Additionally, the solar bottle light pipes will improve indoor air quality by reducing fuel combustion inside.

Solar Rights and Access

While the solar resource from the sun is available at no cost to us, there are laws that may restrict the way we intend to use the sun for purposeful work. Designers will often call the accessible area for solar implementation the "solar envelope," but how do we maintain the legal rights to make use of or access our own solar envelope, and can we make sure that solar technologies can even be installed in our locale? Legal structures for solar energy is not a new concept. In ancient Rome and Greece, legal structures were set up in the form of easements, allocated government lands, and sometimes strict urban planning for orientation and elevation limitations on entire communities.

Solar rights define access to solar energy and hold significant economic consequences. They dictate whether a property owner can grow crops, illuminate his space without electricity, dry wet clothes, reap the health benefits of natural light, and perhaps most significantly in our modern era, operate solar collectors.

In the USA, we distinguish between solar rights and solar access.

• Solar rights give you the option to install a specific solar energy system within residential or commercial properties otherwise subject to private restrictions.
• On the other hand, solar access ensures that a structure receives sunlight across property lines without obstruction by neighboring objects, including trees.
• Examples of common private restrictions are bylaws that forbid PV on roofs, or clothing drying lines anywhere.
• Over 40 states have adopted solar access laws either in the form of a Solar Easement Provision or/and a Solar Rights Provision.

Solar Power Entrepreneurs

Figure 1.8: Prometheus 100 solar concentration systems for steam generation

Credit: Wissenz, E. (2010, November 23). Prometheus [Photograph found in Solarfire.io]. In 1145154891 861647994 L. Symington (Author). Retrieved from Symington Solar Fire

Entrepreneurs are generally great contributors to the commercialization of interesting and useful technology. The field of solar energy is no different. An important character in the development of SECSs is Frank Shuman, an eclectic inventor in the late 1800s. Shuman formed the Sun Power Company in 1910 and successfully harnessed solar power physics to generate steam pump power in Egypt in 1911.

New entrepreneurial ventures in solar are often also humanitarian and ecological in nature. SolarFire.org and Liter of Light are two examples.

The Prometheus 100 solar concentration systems for steam generation can be seen in the image above. Mirrors (the aperture) are focusing shortwave light onto an upper central receiver (glowing bucket), where steam is produced. The steam is running a small steam generator pictured in the lower left of the image. The supply water is pumped in from the tube seen in the upper right. The entire system plans are available as open-source information, and can be machined with accessible local technologies and inexpensive materials. This system was installed in Rajkot, India.

Solar Ecosystems Services

Any solar technology will have an impact on the ecosystem in which it is deployed. In addition, it could add ecosystems services to the area if designed with an awareness for landscape architecture and ecology. Presently, design teams discuss manners in which photovoltaic arrays can add desirable shading in addition to power generation (desirable shading would be considered a preferred solar service). One common method is to design and install a solar panel to also serve as a shading structure for cars in a parking lot.

Figure 1.9: The parking lot at the Cincinnati Zoo has solar panels over the vehicles. These provide a significant portion of the zoo's electric needs.

Credit: quadell, via Wikimedia Commons is licensed under CC BY-SA 3.0

• Supporting services or habitat
• Provisioning services
• Regulating services
• Cultural services

You may wish to read the short descriptions of the various services from The Economics of Ecosystems and Biodiversity (TEEB) website. They have created a fairly concise list with descriptive sections that clearly identify valued processes that emerge from a resilient ecosystem. Remember: our technologies and our societies are always a functioning part of our ecosystems in the locale that we operate, even if it doesn't quite seem that way in our daily lives.

Download System Adviser Model (SAM) Simulation Software

Directions

1. Create a User Account and choose Photovoltaic as the Technology Focus at the bottom of the page.

2. Follow the download and installation instructions.

   NOTE: SAM is an Open Source project! The version of System Advisor Model as of the update of this page is SAM 2024.12.12 (and there will likely be newer versions each semester). It requires about 1 GB of disk space, and either Windows 10/8/7 or OS X 10.9 Intel or later. SAM is a 32-bit program that will run on both 32-bit and 64-bit operating systems. If you do not have one of these operating systems, you can browse their list of Legacy Versions as an alternative.

3. Install and launch SAM on your computer. The very first time, you will need to enter your email and click the "Register" button. SAM will send you a code to use in the next entry for "Key". Paste it in and get rolling!
4. Try to "Start a New Project" with Photovoltaic Detailed Model for a Distributed scenario. The defaults are pretty reasonable in SAM. If you've never tried something like SAM, don't worry. This is really just an exploration step, and you can't really break anything by opening a new project and running it. So, just explore a little and have some fun.
5. If you successfully create a new project, you can browse through the system parameters and options on the left side menu. Check the defalt numbers. You will see that you can change the values in the white boxes, and numbers in the blue boxes will calculate automatically.
6. Hit the big blue box in the lower left labeled SIMULATE >. The program will run a year's solar data and will output a heap of results. The output in the table is the summary of stats for the project, usually estimating 25 years of a solar project.

Deadline

There is no deliverable for this activity, but I strongly encourage you to take initial steps for installation and creating a project in SAM this week. Lesson 2 will give you some work to complete in SAM, so it will be useful to have it up and running.

Yellowdig Conversation

Feel free to share your thoughts, questions, and tips on the SAM software in the Yellowdig space. Use the topic System Adviser Model for your posts. This is not a required activity, but it can still boost your participation score for this week. 

Summary

We have just finished looking at the historical and modern contexts for valuing solar energy (and SECSs) in society. I wanted to put you in the frame of mind that solar energy as a valued resource is a flexible concept. The value expands with energy constraints and with positive health and safety implications; the value shrinks with the reduced costs of alternatives such as fuels. There are many different ways that society values the solar resource, however, and as a part of a design or engineering team (or part of a policy team), we should remain creative and persistent in trying to develop and expand SECS deployment into society.

You have made your first step toward the solar assessment project that we will present to our peers in Lesson 12 at the end of the course. I would like you to make sure that you have found the SAM (System Advisor Model) website and downloaded the software onto your systems. Your future clients/stakeholders will be informed by your creative ability to present them with a valuable solar resource in their locale, one which also yields financial benefit, social benefit, and/or greater ecosystems services. SAM is a useful complementary tool in that communication.

Overview

This is the first of three fairly intense lessons covering the fundamentals of solar energy. You will need to distill a lot of information and work hard to internalize the key topics. Make sure that you use the discussion forums to communicate with your peers, and be sure to ask questions. Most of us have learned bits and pieces of the following materials, but never together in one setting. And for some of us, this is the very first time we are learning to juggle all the balls that tie together solar energy. You can do it!

Time and Space are related! This lesson will discuss the tools needed to evaluate spatial and temporal relationships:

• of the Sun relative to the Earth;
• of the Observer on the surface of Earth relative to the Sun at any given time;
• while identifying the angles used to describe the orientation of a Solar Energy Conversion System (SECS) surface relative to the moving Sun;
• also identifying the times that local shadows might obscure our SECS. We will use sun charts to analyze shadows with respect to solar collectors.

Just like with navigation in a ship or an airplane, time and space relations are linked together in Solar Energy and can be represented and communicated as geographic information. We input that geographic information in terms of angles and use key relations from spherical trigonometry to make time and space relations easy to calculate with a computer. For our purposes:

angles = coordinates in space and time.

The tools we develop are going to explain the sun’s position relative to any point on the surface of the Earth. Once developed, our useful equations can also be applied to estimate the time and location of shadows that block SECSs or tracking technologies for SECSs.

Figure 2.1: Celestial Sphere - This blue sphere is a simple representation of the Earth within a larger sphere representing the celestial sphere, an imaginary sphere projected out onto the sky around the Earth. The equator is shown as a ring on the celestial sphere, tilted 23.45 degrees away from the Ecliptic ring, which is parallel with the orbit relative to the Sun.

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

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

• identify and apply the Earth-Sun Angles and the relations/equations between Solar Time and Watch Time (Standard/Daylight Savings);
• identify and apply the Observer-Sun Angles and be able to create a Sun Chart for shading analysis linked with the SAM software;
• identify the Collector Angles used to describe the orientation of a collector surface relative to the moving Sun (fixed or tracking) for power output analysis linked with the SAM software;
• list the important roles of geospatial relations to the three-part goal of Solar Energy Design.

What is due for Lesson 2?

This lesson is loaded with material on Sun-Earth geometry and will take us two weeks to complete. Please refer to the Course Calendar in Canvas for specific timeframes and due dates - those can vary from semester to semester. Specific directions for the assignments below can be found further within this lesson.

Questions?

If you have any questions, please post them to the Questions thread in Yellowdig. I will check this forum regularly to respond. Feel free to go through the comments and post your own responses if you are able to help out a classmate.

Solar Energy Journal was established for the International Solar Energy Society (ISES) and has been around for some time now. Solar Energy Journal stands as an important forum for peer to peer sharing of solar research for energy conversion and human applications of solar energy. What I want to establish here is that there is precedent for the complex system of notation used in the solar energy world that has been in use for decades. The original authors have established the following observations:

"Many disciplines are contributing to the literature on solar energy with the result that variations in definitions, symbols and units are appearing for the same terms. These conflicts cause difficulties in understanding which may be reduced by a systematic approach such as is attempted in this paper.

It is recognized that any list of preferred symbols and units will not be permanent nor can it be made mandatory, as new terms will emerge and old ones become less used with the development of the subject. But in the meantime, a list would be appreciated by the many workers who are entering this multi-disciplined field...

...Energy: The S.I. (Systèm International d'Unités) unit is the joule ($J=kg{m}^2{s}^{-2}$). The calorie and derivatives, such as the langley (cal cm^-2), are not acceptable.

No distinction between the different forms of energy is made in the S.I. system so that mechanical, electrical and heat energy are all measured in joules. However, the watt-hour (Wh) will be used in many countries for commercial metering of electrical energy...

Power: The S.I. unit is the watt ($W=kg{m}^2 s^{-3}=J/s$). The watt will be used to measure power or energy-rate for all forms of energy and should be used wherever instantaneous values of energy flow are involved. Thus, energy flux density will be expressed as W/m² or specific thermal conductance as $W{m}^{-2} K^{-1}$. Energy-rate should not be expressed as $\mathrm{J} / \mathrm{h}$.

When energy-rate is integrated for a time period, the result is energy which should be expressed in joules, e.g. an energy-rate of 1.2kW would if maintained for one hour produce 4.3 MJ."

In summary: received energy flux density (or power density, called irradiance) can be expressed in units of W/m². We also note that the received radiative energy density (called irradiation) can be expressed in units of J/m², or in units of Wh/m². Notice that we did not use radiation, which is an expression of light glowing outward (emitted light, different direction than what we want).

In today's maps of the solar resource, you will often see the units expressed in kWh/m². You should be aware that these are still only representations of solar light energy density, and not the hourly/daily/annual quantity of potential electricity that could be produced. To find that value, we need a simulation tool like SAM (System Advisor Model, which you should have downloaded at the end of Lesson 1), which takes irradiation data and converts it into power data.

I would like you to now take a short self-quiz to see if you recall the common uses of the notation and descriptions for solar energy (used in particular in this class.).

When we want a shorthand to describe spatial relationships on continuous surfaces that are sphere-like, as with the Earth and the surrounding sky and stars, we choose to use Greek letters. In contrast, when we are trying to communicate things like linear distances, lengths, time, or simple Cartesian coordinates, then we will tend to use Roman letters for our shorthand.

You may notice in your reading of older textbooks that several systems of sign convention for the angles have emerged for practical use. Also, the various systems can have different approaches to azimuth that we should be aware of. For instance, the software SAM (System Advisor Model) will use both the ${360}^{\circ }$ clockwise standard (from Meteorology) as well as the $\pm {180}^{\circ }$ standard used extensively in the component-based models of TRNSYS and SAM. We will be sure to become familiar with both.

Below are four tables showing the Angular Symbols for Standard Solar Relations.

General Angles

Earth-Sun Angles

Sun-Observer Angles

Collector-Sun Angles

Figure 2.2 The axis of the Earth currently tilts approximately 23.5 degrees from the perpendicular (dashed line) to its orbital plane

Credit: D. Babb © Penn State University is licensed under CC BY-NC-SA 4.0

Earth's Rotation

As we have seen in our reading, the Earth rotates with a roughly constant speed, so that every hour the direct beam (a ray pointing from the surface of the Sun to a spot on Earth) will traverse across a single standard meridian (standard meridians are spaced 15° apart). The implications are that the unit of one hour is equivalent to the rotation of Earth 15 degrees. When Earth rotates such that the beam of the sun shifts +1° of longitude from East to West: it takes 4 minutes of time.

• 1 h = +15° Earth rotation
• 4 min = +1° Earth rotation

Wild fact: a time zone change of one hour is really just 15 degrees of separation between standard meridians.

The axis of rotation of the Earth is tilted at an angle of 23.5 degrees away from vertical, perpendicular to the plane of our planet's orbit around the sun.

The tilt of the earth's axis is important, in that it governs the warming strength of the Sun's energy. The tilt of the surface of the Earth causes light to be spread across a greater area of land, called the cosine projection effect.

Cosine Projection Effect

When you tilt a surface away from a beam of light, you spread the same density of light across a larger area. Recall that irradiance is in units of W/m², so a larger denominator means a smaller value of irradiance, right?

Explore the concept of the cosine projection effect in the following experiment.

Seasons and the Cosine Projection Effect

The sun is about 93 million miles away from the Earth (equivalent to ~150 million km). That is so far away that the photons from solar irradiation effectively travels in parallel rays. So, unlike the flashlight experiment, the tilt of the sun has no bearing on the intensity of the radiation reaching the Earth's surface. Instead, we find that the Earth's tilt controls the intensity of irradiation and the seasons.

Keep in mind that the Earth's axis points to the same position in space (toward the North Star, Polaris). As the Earth travels in a near spherical (a very small eccentricity into an ellipse) orbit around the sun, the Northern Hemisphere can be tilted toward or away from the sun, depending on its orbital position.

Figure 2.4: From late spring to late summer, the sun never sets at Barrow, Alaska (as this multiple exposures of the sun reveals)

Credit: Colin Monteath

Forecasters and meteorologists use different criteria to determine the "meteorological seasons." For example, meteorological winter in PA runs from December 1 to Feb 28/29, a period that statistically includes the three coldest months of the year. This is also centered on a time about 25 days after the Winter Solstice.

Meteorological summer runs from June 1 to August 31, a period that includes the warmest three months of the year. Again, this is a period centered about 25 days from the Summer Solstice.

Figure 2.5: Please review the NASA movie from 2000-2001 above, showing the rhythms of the most intense ultraviolet radiation coinciding with the most direct rays of the sun (around the summer solstices). Again, what may be a surprising observation is that the average air temperatures lag the sun's most direct days.

Credit: NASA

As one more example, review Pittsburgh's plot of annual average high temperatures. The maximum daily temperature occurs in late July, long after the summer solstice.

Figure 2.6: The annual variations of average, record-high, and record-low maximum temperatures at Pittsburgh, PA. Access the annual temperature stats at other cities

Credit: Data/image provided by the NOAA/OAR/ESRL PSL, Boulder, Colorado, USA, from their Website at http://psl.noaa.gov/

As we see in the reading, time is a critical parameter in solar energy resource assessment, and we use a "different" time from your mobile phone (or if you have one, a watch). The time that we use in solar energy is the apparent time and path of the sun relative to the aperture or collection device, called Solar Time.

• A solar day is 24 hours long, and Solar noon is always used locally as the center of time.
• Solar noon is defined as the moment when the Sun is at its highest point in the sky.
• The hour angle for solar noon is $\omega =0°$ (given the symbol of lowercase omega).
• Time before solar noon counts backward from $\omega =0°$ , and so the angles are negative.
• Time after solar noon counts forward from $\omega =0°$ , and so the angles are positive.

Correcting Time for Big Longitude Changes: Standard Meridians

The time that you are used to using on your laptops, phones, and (if you still have them) watches is called Standard Time, and is referenced back to the Coordinated Universal Time (UTC), the primary time standard by which the world regulates clocks and time.

Our notion of time is also tightly coupled with our system of longitude (the longitude symbol for us is $\lambda$). We have used lines of longitude, or meridians, as a reference for time and position E-W. Because time and angles are all linked together, we cannot escape the sexagesimal (base 60 math) system for geographical locations. As we demonstrated earlier in the lesson, each standard meridian (a major line of longitude) is spaced 15° apart, beginning with the Prime Meridian ($\lambda =0°$) in Greenwich, England, and continuing for 360 degrees, or 24 hours.

I live someplace other than Greenwich. How do I account for Longitude ($\lambda \ne 0°$)?

Your standard time zone will tell you the standard meridian (${\lambda }_{std}$). For example, the EST is -5h from UTC, while Central European Time (CET, like Paris) is +1h from UTC.

• For every standard meridian shift to the West, you will need to subtract 15 degrees per hour.
• For every standard meridian shift to the East of the Prime Meridian, you will need to add 15 degrees per hour.

Correcting for Little Longitude Changes: Inside Time Zones

Where you live, or where your future solar site assessment will occur, will likely be well within the edge of a time zone (meaning ${\lambda }_{std}-{\lambda }_{loc}\ne 0°$ ). We already learned that every 1° of angular rotation on Earth is equal to 4 minutes of time. Standing in one spot on the surface, this means 4 minutes of relative time correction locally per degree of deviation from a Standard Meridian (${\lambda }_{std}$ ). So, locales will have a local longitudinal refinement to account for, in order to account for not living directly on a 15-degree incremental Standard Meridian on Earth.

Standard Meridians define the beginning of a time zone, and not the end of a time zone. So, you are always going to look to the start of a time zone to find the Standard Meridian.

There are a few other cities that actually are well seated for solar time zone correction (close enough for our calculations):

• Philadelphia is fairly close to the EST standard meridian of -75°.
• Denver is fairly close to the MST standard meridian of -105°.

My client lives someplace other than a Standard Meridian, how do I account for that?

First, go to Google and type "<insert city name> longitude". You should get a quick response of both the Longitude (lambda) and the latitude (our symbol for latitude is lowercase Greek "phi": phi), represented in decimal form (more useful to us for trigonometry and angles).

Have you noticed that real time zones are more often political boundaries that zigzag around, rather than following an actual Standard Meridian? So, actually, there can be locales for clients that are East of their own time zone Standard Meridian, instead of the normal relative locations West of the time zone Standard Meridian. This is why, in the reading, you will see $\pm 4$ minutes per degree of local longitudinal shift away from the time zone's Standard Meridian.

Correcting with the Equation of Time: Accounting for Wobbles

Even in Greenwich, where no longitudinal correction is necessary, "noon" UTC will generally not be the time when the sun is directly overhead. We can see in the plot below that watch time and solar time are the same in Greenwich for only 4 days in the year.

• There are deviations of up to $\pm 16$ minutes (regardless of your location on the planet).

As you will have read, our interpretation of watch time assumes an even progression for Earth's planetary rotation, with no weebles or wobbles or precession of the polar axis. However, you will now know that wobbling occurs, and there is great variability in the rotation of the earth throughout the months of the year. This is why we add leap years and leap seconds to our calendars. So, we create a "mean time" based on the length of an average day to keep things simple. Solar time has to correct for this mean time approximation. Equation of time correction versus day of the year is shown in Figure 2.7. As an exercise, you can try to calculate these curves based on the empirical equations (6.10) and (6.11) in Brownson textbook.

Figure 2.7: Equation of time function represented over all the days of a year. Note how the minimum and maximum do not exceed 16 minutes.

Credit: Jeffrey R. S. Brownson © Penn State University is Licensed under CC BY-NC-SA 4.0

The following picture was a composite of images, taken at the same watch time every few days for an entire year, to record the position of the sun. We call the shape an analemma. Notice how there is a big loop and a little loop, and compare the same big waves and little waves in the first image of the Equation of Time correction above. If you were to draw a line down the center, you would have removed the error from watch time, and you would be one step closer to solar time.

Figure 2.8: Analemma photograph taken from Bell Laboratories, circa 1998.

Credit: Analemma Fishburn by J. Fishburn from Wikipedia is licensed under CC BY-SA 3.0

For views of amazing solar analemma photography by Anthony Ayiomamitis, also, please visit the Stanford SOLAR Center.

These images were taken at the same time and location every day for one year. You will see the curve described by the Sun over that year. An analemma is a beautiful way to capture both the range of declination $\delta$ (along the length of the analemma) and the Equation of Time Et (the expansion or width of the analemma) in a graphical format.

Putting Time Correction Together:

As we have seen in the reading, we have a method to correct local watch time to solar time, to correct for the true time of day according to the sun relative to the meantime.

The time correction factor is a function of the equation of time, the meridian of the local standard time zone (L_st), and the longitude of the collector/observer (L_loc), and the Equation of Time (E_t). The equation of time correction accounts for the wobble and is the first step. Then we need to correct for the change in longitude leading to time zones (standard meridians occur every 15 degrees) and the change of time for locales that are not located along standard meridians.

In these conversions, each year is assumed to begin just after midnight, Dec. 31, and time counts up from there. The time corrections here are in terms of minutes, not hours. The Equation of Time corrects the time to mean solar time (by adding or subtracting up to 16 minutes of correction). The Time Correction Factor corrects time for your shift in longitude from each Standard Meridian (which occurs every 15 degrees away from the Prime Meridian). Daylight Savings Time is an optional correction, as there is a +60 minute difference from Standard Time between March and November in the USA (and some other regions of the world).

Now, let's convert "time" into an angle, for our future trigonometric relations:

When we convert time to an angular value, we can no longer use a 24 hr format. We need to convert hourly time into a useful angle based on the properties of a sphere, again using spherical trigonometry.

Video: Hour Angles (5:03)

Finishing Step for Time Conversions! The Hour Angle ($\omega$) in decimal degrees.

We represent the apparent displacement of the sun away from solar noon, either as a negative or positive angle. An $\omega$ of zero indicates that the sun is at its highest point for that given day.

• The sign of the hour angle before noon is negative, because we have to count backward from the "zero hour" of solar noon.
• The sign of the hour angle after noon is positive, because we are counting forward from the "zero hour" of solar noon.

Another way of looking at it is the angular difference between the local meridian of the observer/collector and the meridian that the beam of the sun is intersecting at a given moment.

$$\omega =\frac{{360}^{\circ }}{24\text{ hr}}(t_{sol}-12)=\frac{{15}^{\circ }}{\text{hr}}(t_{sol}-12)$$$$\omega =\{ \begin{array}{c}-0-\mathrm{180 }\text{degrees},\text{ if before noon (morning)} \\ +0-\mathrm{180 }\text{degrees, if after noon (evening)} \end{array}$$

Now, the day won't really begin at -180 degrees, anywhere between the arctic circles. However, I wanted to emphasize that the day only begins at -90° on two days a year. Those days occur during the Equinox moments in the orbit of the Earth about the Sun, and the length of those days is actually 12 hours long. All other days are either shorter than 12 hours, or longer than 12 hours. As such, they end either less than 90° or greater than 90°.

Figure 2.9: The Sun Path projected onto graphed sphere for a latitude of 50 degrees, and the day of an Equinox (12 hours). The hours for 8h00, 12h00, and 14h00 are listed in solar time, along with the associated hour angles of -60°, 0°, and +30°.

Credit: Original by Tau'olunga from Wikimedia Commons licensed under CC BY-SA 2.5 - Modified by J. Brownson. 

The images below demonstrate singular arcs of the Sun for each hour in solar time, at five different latitudes on Earth (no analemma correction necessary). The peak hour (or the hour with the highest solar altitude angle) is defined as solar noon. You will notice that the solar equinox has twelve sun spots for latitudes below the arctic circle, and that the sun rises due East, while setting due West. During the solar solstices, you see multiple arcs: one for winter and one for summer. Notice that there are more hours of the day in the summer, and the sun rises farther from the equator in the Summer (sun rise in the northeast for the Northern Hemisphere).

What else do you notice in comparing the four critical times of year at different latitudes?

Solar Equinox

Figure 2.10: Solar Equinox

Click on the images above to see full-size versions with descriptions.

Credit: All images are by Tau'olunga from Wikimedia Commons licensed under CC BY-SA 2.5

Solar Solstice

Figure 2.11: Solar Solstice.

Click on the images above to see full-size versions with descriptions.

Credit: All images are by Tau'olunga from Wikimedia Commons licensed under CC BY-SA 2.5

Now, we are ready to use hour angle to find out positions in our solar design projects!

Remember that the Earth rotates at 15 degrees per hour, and 0.25 degrees per minute. It can get confusing when you're comparing spatial seconds with temporal seconds, right? That's why we will stick with decimal notation in all of our references to latitude ($\varphi$), longitude ($\lambda$$$), and angles (degrees).

Step 1: Correcting for Standard Time (Standard Meridian) in Hours

Find the time zone of your client. The hourly longitude correction is plus or minus X hours from the Prime Meridian, where UTC = 0h. Multiply the positive or negative hour value by 15°, and you will know your standard meridian for the Time Zone.

Key: Your standard meridian for your time zone begins on the East side of the time zone. (Sun rises in the East, right?)

Step 2: Correcting for Time from the Local Longitude Relative to Standard Meridian in Minutes

You need to know the longitude for the standard meridian of the client ( ${\lambda }_{std}$) from their local time zone, and the local longitude of the client's location in question (${\lambda }_{loc}$). We calculate the longitudinal correction, $t_{\lambda }$ from these two.

Keep in mind: Time zone borders are political boundaries, and can be constructed on both sides of a Standard Meridian. A locale to the east of the Standard Meridian would still be input as a positive value (the resulting minutes would be positive).

$$t_{\lambda }=-4(\frac{min}{deg})({\lambda }_{std}-{\lambda }_{loc})[min]$$

Note: we use the sign convention that longitudes are positive valued for to the East of the Prime Meridian, and negative valued to the West of the Prime Meridian. This equation is valid for both sides of the Prime Meridian. The exterior negative sign is there to make the time correction algorithm work correctly.

Step 3: Calculating Equation of Time (Analemma) Correction in Minutes (E_t)

We begin with the two simple coefficients of n (the day of the year, from 1-365), and B (see the first equation). Our assumption is that the year begins at midnight of the new year, and the trigonometric portions of the equation of time will take an argument of "B" in degrees.

$$B=(n-1)\frac{{360}^{\circ }}{365}$$
$$\begin{gathered} E_t=229.2(0.000075)+229.2(0.001868\cos B-0.032077\sin B)- \\ 229.2(0.014615\cos 2B+0.04089\sin 2B)[min] \end{gathered}$$

You have seen that the Equation of Time has a graphical representation, the analemma. Once we determine a correction in the scale of minutes, we can use it in the Time Correction Factor, TC.

Step 4: Completing the Time Correction Factor ($\mathrm{TC}$)

The time correction factor is a time shift in minutes.

$TC=t_{\lambda }+E_t$

Recall that 0.25° of longitudinal rotation (of the planet) will consume 1 minute of time. That would make each degree of change equivalent to four minutes. Hence, we need to multiply our longitudinal correction by a factor of four $$\frac{\min }{\mathrm{deg}}$$ to yield a consistent unit of minutes in time. This is shown as the value of the longitudinal correction (L_c) in units of minutes (temporal, not geospatial).

Step 5: Accounting for Daylight Savings Time (DST) in 60 minutes

The equations do not tell you when DST occurs from country to country. There is a +60 minute difference between March and November in the USA. So, if we had to correct for DST, then we would need to subtract that 60 minute addition back out.

$$LocalSolarTime(tsol)=\{ \begin{array}{c}StandardTime+TC\text{ if Standard time.} \\ StandardTime+TC-60\text{ if Daylight Savings time.} \end{array}$$

Again, make sure that the data is presented in minutes, rather than hours.

Continuing Conversations in Yellowdig!

I hope you are getting the hang of Yellowdig conversation platform and are ready to pick up the pace! You can access the discussion platform through the Canvas menu.

Lesson 2 Discussion: Reflection on Time Conversions

Tagging

Yellowdig Tip: When you create a post in the Yellowdig discussion space, you are required to choose a topic tag. For Lesson 2 discussions, use any of the following:

Know that you can tag your post with one or several of these topics depending on its content. It gives you flexibility to discuss these things cumulatively or, if you prefer, to break your writing into several smaller posts.

Importance of interaction

Once again: the more you participate, the more opportunities for your discussion score to grow through the week. Comment, ask questions, react, throw in additional thoughts – it all is in your benefit!

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) if you are feeling active. That may help you to make up for some low-activity weeks. 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.

The Greek notation used below is now fairly standard for the field, but you may see different approaches in informal settings or unusual textbooks. I follow the established nomenclature defined by Beckman, et al., in the research journal Solar Energy in 1978, reprinted in Solar Energy in 1997. As noted earlier, the document is available to you from the Library E-Reserves.

Figure 2.12: We are showing a vector S' (S-prime) originating at the center of Earth (point C) and directed toward the Sun. The position of the collector (point Q) is set on the surface of the Earth. The location of Point Q defines the meridional axis, based on the collector meridian, and serves as a reference for the hour angle $\omega$.

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

Hour Angle ($\omega$):

Again, this is the way we represent the apparent displacement of the sun away from solar noon. An hour angle of zero degrees indicates that the sun is directly above, and the sign of the hour angle is determined by occurring either before noon (negative) or after noon (positive). Another way of looking at it is the difference in angle between the local meridian of the observer/collector and the meridian that the beam of the sun is intersecting at a given moment.

Angle of Declination ($\delta$)

This is not an observed angle relative to the surface of the Earth and the Collector. Declination is the observed angle (due to the polar tilt) between the plane of the Earth’s equator and the plane of the ecliptic (the plane in which the Earth's orbit about the Sun lies). Declination has a maximum angle of 23.45° at either solstice. In this case of coordinates, the sun observed in the North is positive, and in the South is negative. One can imagine this as a series of sun paths over the course of a year. In contrast, the declination reaches a midpoint at either of the equinoxes. The range of declination is limited to Earth’s tilt: −23.45° (winter solstice) $\le \delta \le +23.45°$ (summer solstice).

Declination is independent of location on the planet!

The declination can be calculated by a simple approximation (first equation) or a Fourier series (second equation).

$$\delta =23.45\sin \left(\frac{360}{365}(284+n)\right)$$ $$\begin{array}{cc}\delta & =(180/\pi )\times (0.006918-0.399912\cos B+0.070257\sin B\\ & -0.006758\cos 2B+0.000907\sin 2B\\ & -0.002679\cos 3B+0.00148\sin 3B)\end{array}$$ where:
$$B=(n-1)\times \frac{360}{365}$$

Angle of Latitude ($\varphi$) and Longitude ($\lambda$)

The complement of longitude ($\lambda$) in geospatial coordinates is the latitude. When combined together, we have identified a singular point on the surface of Earth. However, separately, they refer to arcs or circles spanning huge distances. We can look up the latitude and longitude of a site on a search engine like Google.

Key latitude angles of interest are:

• Arctic Circle $\varphi$ = +66.56° North of this, the sun is above/below the horizon for 24 continuous hours at least once per year (during the solstices).
• Tropic of Cancer $\varphi$ = +23.45° The maximum tilt of the North Pole to the Sun.
• Equator $\varphi$ = 0°
• Tropic of Capricorn $\varphi$ = −23.45° The maximum tilt of the South Pole to the Sun.
• Antarctic Circle $\varphi$ = −66.56° South of this, the sun is above/below the horizon for 24 continuous hours at least once per year (during the solstices).

Figure 2.13: We are showing azimuth orientation Convention I, where the vector S is pointing from the surface of Earth toward the Sun, given the zero basis for the azimuth is directed toward the Equator (±180°). Convention I follows the vectorial form of S = S_z i + S_e j + S_sk. Convention II (the meteorological standard) is where the zero basis is directed to the North (0-360° clockwise).

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

The Solar Altitude (${\alpha }_s$) measures the angle between the central ray from the Sun (beam radiation), and a horizontal plane containing the observer. Note that the subscript "${}_s$" is there to indicate that the altitude relative to the observer of the Sun. This will become important in evaluating the altitude angles of other objects projected onto the sky dome, like buildings, overhangs, wing walls, and arrays of solar receivers.

$$\sin {\alpha }_s=\sin \delta \sin \varphi +\cos \delta \cos \varphi \cos \omega$$

$$\cos {\alpha }_s\sin {\gamma }_s=-\cos \delta \sin \omega$$ $${\alpha }_s={\sin }^{-1}[\sin \delta \sin \varphi +\cos \delta \cos \varphi \cos \omega ]$$

The Zenith Angle (${\theta }_z$) is the geometric complement of the solar altitude angle. We direct your attention to the use of $\theta$ here, as the general concept of the angular deviation of the Sun's ray from the normal projection of a surface is called the angle of incidence, $\theta$. In effect, the zenith angle represents the angle of incidence for a horizontal surface.

Recall: "normal" means perpendicular to a surface.

$$\cos {\theta }_z=\sin \delta \sin \varphi +\cos \delta \cos \varphi \cos \omega$$$$$$ $${\theta }_z={\cos }^{-1}[\sin \delta \sin \varphi +\cos \delta \cos \varphi \cos \omega ]$$

The Solar Azimuth ($\gamma s$) measures the angle on the horizontal plane between the meridian of the 0 degrees axis (South, for the Northern Hemisphere, opposite Down Under) and the meridional projection of the Sun's central beam (the Sun's meridian). The convention we will use is also used in the advanced design tools for solar energy, TRNSYS (UW-Madison: Transient eNergy Simulation Software), and PVSyst. The angle varies from 0 degrees at the South-pointing coordinate axis to $$\pm 180$$ degrees. East (earlier than noon) is negative and west (later than noon) is positive in this basis. This is a well-used standard taken from the original text of M. Iqbal.\cite{iqbal83}

$${\gamma }_s=\text{sign(}\omega \text{)}\left|{\cos }^{-1}\frac{\cos {\theta }_z\sin \varphi -\sin \delta }{\sin {\theta }_z\cos \varphi }\right|$$

Note: the function "sign($\omega$)" is specifically defined as a cases form of positive and negative notation (meaning there are two alternate cases to choose from).

$$\gamma s=\{\begin{array}{c}+{\cos }^{-1}\frac{\cos {\theta }_z\sin \varphi -\sin \delta }{\sin {\theta }_z\cos \varphi }\text{ if }\omega \text{>0,}\\ -{\cos }^{-1}\frac{\cos {\theta }_z\sin \varphi -\sin \delta }{\sin {\theta }_z\cos \varphi }\text{ if }\omega \text{<0.}\end{array}$$

There are several texts and software available that use a solar azimuth, measuring clockwise on the horizontal plane from a North-pointing (0 degrees) coordinate axis. This is also the convention for the field of meteorology and for the wind industry. This azimuth convention uses 360 degrees for the meridional projection of the Sun's central beam. SAM Software, PVWATTs, and University of Oregon's Sun path tool - all use this convention as well, so you must be aware of the difference, as the math changes with the two methods.

The following angles describe the orientation of the collector surface and the relation of the collector surface to the Sun. As these three angles describe our primary surface of interest, the SECS, they do not have a subscript for the two coordinate angles of collector tilt and collector azimuth.

• Tilt: the angle between the plane of the collector (or aperture) and the horizontal. Denoted by the symbol beta, β.
• Azimuth: the planar rotation East or West that an aperture will have. Denoted by the symbol gamma with no subscript, $\gamma$.
• Angle of Incidence: the angle between the vector perpendicular to the collector plane, called the normal of the plane, and the projection of the Sun’s central beam to the collector surface. Denoted as theta with no subscript ($\theta$).

Figure 2.14: We depict the SECS Collector-Sun Orientation here: the collector tilt (beta, $\beta$) and azimuth (gamma, $\gamma$) are positioned to reflect a site somewhere in the Northern Hemisphere. The Sun's position is described fully using the solar altitude angle (${\alpha }_s$) and the solar azimuth angle (${\gamma }_s$).

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

For general cases, where the collector has a non-horizontal orientation ($\beta \ne 0$), the angle of incidence is not the same as the zenith angle ($$θ_z). In fact, the zenith angle is a special case of an angle of incidence for horizontal surfaces, where the zenith is referenced to the aperture as a normal projection.

The first and second angles of tilt and surface azimuth ($\beta$ and γ$$) are typically known for fixed surfaces. The third key angle is the angle of incidence (θ$$), which uses the following rather lengthy equation:

$$\begin{gathered} \cos \theta =\sin \varphi \sin \delta \cos \beta -\cos \varphi \sin \delta \sin \beta \cos \gamma +\cos \varphi \cos \delta \cos \beta \cos \omega \\ +\sin \varphi \cos \delta \sin \beta \cos \gamma \cos \omega +\cos \delta \sin \beta \sin \gamma \sin \omega \end{gathered}$$

In order to generate an actual value for theta, we will need to also take the arccosine of the long equation. For your calculators and math programs, all of the arguments are in terms of degrees, not radians. You will need to convert degrees to radians in most programs.

However, this is a really long equation that can actually be broken down into parts. We will break up the equation for the angle of incidence (theta, $\varphi$) into three lines. Take a look at them, and look for common arguments to the sine and cosine functions.

• ($\varphi$, $\delta$, $\beta$: latitude, declination, and tilt)
• ($\varphi$, $\delta$, $\beta$, $\gamma$: latitude, declination, tilt, and then collector azimuth)
• ($\varphi$, $\delta$, $\beta$, $\gamma$, $\omega$: latitude, declination, tilt, collector azimuth, and then the hour angle)

$$\cos \theta =\sin \varphi \sin \delta \cos \beta -\cos \varphi \sin \delta \sin \beta \cos \gamma +$$$$\cos \varphi \cos \delta \cos \beta \cos \omega +\sin \varphi \cos \delta \sin \beta \cos \gamma \cos \omega +$$$$\cos \delta \sin \beta \sin \gamma \sin \omega$$

Mechanisms to Maximize Solar Utility:

In the introduction of the textbook, there is a reference to the goal of solar energy design: to maximize the solar utility for a client in a given locale.

There are three main design mechanisms that will increase the solar utility of a SECS for a client or group of stakeholders.

1. Decrease the cosine projection effect: This is done by tilting the collector toward the Sun's average annual noontime position. The higher the latitude of the locale, the more tilt a collector will need. Seasonal tilt changes can also slightly improve the solar gains. We also direct the collector toward the equator, although there is significant flexibility in both tilt and azimuth.
2. Minimize the angle of incidence: This is a refinement of the first mechanism over the course of a given day, particularly relevant to solar tracking systems. By "pointing" the collector normal at the Sun during the day, the angle of incidence is minimized, and more light can be collected.
3. Minimize or remove shading effects from the collector: We will cover this in the next few pages. It should make sense that when shadows cover a collector, then the majority of the Sun's light for that unexposed area is no longer providing power. Photovoltaics will be much more susceptible to shading issues than solar thermal systems, due to the near instantaneous generation of charge carriers in PV vs. the slower reaction from a thermal response of fluids.

In a spherical coordinate system, the angles are the coordinates. So, if I were standing in a field in North Dakota, looking at something tall like an enormous wind turbine, I could define the position of the top of the nacelle relative to me by stating the general azimuth angle ($\gamma$, the rotation across the horizon from due South) and the general altitude angle ($\alpha$, the rotation up from the horizon). Effectively, this is my x ($\gamma$) and y ($\alpha$) coordinates on an orthographic projection of the sky dome on a flat surface.

Figure 2.15: A common example of spherical coordinates (r, $\theta$, $\varphi$) commonly used in physics: radial distance r, polar angle $\theta$ (theta), and azimuthal angle $\varphi$ (phi). The symbol $\rho$ (rho) is often used instead of r.

Credit: 3D Spherical Coordinates by Andeggs from Wikimedia (Public Domain)

Many of you will be familiar with Cartesian coordinates in space (x, y, z). However, when dealing with spatial relations of spherical objects like the Earth and the Celestial Sphere, we find that working with basic spherical coordinate systems makes trigonometry available to us to solve for space and time equations. For spherical coordinates, we need information of radial distance, zenith angle, and azimuth. However, in solar positioning studies, a radius of one (unit radius) is all we need to establish a unit vector, and we are left with equations for only the zenith angle and azimuth (and the complement of the zenith angle, the altitude angle). Note how the zenith angle in Figure 2.15, above (the generic $\theta$ angle), is congruent with the solar zenith (${\theta }_z$) of the Sun, and the generic azimuth angle ($\phi$) is congruent with the solar azimuth (${\gamma }_s$).

The following equations describe the Cartesian coordinates (x, y, z) for unit vectors, followed by the equivalent functionals using the complementary altitude angle.
$$\begin{array}{c}\begin{array}{ccccc}z& =& \cos \theta & =& \sin \alpha \\ x& =& \sin \theta \cos \phi & =& \cos \alpha \cos \phi \\ y& =& \sin \theta \sin \phi & =& \cos \alpha \sin \phi \end{array}\end{array}$$

As seen in Figure 2.16, we need to pull back to our old trigonometry mnemonics! Recall "Soh Cah Toa" when looking at the figure:

Figure 2.16: Right Triangle with side lengths [a (opposite), b (adjacent), h (hypotenuse)] and angles [A, B, C].

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

• Sine(A): Opposite over Hypotenuse (a/h)
• Cosine(A): Adjacent over Hypotenuse (b/h)
• Tangent(A): Opposite over Adjacent (a/b)

Sun Charts: Projections of Solar Events and Shadowing from the Sky Dome

The emphasis of this lesson is the Sun Chart tool (or Sun Path). These flat diagrams are found in many solar design tools, but may look completely foreign to the new student in solar energy. How do we interpret the arcs and points plotted on a sun chart? Why do we have two different types of plots (one looks like a rectangle, and one looks like a circle)? Why do some plots go from 0-360°, while others go from -180° to +180°?

Video: Angles Sunchart 1 (4:45)

What are Sun Charts?

If we want to visually convert our observations of the sky-dome onto a two-dimensional medium, we can either use an orthographic projection or a spherical projection on a polar chart. These projections are useful for calculating established times of solar availability or shadowing for a given point of solar collection.

The Sun Path describes the arc of the sun across the sky in relation to an earth-bound observer at a given latitude and time.

Figure 2.17: We display the path of the Sun across two days for the Northern Hemisphere. One day in summer and one in winter, where the trail of the beam has been projected onto the sky dome using angular coordinates of solar azimuth (${\gamma }_s$) and solar altitude (${\alpha }_s$).

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

All light incident upon Earth's surface must pass through the atmosphere and be attenuated (lost from absorption or back scattering). In order to simplify the many points of origin of light, we divide the sky and the Earth's surface into components, or spatial blocks of an imaginary hemispherical projection on the sky. The Sky Dome refers to the sum of the components for the entire sky from horizon to zenith, and in all azimuthal directions. In our following sections, a collecting surface is assumed to be horizontal first, as a pyranometer measuring device is mounted horizontally and facing the sky to measure the Global Irradiance/Irradiation in the shortwave band for the sky dome. Most of our solar collectors will be tilted up from horizontal in some way (PV, solar hot water, windows, walls, even your eyes). Those surfaces oriented otherwise are termed a Plane of Array measurement (POA), requiring specific tilt and azimuth information in the description. For those solar collecting surfaces that are not horizontal, the reflectance of the ground is an additional source of light, through the albedo effect. The beam, sky diffuse, and ground diffuse light sources incident upon the tilted collector are estimated using models of light source components.

Projections

The sky dome can be projected onto flat surfaces for analysis of shading and sky component behavior.

Figure 2.18: The sky dome as projected to the right in orthographic form, and as projected upward in polar form.

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

Video: Angles Sunchart 2 (6:01)

1. Orthographic Projection: takes the sky dome and projects altitude and azimuth values outward onto a surrounding vertical cylinder. The cylinder is then opened flat. Figure 2.19, below, shows the sun rising in the East (to the left) and setting in the West (to the right). Proper observation shows that the largest arc in the chart at the top, June 21, is the Northern Solstice, while the smallest, December 21, is the Southern Solstice.

   

   Figure 2.19: Orthographic Projection.

   Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

2. Polar Projection: takes the sky dome and projects altitude and azimuth values down onto a circular plane. However, in the polar projection, the arc for December 21 is at the top while the arc for June 21 is at the bottom. This happens because we are effectively lying on the ground with our heads facing south, and holding that large piece of paper straight up to the sky.

   

   Figure 2.20: Polar Projection

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

How do We Make and Read Sun Charts?

Go to the University of Oregon Solar Radiation Monitoring Laboratory website. The scientists at the Laboratory have provided an excellent tool for plotting sun paths onto orthographic projections or polar/spherical projections. The default page is for creating an orthographic projection of your site of interest. The alternate page for polar projections will use the same data you can input, but will output the alternate form. Note that both use the meteorological standard for azimuth angles, where North is set at 0°, South will correspond to 180, and the azimuth values are increasing clockwise to 360°.

So how do you use this tool? Go through the following steps:

1. Specify the location by $\varphi$ and $\lambda$. (Latitude is important for our calculations of sun-observer angles).
2. Specify the time zone (this is optional - for most time zones the software makes this correction from UTC to local time zone automatically based on the coordinates provided).
3. Choose months to be plotted - you can do the full year or isolate a certain month or even day. Note that the plots are symmetrical between the first half and second half of the year versus summer solstice (when calculated in solar time). December through June data will look the same as June through December.
4. Choose projection: orthographic (Cartesian) or polar.
5. Further you can specify a few additional parameters. We do need time contours and labels, so keep those checked.
6. Once you click "Submit", the plot will be generated, and you will be given options to download the image and data.

What about Shadows?

When designing a solar energy conversion system for any application, we must pay special attention to the occurrence of shadows throughout the year. Later in this lesson, we will discuss a method to assess the shading using 2-D projections. Specifically for one of your assignments, you will use the polar SunChart projection for shading analysis.

The next page gives you an opportunity to print and analyze your own Sun Chart.

Now, based on your understanding of the SunCharts, work through the self-check questions below. While you work through these steps, try to think about all the calculations that went into each plotted point on the curves. You should reflect on the fact that the SunChart tool is simply plotting points and lines based on solar calculations of time and longitude. The same calculations that you are mastering now in class. Pretty exciting!

Self-Check Questions - based on the Cartesian SunChart for State College, PA

Answer the same questions for your own locale. Are the answers different or the same compared to State College, PA?

If you check out the polar projection of the Sun Chart, you will see that it looks quite different, but the plot is based on virtually the same data. Here is the polar chart for State College, PA, location. Note that in this case the coordinates used are solar azimuth and solar zenith angle (SZA) as opposed to the solar elevation angle in the cartesian projection (I wish there were an option to switch between those two). If you need to get the solar elevation angles from this plot, just remember that those angles are complementary:

$${\alpha }_{s }= 1 - {\theta }_{z }$$

This is the projection you will be using for shading analysis in your homework. So take some time studying this plot.

• What is each blue curve represents here?
• Pick a point on a curve. Can you determine the solar azimuth and solar zenith angle for this point from the plot? What would be solar elevation angle at that point?
• Which point on the plot would correspond to 3 pm on February 21st (tip: look for month and hour labels)

Going forward, you can always check your solar coordinate calculations versus the Sun Chart or use them for quick estimates of the Sun position.

Quick review of the Charts:

First, we will go over the key features of the orthographic plots with the arcs of six days plotted out for the first half of the year.

Video: Sunchart Ortho Intro (4:42)

Second, we can compare the key features of the orthographic plots to the polar plots, again with the arcs of six days plotted out for the first half of the year. You should notice the similarities (East is on the left, solar time is represented, the same location is plotted), as well as the distinct differences (the June and December arcs are "flipped").

Video: SunChart Polar Intro (5:49)

How to integrate shading as an overlay

Now, we need to add an additional layer of information to the plot. I'm going to talk through the addition of critical points on the sun chart, followed by connecting those points and shading the areas correctly. In each of the following examples, we will use orthographic projections, but there is no reason why you couldn't use polar plots instead.

The first example will come from the textbook. We will be plotting shading relative to a single receiving point: X, with three critical points of shading (A, B, and C).

Video: Shading Wing Demo (5:52)

In the next example, we will look at setting up the problem to assess a PV array shading problem. Our intent is to plot shading relative to multiple receiving points: A, B, and C, with three critical points of shading (1, 2, and 3). The result is nine values for altitude coordinates ($\alpha$, no subscript) and nine values for azimuth coordinates ($\gamma$, no subscript).

Video: Shading Array Demo 1 (6:08)

You will notice how the horizontal surfaces of the building that create shadows are transposed to the projection as an arc, not as a horizontal line, while the vertical surfaces remain vertical. This has to do with the manner in which spherical data is distorted in an orthographic projection. Hence, the plot of a building shading a point on a window will look a lot like a slice of bread, flat on the sides with a soft curve across the top. The same will be found for this example, where the receiving points A, B, and C are shaded at different times by critical points 1, 2, and 3.

Video: Shading Array Demo 2 (5:57)

Next, we will be interpreting our results, and inputting the shadow data into SAM.

System Advisor Model

I hope you were successful installing SAM software and getting it ready to use in the last lesson. Now you will be applying your interpretation of the shading diagram to determine shading factors and input them into SAM for system energy performance simulations where shading interferes with the solar resource.

We have come a long way in interpreting sun path diagrams and plotting shaded areas as overlays onto the sun path charts. How can we input those shade/no-shade conditions to the PV performance model in SAM? The video below provides a demo of how shading conditions can be applied in SAM simulations.

Video: SAM Shading Intro (6:26)

So, the important take-aways are that we can use SunCharts or other geometric shading data to get us to a shade-based performance adjustment of PV performance simulations, and that shading matters in solar energy. How significant can it be? Quite significant, but you will get a more accurate answer after performing your homework assignment in this lesson! We use these SAM simulations in solar project design, and this will be the way to assess the shading losses for any specific scenario (and in your final course project, eventually).

When working with SAM shading table, we can input partial values for hours that are on the shade/no-shade borderline (e.g. 50% etc.). SAM conveniently grades the color scheme from white (full sun) to red (full shade) in the process. Also, note that the locale matters! Do not forget to set your location in the Location and Resource tab first: the default for SAM is often in the Southwest USA, and you will need a correct solar resource file before running your simulations.

This activity allows you to apply the concepts of time and space coordinates you learned in this lesson to a specific example of a solar energy conversion system. In the process, you will work with both Sun Chart and SAM software to model the performance of a PV array. You will be required to demonstrate your learned skills for Sun Chart interpretation, shadow tracking, and including shading information into SAM simulations.

PV Array System

• A fixed-axis array of PV modules installed in the Baltimore MD area.
• The array consists of two rows of 8 modules stacked together (see more description and picture in Chapter 7 of the SECS Book), each module is 1.25 m in height and 1 m wide.

Figure 2.21: Sample array

Credit: Mark Fedkin © Penn State University is licensed under CC BY-NC-SA 4.0

• Orientation: azimuth -9^o (i.e. it is facing a few degrees East of South - in standard 360^o degree notation, surface azimuth = 171^o)
• Tilt: 35^o (fixed)
• The array is assumed to be part of a larger solar installation, meaning that a similar array positioned in the front can cast shadow to our array of interest.
• Spacing between the arrays in the field is 3 m.
• Nominal array capacity 4 kW
• Assume PV cells and modules are connected in series, so partial shading along the base will affect the entire array (simplified case).

Task

Model the effect of shading on the PV array performance (kWh of energy generated) over a year. So, in the end, you will need to produce the energy output data from the array for the full-sun and shaded scenarios and observe the difference.

Directions

1. SunChart. Create the Sun Chart for sun trajectory of the Baltimore, MD, location using the University of Oregon Solar Radiation Monitoring Laboratory solar tool. You are to use the polar sun chart in this activity. Download your Sun Chart diagram as a PDF file. You have seen examples of this in the videos included in this Lesson. You will use this chart further to put your shading information on.

2. Apply shading. Study the “Array Packing” example in Chapter 7 of the J. Brownson’s SECS Book, understanding how shading coordinates can be obtained for a specific system geometry. Plot on your Sun Chart all the critical points by shading coordinates given in Table 7.3. List of critical points to plot is also provided in Canvas for your convenience. Connect the points with a smooth line to show the shaded zone on your diagram (see lesson videos and textbook for more guidance on how to do it). You can use a graphical software for this purpose or do it by hand if that is easier.

   NOTE: the solar azimuth coordinates used by SunChart are different from those Brownson's book. The former considers 180^o as true south, while the latter considers 0^o as true south. So, you would need to convert the solar azimuths from the book by adding 180 in order to correctly plot the points on the SunChart.

3. SAM Simulaton A (you have already downloaded SAM as instructed in Lesson 1):
   • Start a new PV project in SAM – choose Detailed PV Model - Residential Owner option when initiating a project
   • Under Location and Resource tab, input Baltimore, MD
   • Under System Design tab, input specifications for the system (4 kW nameplate capacity, array tilt and azimuth)
   • For the first round, do not include shading data
   • Run the simulation by pressing the blue 'Simulate' button at the bottom left of the screen
   • To get the monthly energy data in table, click on DataTables tab on top. Then choose output variables: you need Monthly Energy (KWh) and total Annual Energy (kWh) for a single year. You can also find the latter by just summing up your monthly values.
   • Export your table to an Excel spreadsheet
4. Sam Simulation B. Repeat the same simulation as described in Step 3 now including the shading data. This is how: Save your project as a new file. Under 'Shading Layout' tab, click 'Edit Shading' button. Then, in the editing window, choose the option ‘Enable month by hour beam irradiance shading losses’. You will be given a table to input shading factors for each hour in each month. For simplicity, we will consider the same (averaged) shading factor for all days in the same month. Looking at your Sun Chart, input 0 for no shading, 100 for full shade, and 50 for borderline or changing conditions. Once done, run the SAM simulation and export data table as described in Step 3. (See demo video in Canvas for this step)
5. Discussion. Provide a brief discussion comparing your shaded and non-shaded results and what you learned from this activity.

Submitting Your Work

Prepare a written report including the following results:

• Sun Chart for Baltimore, MD with critical points and shaded zone plotted on it.
• Table of SAM simulation results for full sun and shaded scenarios. This table should contain monthly energy generated as well as total annual energy delivered by the array. In your energy performance table, your numbers should be rounded to the nearest whole kWh (no decimals).
• Screenshot of shading factor table from SAM.
• A paragraph with a discussion of your results.

Upload your report file to the Lesson 2 Learning Activity DropBox in PDF or docx format in Canvas.

Grading Criteria

• Sun Charts (10 pt). This part will be graded based on your ability to plot the calculated critical points and identify shaded versus non-shaded conditions for the system at the specific time and location.
• Energy Tables (10 pt). You will be given 1 pt per month based on the reasonable correctness of the numerical values. The purpose is not necessarily to get the exact "right" answer, but rather to have done the process and understand what you are doing. So discrepancies within +/- 30 kWh will not cause point deductions.
• Discussion (5pt).
• Screenshot of the Table with shading factors used for SAM simulation (5 pt).

Deadline

See the Canvas Calendar for specific due dates.

Summary

So far, we have delved deep into the world of angles, time, and shading. Why have we done this? The solar resource is all about timing and placement of the SECS relative to the Sun, and the use of angles as coordinates in time and place are fundamental building blocks to the solar expert. We now have computational tools that make the work of calculating details trivial, but one must always know what the foundations are underneath those tools.

Who knows, maybe you will be the next open software developer to create a simple solar tool for resource assessment. You now have the keys to access many of those computational tools. More to the point, these fundamentals are not shrouded in mystery, and you don't necessarily need to pay for software to get access to them!

Looking ahead, I can tell you that students in residence at Penn State have already found a solar systems design plugin for Trimble SketchUp called Skelion, which does shading analysis just like you performed, but on the fly inside of the SketchUp design software. Both are free to use, and I'd recommend you take a look at each in preparation for your end of semester design projects! This is an untapped resource for you to explore, now that you know "how" the shading calculations work.

Knowing these principles of angles and time also exposes us to the strengths and potential weaknesses of purely geometric relations in the solar resource. As we shall see in the next lesson, the role of the atmosphere and meteorology will tend to muck up our ideal angles of beams of light, and produce anisotropic (uneven) intensities of irradiance over the day, which will of course influence our solar resource estimations.

On to the next lesson--let's learn about the role of weather and the sky dome in estimating the solar resource!

The Goal of Solar Design and our Three New Mechanisms

The Goal of Solar Design is to:

1. Maximize the solar utility
2. for the client
3. in a given locale.

Given the goal of solar design, we have learned of three mechanisms to leverage during the design process that will increase the solar utility for our client in their locale of interest:

1. Reduce the cosine projection effect on an aperture/receiver (the extreme angles of incidence, $\theta$ or low glancing angles $\alpha$),
2. Reduce the angle of incidence on an aperture/receiver (refinement on minimizing $\theta$),
3. Reduce losses from shadowing on an aperture/receiver.

In order to leverage these three tools, we have demonstrated that one needs to know where and when the Sun will be relative to our collector system.

Did you know that everything around you is glowing right now, even if you can't see it? All objects, from your skin to the atmosphere, emit energy in proportion to their temperature, and this "glow" occurs across a broad spectrum of wavelengths. Light is spectral and some of that “glow” is visible to us (like sunlight or charcoals in the fireplace), and some of it is not.

At the start of this lesson, we will review the basics of electromagnetic radiation, including invisible spectral bands, and explore how atmospheric scientists use satellite and radar imagery to interpret radiation signals.

The Sun provides shortwave radiation to the Earth’s surface, while the Earth emits longwave radiation back toward the atmosphere. But what is the role of the atmosphere in the radiative energy balance on Earth, and how does the atmosphere affect the bands of light that we collect and find useful at the Earth's surface? As we will learn, the atmosphere plays a key role by absorbing, scattering, and reflecting radiation, largely determining the amount of the shortwave radiation that reaches our solar conversion systems.

Lesson 3 will provide you with a comprehensive tour of atmospheric science as it applies to solar resource assessment. Check the learning objectives on the next page, and let’s go!

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

• identify the seven key properties of sunlight;
• differentiate between technical air mass for lab/field-testing and meteorological air masses;
• explain the concept of climate regimes;
• apply clear sky models (REST2 or Bird Clear Sky) to a location and compare the result to real measured data;
• identify the contributions that relate to the solar resource other than the sun (clouds and ground albedo);
• explain Taylor's hypothesis and how it relates to solar intermittency (moving clouds).

What is due for Lesson 3?

This lesson has two learning activities and will take us two weeks to complete. Please refer to the Course Calendar in Canvas for specific timeframes and due dates - those can vary from semester to semester. Specific directions for the assignments below can be found further within this lesson.

Questions?

If you have any questions, please post them to the Questions thread in Yellowdig. I will check this forum regularly to respond. Feel free to go through the comments and post your own responses if you are able to help out a classmate.

Radiometry

For solar resource assessment, radiometry (the measure of electromagnetic or radiant energy) is more valuable than thermometry (the measure of temperature). Solar energy is comprised of the shortwave band of light found between 250-2500 nanometer wavelengths of light ($1 nm={10}^{-9}m$, or one billionth of a meter). Within the solar field, we measure the shortwave band in terms of irradiance, as W/m² (Watts per square meter, a flux of light per receiving area). If we group irradiance over a block of time, say an hour, we call the measure irradiation, in units of Wh/m² (Watt-hours per area, similar units to electrical energy measure).

Traditional silicon photovoltaics collect energy for electricity production from wavelengths <1100 nm. Other systems like solar hot water panels will collect almost all of the spectrum from the Sun. In fact, almost all of the opaque surfaces about our environment (buildings, roads, water) tend to absorb strongly over the entire shortwave range (leading to an increase in temperature!).

And yet, our wonderfully adaptive human eyes only capture the tiny visible band from 380-780 nm. Thanks to the complex feedback systems from our irises, lenses, and eyelids, eyes can adapt well to extreme conditions of bright or dim lighting but cannot be used to quantitatively gauge irradiance conditions that energetically drive our buildings and photovoltaic systems. Our eyes impart important information, but because they are highly sensitive and adaptive systems, our eyes cannot be used to reliably distinguish and evaluate the solar resource (bare skin may actually be a better receptor for the shortwave band on days that are not windy).

Notice that the "visibility" of a photon is really limited only by the type of detector being used. Let's review the distribution of photons across the electromagnetic spectrum, and then we will discuss types of photon detectors beyond the rods and cones in our eyes. As a reminder, 1 micrometer wavelengths (also called 1 micron wavelengths) are equivalent to 1000 nanometer wavelengths (by unit conversion). It is often easier to use units of nanometers (nm) for the shortwave band, while using units of micrometers (um) for the longwave band. Either will work, but it is helpful to be aware of the relationship.

Figure 3.1: We can view a diagram of the broad possible spectrum of electromagnetic radiation.

Click here for text alternative for Figure 3.1

Diagram of the broad possible spectrum of electromagnetic radiation from left to right: Gamma Ray, X-Ray, Ultraviolet, Visible (small section), Infrared, Microwave, Radio

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

Now, let's zoom in to the shortwave and longwave bands important to SECSs. Wavelengths are expressed either in nanometers (nm) or micrometers ($\mu \mathrm{m}$, also called microns). For wavelengths greater than 380 nm, electromagnetic radiation transitions from the ultraviolet (UV) to the violet visible range for the human eye. As we will observe in the Granqvist figure below, the red visible range ends for wavelengths greater than 780 nm (to the human eye). Notice how the "infrared" crosses over both the shortwave and longwave bands of light.

• SECS have a different operational "grouping" of bands than traditional spectroscopy or remote sensing. Get used to shortwave and longwave bands, as we describe below.

Figure 3.2: The visible and infrared sub-bands of electromagnetic radiation representing the shortwave and longwave bands.

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

Video: Temperature and Wavelengths (0:57)

All objects glow with energy in proportion to temperature. As temperatures increase, the wavelength oscillations become shorter and the density of photons measured is effectively increased. So, the light becomes more intense (more photons), and each photon is packed with more energy.

Most photons are emitted from a thermal surface, where the constituent atoms are vibrating in the material (this means: temperature). Every material has a thermal property, and hence "everything glows." This concept works well for something called "blackbody emission" (zero emittance) or "greybody emission" (non-zero emittance) but not so well to describe your standard laser pointer or microwave oven. So, just to clarify all cases, there are also photons emitted from the Sun and from solid state devices that are "stimulated emission" (lasers), which can allow for photon emission from surfaces that are high in energy, but not high in thermal temperature.

First rule of Solar Energy: Light is Directional.

This is our first principle of seven for the behavior of light. So, let's begin with the simple yet important statement: Light is directional. Light, as a photon, is born (emitted) from a surface in many directions and then impinges upon other surfaces, where it is either absorbed, reflected, or transmitted (and refracted). We use that directionality to describe the resource. In the text chapter, we have defined a visual shorthand for light that is emitted, transmitted, reflected (scattered), and/or absorbed by various surfaces.

• Irradiance (W/m²): light that impinges upon a receiver surface, interpreted as the instantaneous rate of change in energy (called power, or Watts) per unit area. Remember that one Watt is equivalent to one Joule per second (a rate of energy exchange).
• Irradiation ($J/m^2$ or Wh/m²): light that impinges upon a receiver surface over a period of time, interpreted as the energy (in Joules or Watt-hours) per unit area.
• Radiance (W/m²/sr): light emitted from a surface, interpreted as the instantaneous rate of change in energy (call power, or Watts) per unit area per steradian (a unit of solid angle). If we were to generalize radiance over all exiting directions or angles ($W/m^2$), we term the energy emittance as radiant exitance.
• Radiation (J/m² or Wh/m²): here, using the convention of the field, radiation means light emitted from a surface over a period of time, interpreted as the energy (in Joules or Watt-hours) per unit area. This is a loose operational definition, as "radiation" can mean many different things to different fields of study.

Notice that the "Ir-" instructs us that the light is incident upon a surface. For example, we measure "irradiance" on a pyranometer, because light is absorbed by the device. Also, notice that my choice of "-iance" or "-iation" determines if the light is a measure of rate (as in power: energy per time) or energy (rate integrated over a span of time).

Figure 3.3: Radiant transfer (light) is directional.

Click here for text alternative for Figure 3.3

Left to right:

Left: An image of the sun is labeled Emitter. Above the sun is the label: Radiance (W/m2) and the image of a stopwatch. Below the sun is the label: Radiation (J/ m2) and the image of a stopwatch with the right half filled in.

Proceeding to the right: Two lines from the sun travel to a Receiver on the right. The top line is a straight dotted line labeled (280-2500nm) shortwave spectra High Energy. The second line is a wavy dotted line labeled Low Energy longwave spectra (2500-30,000 nm)

Right: Above the Receiver is the label: Irradiance (W/m2) and the image of a stopwatch. Below the receiver is the label: Irradiation (J/ m2) and the image of a stopwatch with the right half filled in.

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

Second Rule of Solar Energy: Light is Spectral.

All objects glow (even the gases in the sky); it is just the intensity and peak wavelength that shifts with respect to their thermal temperature. This brings us to the second of the seven principles of light behavior. Light (e.g., derived from the sun) has a broad spectrum of energies, which are discussed as wavelengths. We tend to group similar wavelengths in the spectrum according to the properties of their emitting surface or receiving surface.

Short Wave Band (250-2500 or 3000 nm)

This is a "group" of high-energy wavelengths of light that are emitted from the Sun (See Light is Directional), comprising the majority of the total energy collected by the Earth's surface or our designed SECS, given the decrease in the light power density with distance to Earth (93 million miles, 150 million km). This bundle of wavelengths of light emitted from the sun includes the ultraviolet (UV), the visible, and the near infrared (IR) sub-bands.

• Shortwave band: The shortwave band of wavelengths is confined from approximately 250 nm to 2500 nm at Earth's surface, because of the Inverse Square Law for light and the nature of our atmosphere as an absorber/reflector of longwave irradiation. Our measurement devices are also limited to measuring this range by the transparency of low-Fe glass covers.

The Sun is effectively the only surface from our surrounding environment that regularly and naturally emits shortwave radiance. We can deliver shortwave band energy to a new surface using a reflector, though, as is the purpose of light concentration onto a central receiver.

Long Wave Band (2500 or 3000 nm - 50,0000 nm)

Long wave band consists of low energy light. The wavelengths of light that are emitted from our skin, from pavement, the sky, ice cubes, and even hot ovens are coming from surfaces that are quite cool relative to the surface of the Sun, right? We are comparing 250-500K surfaces to a 6000K surface. Planck's Law (discussed in the next page) suggests that the distribution of wavelengths will be very different from cool bodies than from extraterrestrial bodies with internal fusion reactors.

The group of wavelengths from cool bodies on Earth is termed the longwave band. This is >2500nm at Earth's surface, but also can be >3000nm if we were to group the wavelengths from space. The longwave band photons are of lower energy, but there is a very wide band of wavelengths included in the group. The longwave band contributes to the greenhouse effect, and keeps our atmosphere comfortably warm. With the addition of CO₂ and water vapor to the atmosphere, we make the sky into a better reflector for keeping longwave energy instead of allowing it to escape into space.

• Longwave band: The longwave wavelengths are found in the range of 2500 nm to wavelengths greater than 50,000 nm, and again our measurement devices are limited to the range of about 30 or 50,000 nm. This second "group" of wavelengths of light is emitted by surfaces significantly cooler than the Sun! This includes the surface of our human bodies, the surface of Earth, and the effective surfaces of Earth's atmosphere (if we were to simplify the atmosphere to two surfaces in a slice of gas and particles).

Now, we're going to take a moment to explore the following multiple figure graphic from Smith and Granqvist. There is a lot of information in here, so take your time and revisit it as the class progresses.

Figure 3.4: Bands of Irradiance and Radiance

Credit: Figure 2.4 from G. B. Smith and C. G. Granqvist (2011) Green Nanotechnology: Solutions for Sustainability and Energy in the Built Environment. CRC Press. Taylor and Francis Group. p. 30

• The top graphic, Figure (a), shows the longwave spectrum of radiance (remember, that means "emitted power") from any surface at "ambient" Earth temperatures (-50C to +150C). You see a series of four humped curves that get more intense (bigger), while the peak shifts toward the left (higher energy) as hypothetical surface temperatures increase from -50C to +100C. These temperatures include the Earth's atmosphere, your body, the interior walls of your homes, even a glacier. Remember, all surfaces "glow." This spectral region is the Near-, Mid-, and Far-Infrared, and you may have seen false color images of these emitted surfaces from IR cameras before. The irradiance scales are from 0 to 0.1 W/m²/nm.
• Next, Figure (b) shows the spectrum of Solar light measured just above the atmosphere. The intensity of solar irradiance (remember, that means "received power") at the atmosphere is reduced in proportion to the inverse square of the distance from Sun to Earth. There is effectively only one temperature for the surface of the Sun, and so only one curve, which is far to the left relative to the curves in Figure (a). Also, notice that the intensity of the curve is significantly greater, with a scale from 0 to 2 W/m²/nm.
• Figure (c) shows spectral regions where shortwave and longwave radiation passes through the atmosphere. This is an absorptance spectrum; so, areas where the curve is near one (e.g., 4-8 micrometers) completely absorb the outgoing longwave from Earth and the surrounding atmosphere. Areas where the curve is near zero (e.g., 8-13 micrometers) will allow longwave light to transmit into outer space. The gap between 8-13 micrometers (8,000-13,000 nm) is called the atmospheric window, or the sky window, where the molecules CO₂ and H₂O do not absorb or reflect, and through which a portion of the longwave band can escape. Soon, we will design terrestrial emitters to selectively send energy out the window. This is where longwave radiation from the Earth and Atmosphere leaks radiant energy out into space. Compare Figure (c) with Figure (a) and notice how much they overlap each other.
• Finally, Figure (d) shows a solid line with a peak near 550 nm, demonstrating the relatively tiny region of sensitivity of the eye for detecting photons under daylight conditions (called the photopic state). This is a pretty small energy band, and does not include the behavior of the iris, the eyelids, and the direction your eyes are pointing with respect to your eye lenses. The double peaked dashed line (around 420 nm and 700 nm) is the efficiency of light absorption for green algae, again confined to a tiny region of the whole spectrum. Both curves are normalized fractional scales from 0-1.

Third Rule of Solar Energy: Inverse Square Law

Light intensity decreases in proportion to the square of the distance between emitter and receiver. This is called the Inverse Square Law, which applies to solar energy as well as to any other light source. In case of the Sun, the emitted energy flux is 6.33x10⁷ W/m² at the surface of the Sun drops down to 9126 W/m² at the surface of Mercury (d=58 million km), and down to 1361 W/m² at the exterior of Earth's atmosphere (d=150 million km).

As shown in the next figure, the reason for the inverse square law is geometric in nature. As light is emitted from a point, like the Sun at a very large distance, the same quantity of photons is spread out over an increasingly larger area with distance. Area is a spatial term in units of distance squared. This same principle works for ordinary surfaces, as photographers well know.

Figure 3.5: Inverse Square Law for Light

Credit: Inverse Square Law by Borb from Wikimedia (CC BY-SA 3.0)

Mathematically, this process of light “dilution” can be represented by the following equation (which is another form of Equation 3.2 in the SECS textbook)

$${\mathrm{G} }_{2 }= {\mathrm{G} }_{1 }\left( \frac{{ \mathrm{d} }_{1 }^{2 }}{{ \mathrm{d} }_{2 }^{2 }}\right)$$

where G₁ is the light intensity (or flux) at distance d₁, and G₂ is the light intensity at distance d₂.
If we take G₁ as the radiative energy flux at the surface of the Sun, we can then estimate the radiative energy flux at the Earth’s orbit (G₂) using this equation simply based on the planetary distances. Try to make this calculation with d₁ being the Sun’s radius, and d₂ being the distance from the Sun to the Earth and see what you get. You will have a chance to share your result in the Lesson 3 Activity further in this lesson.

Kirchoff's Law

This radiative transfer law is very important when considering energy balance. It states that at thermal equilibrium, the emissivity ($ϵ$) of a body or surface equals its absorptivity ($\alpha$).

Mathematically, we can conceptualize Kirchoff's law as

$$\frac{E}{E_b}=ϵ=\alpha$$

The radiant energy emitted from a real surface is represented as E (W/m²), while that of a blackbody (a theoretical condition) is given by E_B (W/m²).

Simply put, a surface at steady state temperature will absorb light equally, as well as it emits light. Though light is directional, surfaces exchange photons in both directions.

Planck's Law

This law is generalized to mean that all objects have some internal temperature, and given that temperature, they all glow. Max Planck was able to establish the dependence of the spectral emissive energy of a blackbody for all wavelengths of light ($E_{\lambda ,b}$), given a known equilibrium temperature of the blackbody.

$$E_{\lambda ,b}=\frac{2\pi h{c}^2}{{\lambda }^5[e^{\frac{hc}{\lambda KT}}-1]}$$

Wien's Displacement Law

The Wien's displacement law provides us with expected values for the most probable wavelengths in the Bose-Einstein distribution of blackbody radiation. The law implies that the distribution of photons emitted from a surface at any temperature will have the same form or shape as a distribution of photons emitted from a surface at any other temperature. Mathematically,

$${\lambda }_{max}=\frac{2.8978\times {10}^{6}nmK}{T(K)}$$

Stefan-Boltzmann Law

The Stefan-Boltzmann Law states that the radiative energy emitted by a surface is proportional to the fourth power of the surface's absolute temperature. The Stefan-Boltzmann Law shows that if you were to integrate all the energies from the wavelengths in Planck's Law, you have an analytical solution of the form below:

$$E_b=\underset{0}{\overset{\text{∞}}{{\displaystyle \int }}}{E}_{\lambda ,b}\text{d}\lambda =\sigma T^4$$

where $\sigma$ = Stefan-Boltzmann constant $5.67\times {10}^{-}8W/m^2{K}^4$

Keep in mind that this is for the surface of the emitter. A surface like the Sun will have a very high value for the energy density on the surface, which then decreases in proportion with the Inverse Square Law from the last page (over the 93 million miles distance to Earth's surface).

Wolfram Alpha website is the Google of math and physics. If you want to do calculations on Wien's Law, you type "wien's law" and you will get a calculator for Wien's Law with all sorts of other information. The purpose of this activity is to practice some basic calculations of physical properties of sunlight.

This video below (6 min) presents a short demo on how to use the Wolfram Alpha site. The Stefan-Boltzmann Law is used as an example here, so it provides you with a tip for solving the second problem.

Submitting Your Work

Prepare a written report with your solutions and upload it to Canvas (Lesson 3 Learning Activity Dropbox) in PDF or docx format. You can use Wolfram Alpha screen shots to present your results for the first two problems (insert the screenshots into your report - don't submit them as separate files). Make sure to present the equations you are using and provide comments to the steps in your solutions.

Grading Criteria

View the Rubric in Canvas by which this assignment will be graded.

Deadline

See the Calendar tab in Canvas for specific due dates.

The action of "reflection" is more appropriately described as "back-scattering" by atmospheric physics, which is why you see that term in the figure of possible paths of light. We also have seen a shorthand diagramming technique from the textbook to describe the life events of ensembles (really big groups) of shortwave and longwave photons.

I would like to pull the concept of photon lifetimes in the following video.

Video: Diagramming Light Intro (2:03)

Figure 3.6 Our symbolic notations for diagramming the emission, transmission, reflectance, and absorptance of light (both shortwave and longwave bands).

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

Each of these phenomena is happening simultaneously, and the next video opens up that discussion.

Video: Light Interactions Descriptive (4:31)

Figure 3.7: Light Interactions image discussed in the video

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

Emission ($ϵ$), absorption ($\alpha$), reflection ($\rho$), and transmission ($\tau$) can all occur at the same time (in fact it always does). We also know that there is a relationship between light energy balances and temperature. When a receiving surface or material absorbs more energy than it emits, the internal temperature of the material will increase (effectively pumping up the system's energy density). Consider a bright summer day, where your rooftop absorbs much more solar radiation than it emits (or conducts away). The roof surface temperature will rise from just after sunrise to the late afternoon.

Video: Light Diagramming Example (5:49)

The Earth is a vast solar energy conversion system! The atmosphere encasing Earth's land and water mass is a collection of gases and particles that vary in pressure, temperature, and chemistry continuously. If we collectively imagine for just a moment that the atmosphere is a simple cover on top of our main absorber (the Earth), we can begin forming a concept of the atmosphere interacting with electromagnetic radiation across broad bands of wavelengths.

Now, let us consider the optical properties of a single material that reflects light for some bands and transmits or absorbs light for alternate bands, just like the atmosphere represented above. We call the surface of such a material a selective surface, because the light interaction occurs at the surface. A selective surface is non-reflective to some bands of light, while being reflective to other bands of light. The atmosphere is a case study for a selective covering surface between shortwave and longwave bands.

For opaque materials, there is a relation between reflectivity and emissivity (the glow of an object) and between reflectivity and absorptivity.

• A surface that is highly reflective for a certain band of wavelengths is also a surface with a low emissivity.
  • Meaning: reflective materials don't 'glow' effectively.
• In contrast, a surface that has low reflectivity for certain wavelengths of light will have a high emissivity.
  • Meaning: non-reflective materials tend to 'glow' effectively.

We now know the relation for surfaces in optics called Kirchoff's Law of Radiation. When a surface is in thermal equilibrium with the surroundings, the emissivity is equal to its absorptivity at each wavelength ($ϵ = \alpha$). This allows us to make the same relations among reflectivities and absorptivities.

• A surface that is highly reflective for a certain band of wavelengths is also a surface with a low absorptivity.
  • Meaning: reflective materials don't absorb light effectively, either.
• In contrast, a surface that has low reflectivity for certain wavelengths of light will have a high absorptivity.
  • Meaning: non-reflective materials really do absorb light effectively.

We can show the ways in which the Earth-Atmosphere is selective in the relative properties of each to absorb, reflect, and transmit different bands of light.

Video: Solar Case Study (6:47)

We have already described shortwave (280-2500 nm at ground level) and longwave (>2500 nm) bands of irradiation incident upon a surface. The study of optics is that of light-matter interactions, regardless of wavelength. We know that materials like glass are semi-transparent in most of the shortwave band, and materials like pure aluminum are reflective in the shortwave band. We are not so familiar with the way that materials behave in the longwave band, and we often have trouble with materials that are opaque vs. semi-transparent.

Let's review the transmittance graphic that I introduced earlier. This plot has a logarithmic x-axis, so, we can count from 0.2 micrometers (200 nm) up to 1 micrometer wavelengths in increments of 0.1 micrometer. Then, we count from 1 micrometer to 10 micrometers in increments of 1 micrometer, and so on...

Figure 3.8: Spectral intensity of downgoing solar irradiation and upgoing terrestrial radiation through the atmospheric window. Prominent absorption bands from Earth's atmosphere (middle panel) linked to the shortwave and longwave light transmitted through the atmosphere (top panel). The lower panel shows absorption spectra associated with major greenhouse gases, plus Rayleigh scattering.

Credit: Atmospheric Transmission by Robert A. Rohde from Wikimedia licensed under CC BY-SA 3.0

We see that from about 0.3 micrometers to about 2.5 micrometers, there is a significant amount of white showing on the plot of the Total Absorption and Scattering, meaning that the absorption and reflection of visible light by the atmosphere is relatively small. In other words, the atmosphere transmits 70-75% of the sun's shortwave light from the top down to the Earth's surface. Along the way, clouds can back-scatter (reflect) some of the visible light into space. In times and places where transmitted sunlight reaches the Earth's surface, then the land, oceans, deserts, grasses, and trees, etc., reflect some of the surface-incident shortwave light back into space (again, with limited absorption along the way).

We also see that from 8-13 micrometers, there is an atmospheric window where the longwave band light is not absorbed or scattered. This is the way that the Earth and the Atmosphere can "leak" energy back into space. If you like, go back to take a look at a similar figure from Granqvist. From which side of the sky window is water vapor absorbing the longwave light, and from which side is CO₂?

Using this example, when incident light (irradiance) is not absorbed or transmitted through the surface and bulk of a material, it is reflected by the surface (the fraction of reflection is called the albedo).

For the good of the engineering community, air masses were "fixed" in 1976 as the U.S. Standard Atmosphere for the ideal clear sky atmosphere in the mid-latitudes of the USA. Yep, and nothing has changed since 1976, right? (cough)

Actually, the American Society for Testing and Materials (ASTM) developed the "Terrestrial Reference Spectra for Photovoltaic Performance Evaluation" so that we could compare and evaluate the performance of our solar technologies, like PV cells and modules. The full documentation of the reference standard is held by the National Renewable Energy Laboratory (NREL AM Standard).

The specified atmospheric conditions are:

1. "1976 U.S. Standard Atmosphere" with temperature, pressure, aerosol density (rural aerosol loading), air density, molecular species density specified in 33 layers;
2. Absolute air mass of 1.5 (solar zenith angle 48.19°s);
3. Angstrom turbidity (base e) at 500 nm of 0.084 c;
4. Total column water vapor equivalent of 1.42 cm;
5. Total column ozone equivalent of 0.34 cm;
6. Surface spectral albedo (reflectivity) of Light Soil as documented in the Jet Propulsion Laboratory ASTER Spectral Reflectance Database.

Actually, we are speaking of an air mass coefficient: a relative measure of the optical path length passing through the Earth's atmosphere, as described for a fixed moment in time and space. We express the air mass coefficient as a ratio of the direct path of the global shortwave irradiance incident upon a specially tilted surface, relative to the path length for a horizontal surface (optical path oriented vertically upwards as the normal).

AM0

The first thing we need to estimate is what the intensity of the global horizontal irradiance would be just "outside" of our thin covering atmosphere. So, how do we determine the solar energy incident upon the extraterrestrial surface for the Earth-Atmosphere system?

First, we begin with the annual average solar constant, in units of irradiance (recently updated as of 2012! No longer 1366 or 1367 W/m² if you knew that value). The average annual Solar intensity will actually vary according to an oscillation linked to 11-year cycles of sunspots. Given a large number of sunspots, the solar constant will be higher (~ 1362 W/m²) while the value will drop to ~ 1360 W/m² when there are not many sunspots (changes about 0.01%) (Source: NASA, accessed 2026).
$$G_{sc}=1361W/m^2$$

Here, G is for Global irradiance, and "sc" stands for solar constant.

Second, we estimate the irradiance of the Sun for the intensity collected on a plane perpendicular to the beam shooting out from the Sun that is also perpendicular to the surface of the Sun (the normal radiant exitance). We would term that "normal global irradiance at AM0" (G_0,n). This would be the equivalent of an estimate at zero cosine projection error, or the angle of incidence is zero. The cosine function in the following Equation delivers the change from zero to one, reflecting the cyclic orbit of the Earth relative to the Sun. The parameter n in this equation is the day number in the year.
$$G_{0,n}=G_{sc}\left[1+0.033\cos \left(\frac{360n}{365}\right)\right]$$

Here, G is for Global, subscript "0" is for Air Mass Zero, and subscript "n" stands for radiant exitance normal to the surface of the Sun (don't confuse it with the day number).

Third and finally, we need to estimate the AM0 irradiance for any given horizontal surface on Earth's surface (G₀). Think about it, a horizontal surface on Earth (or just outside the atmosphere) will be tangent to the curvature of that locale on Earth. We should notice in the following equation that the Earth-Sun relations of declination ($\delta$), latitude ($\alpha$), and hour angle ($\omega$) are all included in this irradiance equation for AMO.
$$G_0=G_{sc}\left[1+0.033\cos \left(\frac{360n}{365}\right)\right]\cdot \left[\sin \varphi \sin \delta +\cos \varphi \cos \delta \cos \omega \right]$$

By comparison with our work from Lesson 2, I can point out that the equation is actually multiplying the Equation for G_0,n with the Equation for the solar altitude angle: ${\alpha }_s$ Another way to write this would be $G_0=G_{sc}\cdot \sin {\alpha }_s$  Wow! Lesson 2 really comes in handy!

As a reminder, the relation to find ${\alpha }_s$ is:
$$\sin {\alpha }_s=\left[\sin \varphi \sin \delta +\cos \varphi \cos \delta \cos \omega \right]$$

Consider that the sine of the altitude angle ($\sin {\alpha }_s$) is the same as the cosine of the zenith angle ($cos{\theta }_z=sin{\alpha }_s$).

• Hourly Irradiation for AM0:

$$I_0=\frac{12\cdot 3600}{\pi }\cdot G_{0,n}\cdot \left[\frac{\pi }{180}({\omega }_2-{\omega }_1)\sin \varphi \sin \delta +\cos \varphi \cos \delta \left(\sin {\omega }_2-\sin {\omega }_1\right)\right]$$

• Daily irradiation for AM0:

$$H_0=\frac{12\cdot 3600}{\pi }\cdot G_{0,n}\cdot 2\left[\frac{\pi }{180}({\omega }_{ss})\sin \varphi \sin \delta +\cos \varphi \cos \delta (\sin {\omega }_{ss})\right]$$

where the hour angle for sunset has been defined in Lesson 2 as:
$${\omega }_{ss}={\cos }^{-1}(-\tan \varphi \tan \delta )$$

AM1.5

The "standard" for testing. The air mass coefficient is defined in proportion to the cosine of the zenith angle (${\theta }_z$): the angle between the beam from the Sun and the normal vector pointing directly up to the zenith of the sky (normal to the horizontal surface).

$$AM=\frac{1}{\cos ({\theta }_z)}\text{[simple, parallel plate]}$$

One needs

• the day number (N),
• the declination ($\delta$),
• the hour angle ($\omega$), and
• the local latitude ($\varphi$) to calculate the zenith angle.

By equivalence, the cosine of the zenith angle is the sine of the altitude angle ${\alpha }_s$, as we just demonstrated above.

Figure 3.9: Schematic of AM 1.5 reference conditions

Credit: Image adapted by J. Brownson, Original image retrieved from DOE/NREL/ALLIANCE  

Figure 3.9 illustrates the concept of airmass with respect to a zenith angle of $\mathrm{\theta }={\mathrm{48.2º}}^{}$ (AM1.5), or an altitude angle of ${\alpha }_s={\mathrm{41.7º.}}^{}$ The hypothetical receiving surface would be tilted at ß = 37º for global irradiance G_t and an angle of incidence of  $$ θ = 11.2º. 

Gueymard has since developed a modified air mass model that will also apply for zenith angles >80°, as the former model tends toward infinity at ${\theta }_z=90°$.

$$AM=\frac{1}{\cos ({\theta }_z)+0.00176759\cdot {\theta }_z\cdot {(94.37515-{\theta }_z)}^{-1.21563}}$$

Source: Matthew J. Reno, Clifford W. Hansen, and Joshua S. Stein. Global horizontal irradiance clear sky models: Implementation and analysis. Technical Report SAND2012-2389, Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550, March 2012.

Meteorological Air Masses

The Air Masses used in engineering standardization for SECS technologies are not nearly as useful as the real, dynamic air masses that we will use for solar resource assessment.

The sky can be divided up into large volumes with common properties. Air masses are large pancakes of gases and particles (we call them parcels) with common properties of temperature, chemistry, and pressure. Aside from the strong role of clouds, those common physical properties each affect the way in which solar energy intensity will be decreased along the particular path length through the sky. Air mass will affect the way that light is absorbed and scattered, and hence will affect the characteristic behavior of light incident upon an aperture. The changes between air masses are weather fronts, and the study of the regional dynamic dance of air masses and accompanying fronts on a sub-annual basis is called meteorology. When we expand our studies of air mass behaviors to multiregional scales (larger spatial scales) and time scales in the range of decades to millennia, this is called climatology.

I want you to think of an air mass from meteorology as a turbulent pancake that interacts with both shortwave and longwave light, resulting in highly variable irradiance conditions at the ground level, and also for satellite remote sensing in orbit. Irradiance conditions are constantly shifting over a given locale, and we will be in need of effective forecasts of irradiation (over different time intervals) for many SECS technologies.

Seasons: the Sky-Locale Relationship

It is always important to solar energy conversion that we figure time and scale into our understanding. We observe that each location under study is influenced by multiple air masses during different times of the year. In the midlatitudes of North America, we call this periodicity seasons (deep thought, yes). Hence, our solar energy conversion systems are effectively in different locales for each period of air mass dominance.

One locale for your client will be divided up into seasons. For us, each season (a block of time) is like an independent region, different from the next season--and we call these regions climate regimes. In the mid-latitudes we observe four climate regimes, while regions affected by monsoonal swings may have two or three climate regimes.

Figure 3.10: These are fingerprints to remind you that the different climate regimes occur for a single given locale in winter, spring, summer, and fall.

Click Here for Text Alternative for Figure 3.10

Four different fingerprints symbolizing the different climate regimes for a given locale in winter, spring, summer, and fall. The first fingerprint here is labeled Dec 1 - Feb 28, the second and fourth fingerprints are not labeled. The third fingerprint is labeled June 1st - Aug 31.

Source: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

From the perspective of design in solar energy conversion systems, the skies allowing sunlight through to Philadelphia from December 1 through February 28 exist in a different climate regime from the Philadelphia skies of June 1 through August 31.

Source Regions and the Bergeron Classification System

Recall that the change of irradiation over seasons is due to the tilt of Earth (which leads to our measure of declination). When the Earth is unevenly energized by the Sun, air masses are mobile. Any locale will observe changes in residential air mass behavior over time. Air masses are created in source regions, where the mass acquires its dominant characteristics of temperature and humidity. Then air masses move from the region of origin into new regions. Source regions have been mapped out in Figure 3.11, below, and they will tend to have lighter winds, allowing the air mass to accumulate the temperature and humidity conditions of the accompanying portion of the Earth's surface (the big solar energy conversion device). Hence, areas affected by jet streams will not be regions to create new air masses.

The Bergeron classification system is accepted and used by atmospheric science and indicates the origin locale. This is important information, affecting the quality of the solar resource. Properties of thermal behavior and humidity are conveyed in the Bergeron classification, and the classification has a relatively simple two or three letter coding.

First, air masses are labeled according to their origin above a land mass, continental (c) or above an ocean, maritime (m). Maritime air masses will contain more humidity derived from the underlying body of water. Next, air masses can be grouped into main thermal categories of the site origin: (A, P, T, E). This grouping is largely separated by jet streams and changes in latitude, which of course are each derived by the tilt of Earth relative to the projection of irradiance from the Sun. By coupling the two letters together, we can then map out the source regions for meteorological behaviors across the planet and through the seasonal shifts.

The relation of air mass to monsoon cycles is less used in continental meteorology of North America, but is highly important to solar development in Asia.

Again, air masses are labeled according to the origin of the parcel above a land mass,

• continental (c): low humidity source
• maritime (m), above the ocean: high humidity source regions

Air mass source regions are also grouped according to their thermal characteristics, the thermal generator that is charging up the parcel:

• Arctic/Antarctic (A/AA): A high pressure regime that stabilizes to the far north.
• Polar (P): Very common air mass origin regime for mid- latitude regions of the USA and Europe.
• Tropical (T): Very common air mass origin regime for mid-latitude regions of the USA and Europe.
• Equatorial (E): A high pressure regime that stabilizes near the equator.

Figure 3.11 A map of the major Air Mass source regions. The mid-latitudes of the USA are affected by continental polar (cP) and maritime tropical (mT) source regions.

Credit: Worldmap wdb combined by David Hall (CC BY-SA 3.0) was used as base for map.

The Role of Clouds and Scattering

Clouds have the ability to scatter and even focus light, which means that sometimes a cloud will remove energy from the solar resource on the ground, and other times clouds will collect and focus light that's even more intense than light on the clearest day in your locale. Yet, we know that clouds are ephemeral and dynamic systems in and of themselves.

Figure 3.12 Cumulus clouds

Credit: David Babb © Penn State University is licensed under CC BY-NC-SA 4.0

The albedo is the reflective fraction of light from a given surface, a fractional value from 0-1.

Milk, Albedo and Clouds

Figure 3.13 Light is transmitted well (high transmittance of the visible sub-band) through a glass of water (upper left). As milk is added, the albedo or reflectance of the mixture increases, and the transmission of light through the glass decreases.

Credit: David Babb © Penn State University is licensed under CC BY-NC-SA 4.0

Let's consider a jar of clean water (upper left in the photograph), into which one may add a small amount of milk (upper right). Milk is a "colloidal suspension" of solid particles supported/floating in liquid. As such, the solid particles of fat reflect light, scattering the light in many directions like a cloud would do.

In the lower left and lower right corners, the milk concentration has been steadily increased. We can see through the clear glass of water, suggesting that the transmission of visible light from behind the glass to an observer standing behind the camera is high. For the low concentration mixture of milk and water in the upper right, the small amount of added milk has slightly decreased the transmission of light. We can still see the louvers of the window blinds behind the jar, however.

With more milk added to the mixture in the glass on the lower left, the transmission of light was further reduced, and one's ability to perceive the louvers on the other side of the glass was diminished. Finally, adding more milk to the glass in the lower right cut the transmission of visible light to very low levels, and we can't see through the glass.

What is not being transmitted or absorbed is being reflected. Consider this experiment in the context of albedo. The albedo of clean water in the visible sub-band is much lower than the increasing albedos of all three mixtures of water and milk. Of the three mixtures, the glass with the greatest concentration of milk has the highest albedo.

Climate Regimes and Seasonal Fingerprints for Locale

One locale for your client will be divided up into seasons. For us, each season (a block of time) is like an independent region, different from the next season--regions that we will call climate regimes. In the mid-latitudes, we observe four climate regimes, while regions affected by monsoonal swings may have two or three climate regimes.

Figure 3.14 These are fingerprints to remind you that the different climate regimes occur for a single given locale in winter, spring, summer, and fall. The grouping of dates for each fingerprint will be different in Maui and Mumbai, and each fingerprint itself will be unique to that region, that climate regime.

Click Here for Text Alternative for Figure 3.14

Four different fingerprints symbolizing the different climate regimes for a given locale in winter, spring, summer, and fall. The first fingerprint here is labeled Dec 1 - Feb 28, the second and fourth fingerprints are not labeled. The third fingerprint is labeled June 1st - Aug 31.

Credit: J. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

I want you to think about the way that seasonal (or synoptic) variations in a locale will generate multiple fingerprints. While each fingerprint is different from another in a given locale (translated: winter solar is not like summer solar), additionally, each set of fingerprints is different from another regional set (translated Mumbai monsoons are not like humid summers in Missouri). Every one of our locales for solar design is going to have "cloudy conditions" at some time, and everyone will have "sunny days" at other times. How can we better understand the variety of intermittencies and trends for our locale and synoptic climate regime (our fingerprint)?

Missouri::Maui::Mumbai

This is just a play on words to emphasize something that you probably can guess: these three locations are not like each other!

• St. Louis, MO is representative of the midlatitude climate regime of the intracontinent. Notably, there are four meteorological fingerprints (seasons).
• Maui (Honolulu, HI) is representative of a Pacific island climate regime, affected by monsoons but without a large landmass.
• Mumbai (Mumbai, Marharashtra, India) is strongly affected by monsoonal swings but is located in the low latitudes of the tropics (two fingerprints).

Lesson 3 Discussion in Yellowdig!

We just introduced a totally foreign (yet intuitive) concept of climate regime to our lexicon in solar design. This is a new concept, but an essential one for advanced project development. You can start the discussion by posting what you perceive the meaning of climate regime to be from your personal reading and thought process. You can also comment on any uncertainty you initially found regarding the meaning, the intent, or application of climate regime to a project design, or to long-term project management. Creative interpretations of potential implications are welcome!

Tagging

When you create a post in the Yellowdig discussion space, you are required to choose a topic tag. For Lesson 3 discussions, feel free to use any of the following:

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: check in the Yellowdig site at least once per day. Commit to making at least one contribution daily – read new posts, ask questions, give your peers reactions and accolades. If reading generates some thoughts, share them, don’t postpone until later. This is a team learning space, so you are also helping others learn by being more active.

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, so all points accumulated by then will represent your weekly grade, and then you start all over again (it’s like playing a set in tennis..)

In the section discussing components of light, we reviewed the effects of the atmosphere on irradiance. Now, we discuss how to model the transparency of a hypothetical sky that is "clear" of the effects of clouds. Clouds are a major contributor to the reduction of terrestrial irradiance; however, particles in the atmosphere also play a significant role. There are physical properties of the sky that we cannot see with our eyes, but which strongly affect the solar resource on a clear day. As we will see in the reading, aerosols and water vapor present in the atmosphere play an important role in scattering light, and they may be present on "clear sky" days when visible clouds are absent.

Daily or monthly irradiance data is required for proper design of any solar energy collection system. However, this data is not always available. This requires the use of well-designed models to estimate irradiance. Hence, the need for clear sky models.

Clear sky models are used to estimate what is called a clearness index. For a location, a clear-sky model must be properly calibrated to provide an accurate measure for the clearness index. We will be looking at two modeling approaches, the Bird Clear Sky Model (which we can download and use as a spreadsheet) and the REST2 model by Gueymard (which can also be downloaded and run as an executable file--we will not do so here).

Bird Clear Sky Model

The Bird Clear Sky Model was developed by Richard Bird and a number of other scientists at what is now the Department of Energy National Renewable Energy Laboratory. The model requires the following input data

• Solar constant (G_o, W/m²)
• Zenith angle (${\theta }_z$)
• Surface pressure (P, (mbar))
• Ground albedo (${\rho }_g$)
• Precipitable water vapor ([H₂O](cm))
• Total ozone ([O₃] (cm))
• Turbidity at $\lambda =500nm$ and/or at 380nm
• Aerosol forward scattering ratio

Many openly available codes incorporate this model. The output is a "clear sky" estimate for the total or global horizontal irradiance (GHI), direct normal irradiance (DNI) and diffuse horizontal irradiance (DHI, or DIF) across wavelengths from 305nm to 4000nm. The model calculates these conditions for a single point in solar time, given the latitude ($\varphi$), longitude ($\lambda$) and the Time Zone.

REST2 Clear Sky Model

The REST2 model has been found to be most accurate, as we shall observe in our reading. We will only need to explore one method (Bird) for this class, but it is important that a resource professional is also aware of the modern application of clear sky modeling. REST2 accepts atmospheric inputs of:

• Air pressure,
• Precipitable water (also as Temp. and relative humidity),
• Reduced ozone and NO2 path lengths,
• Scattering factors for Ångström’s exponents of scattering (wavelengths above and below 700 nm),
• and Aerosol Optical Depth (AOD).

The REST2 model will then output estimations of diffuse horizontal irradiance (DHI), direct normal irradiance (DNI), and global plane of array (POA) irradiance.

Clouds: the major factor influencing intermittency

Clouds are emergent phenomena within the atmosphere, and strongly perturb the behavior of the solar resource in a given locale. When we do not have a clear sky day in our locale (typical in many locations on Earth), the effects of clouds will strongly draw down the beam component of our solar resource and increase the net fraction of diffuse sky irradiance.

Clouds can develop in environments that are termed active and passive, as well as from updrafts near the Earth’s surface. As we have seen in the reading, clouds have the ability to either scatter and reduce incident light, or to act as a lens at the perimeter, focusing light well above clear sky or even AM0 irradiance conditions.

From the perspective of an observer standing on the Earth's surface, clouds can be classified by their physical appearance. Accordingly, there are essentially three basic cloud types:

• Cirrus, which is synonymous with a "streak cloud" (detached filaments of clouds that literally streak across the blue sky),
• Stratus, which, derived from Latin, translates to a "layered cloud," and
• Cumulus, which means "heap cloud."

Let's review some basic types of clouds. Please do comparative reading between the figure below (with images) and your list of cumuliform, stratocumulus, and stratiform clouds in Ch. 5 of SECS.

Clouds are listed here with images that pop up when you click on the red dots. We see variants of cumuliform clouds, stratocumulus clouds, and stratiform clouds, as noted in our reading.

There are four general classifications of clouds: high, middle, and low clouds as well as clouds of vertical development. The table below summarizes each of these classifications while giving you a sense for the typical altitudes at which their cloud ceilings (the height of their bases) are observed, and the basic chemistry of the clouds (ice and water interact with light in different ways).

General Cloud Classification
Click on images for a larger version

Type of Cloud	Definition	Image
High Clouds	Observed over the middle latitudes. Typically reside at altitudes near and above 20,000 feet. At such rarefied altitudes, high clouds are composed of ice crystals.
Middle Clouds	Reside at an average altitude of ~10,000 feet over the middle altitudes. Keep in mind that this is an average altitude, so middle clouds can form a couple of thousand feet above or below the 10,000 foot marker. Middle clouds are composed of water droplets and/or ice crystals.
Low Clouds	Can form anywhere from the ground to an altitude of approximately 6000 feet. For the record, fog is simply a low cloud in contact with the earth's surface.
Clouds of vertical development	Cannot be classified as high, middle, or low because they typically occupy more than one of the above three altitude markers. For example, the base of a tall cumulonimbus cloud often forms below 6000 feet and then builds upward to an altitude far above 20,000 feet.

Researchers are now trying to predict cloud behavior with respect to GHI and DNI variation in a given locale. We are still a few years off, but soon we may see solar forecasts that include cloud interference for solar resource assessment.

Acknowledgment: Content of this page comes from Meteo 101: Understanding Weather Forecasting; author: Lee Grenci and David Babb.

Clouds (and weather fronts) occur on multiple scales of space and time. These scales contribute to the concept of solar fingerprints or climate regimes. In our reading, we learn about Sir Geoffrey I. Taylor and his work on turbulence theory. Clouds lead to intermittent solar conditions (POA and DNI irradiance) that, in turn,  affect our solar energy conversion technologies, such as PV and building systems.

The intermittent variation of clouds as they affect the solar resource is crucial when solar is deployed as a large-scale farm, or as a large community of decentralized PV arrays on buildings. Variable peaks and valleys of electrical power can be detrimental (costly) to utilities if there are no other ways to store or shave variation on the grid. Now, storage solutions are emerging slowly in research, but right now we need to address the intermittency problem by better understanding the drivers and the basic science underneath those drivers.

Taylor's Hypothesis:

A series of changes in time at a fixed place is due to the passage of an unchanging spatial pattern over that locale. That is, when observing a cloud or thunderstorm passing overhead, the clouds of the thunderstorm floating by are effectively "unchanging spatial patterns" (big blocks of cloud). Put another way, the lateral change in the cloud conditions across regions of the meteorological event (e.g., cloud-sky-cloud-sky-cloud) can be directly connected locally with a variation in irradiance measurement over time (e.g., a periodic measure of dark-bright-dark-bright-dark).

Taylor’s hypothesis states that events that change in time for a fixed place are due to the flow or passage of unchanging spatial patterns over a locale. This is like observing a thunderstorm passing by directly overhead and making the connection to the rate of the clouds advecting with the thunderstorm. Taylor's hypothesis from the 1930s allows us to flip from the Eulerian frame of reference (time sequences) to the Lagrangian frame of reference (spatial changes).

The Eulerian frame of reference: When an observer is stuck in one place, only watching the changing phenomena as it passes by.

The Langrangian frame of reference: When the observer moves with the meteorological phenomena instead of remaining fixed. Imagine a flying carpet floating along with a cumulus cloud moving from one county to the next.

Hence, all scales of time (or frequency) are also spatial scales! Taylor's Hypothesis holds so long as the advective wind speed is much greater than the timescale of the evolving meteorological event being investigated, as is often the case. When you have a lazy cloud day, where the clouds are changing form faster than they move, the time-space connection doesn't hold anymore.

Connecting Scales of Space with Time

By using spatio-temporal scales of cloud features established by Ted Fujita, we can estimate an average translation (advection) speed of 17 m/s for meteorological phenomena. We can then convert the spatial scales of variability into a relevant timescale. Spatial scales associated with power transmission congestion are distances of 25-1000 km. These distances are relevant for meteorological phenomena within time scales on the order of 25 seconds to 16 hours.

Cumulus 2-5 km, which means 10-100 minutes.

Cumulonimbus (including anvil) 10-200 km, which means 1-5 hours.

Cumulonimbus cluster (including merged anvils) 50-1000 km, which means 3-36 hours.

Synoptic (including cyclone waves, short and long Rossby waves) 1000-40000 km, which means 2-15+ days.

Figure 3.16: Logarithmic scales of weather patterns that link spatial scales to time scales. Short distance/long time is synoptic weather, long distance/short time is cumulus. The peaks for "diurnal cycles" are not from weather, rather from harmonics in transforming the diurnal behavior of day-night across a year into periods or frequencies. By inspection of the phenomena on Earth, we can identify an average advection rate of 17 meters per second, which becomes our conversion tool.

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

If we plot all of these phenomena and draw a line down the middle, we have a really rough estimate of the average advection rate of meteorological phenomena on Earth. Here, we have represented that rate in three different unit scales:

• 17 m/s [easy to remember this one, 17 is a prime number] or
• 1 km/min
• 61 km/hour (or 1470 km/day)
• 38 miles/hour (or 913 miles/day)

As such, we can connect Synoptic, Mesoscale, and Microscale meteorological phenomena between spatial and temporal scales!

Taylor’s Hypothesis “works” when the air in the sky moves significantly faster (advection: wind speeds) than the evolution time of a cloud or a thunderstorm of clouds. So, this approximation breaks down for those days when the cumulus clouds just "hang" in the sky all day.

Clear Sky Model and Measured Irradiance Data

The following readings will be helpful for completing this lesson activity.

Tasks

The goal of this activity is to use the BIRD Clear Sky Model to predict the solar irradiance at a specific time at a specific locale and further compare those predictions to actual irradiance measurements.

These two tasks will be performed for a specific date - July 31, 2007 (in this assignment) for the specific locale - SURFRAD Meteorological Station at Rock Springs, located just outside State College, PA.

In the end, you will need to assess how the modeled (predicted) and measured data fit and provide some discussion on it.

Part 1. Bird Clear Sky Model - Instructions

The Bird model is an old but advanced clear sky model used by solar professionals to estimate clear sky conditions at a locale. The clear sky model for a horizontal surface is the basis for almost all modern comparisons of "ideal skies" to actual skies (with clouds and dynamic light interference effects). You will see what the global, beam horizontal, and diffuse components of solar light should look like when you set the meteorological parameters affecting the sky clearness. The model could also provide DNI (Direct Normal Irradiance), which would show irradiation values higher than the global horizontal values for the mornings and evenings.

• Go to http://rredc.nrel.gov/solar/models/clearsky/ to download the Bird Clear Sky Model. It is a free download, and the tool comes in the form of an Excel spreadsheet. I suggest that you rename the original file for any case study you perform further.
• Study the instructions on the spreadsheet to learn how to use the tool and make a note of the input and output parameters.
• Modify the inputs for the State College, PA, locale. The following parameters can be obtained from the SURFRAD site (see part 2):
  • Latitude 40.72
  • Longitude -77.93
  • Time zone UTC -5
  • Pressure (mbar) - average for the day
  • Aerosol optical depth (AOD)

Note: access the AOD data through this graphical page. Take the daily average as input for the Bird model. In this case, 415nm AOD can be used as a proxy for 380nm AOD input and 500nm AOD data can be used as is.

• You can leave other inputs at their default values
• Expand the spreadsheet (as explained in the instructions) to generate output for the entire year, then extract the data for July 31st (day # 212) and copy values to a separate file.
• Plot global horizontal irradiance (GHI), direct horizontal irradiance (DHI), and diffuse horizontal component (DIF) versus time for the day

The model plot will look similar to the one below. This is what you need to produce.

Figure 3.17: Model plot

Credit: Mark Fedkin © Penn State University is licensed under CC BY-NC-SA 4.0

Part 2. SURFRAD data - Instructions

The SURFRAD site at Penn State collects real-time data for solar irradiance (using local pyranometers) and a number of other atmospheric parameters at 3-minute time intervals. These data are accessible through the Earth System Research Laboratory website. This site provides you with access to data collected at the Penn State location. For each year, you can open the parent directory with .dat files, which are named by the day number. So if you are looking for July 31st, for example, that will be day #212, so check the file psu07212.dat.

Here are the data labels in order that correspond to the numbers in the .dat file (omit 0-value columns):

Year, jday, month, day, hour, min, dt (decimal time), zen (degrees), dw_solar (W/m^2), uw_solar (W/m^2), direct_n (W/m^2), diffuse (W/m^2), dw_ir (W/m^2), dw_casetemp (K), dw_dometemp (K), uw_ir (W/m^2), uw_casetemp (K), uw_dometemp (K), uvb (mW/m^2), par (W/m^2), netsolar (W/m^2), netir (W/m^2), totalnet (W/m^2), temp (degC), rh (%), windspd (m/s), "winddir (degrees, clockwise from north)", pressure (mb)

From this list, you will specifically need:

dt (decimal time) - your time coordinate for data plotting (Column G in MS Excel)

dw_solar - Downwelling global solar (W/m^2) = corresponding to Global Hz (GHI) in BIRD model (Column I in MS Excel)

netsolar - Net solar (W/m^2) = corresponding to Direct Hz (DHI) in BIRD model (Column AG in MS Excel)

diffuse - Real downwelling diffuse solar (W/m^2) = corresponding to Dif Hz (DIF) in BIRD model (Column O in MS Excel)

Also, 'pressure (mb)' - the last value in each array of data - daily average should be used for your Bird model input (Column AU in MS Excel).

Figure 3.18: Example of a data string

Click for a text description of Figure 3.18.

Example of data string:

2007  212     7  31  15   57   15.950   28.61      911.5  0      161.4  0     865.1  0      116.8  0

355.2   0       304.2.  0       303.9.  0     492.3 0      300.9    0      301.2  0   192.7  0     378.5   0

714.9   0     -137.0   0       577.9   0.      25.5 0         50.6   0          3.3  0     54.1  0     972.4   0

911.5 = GHI

116.8 = DIF

714.9 = DHI

972.4 = Pressure.

Credit: Mark Fedkin © Penn State University is licensed under CC BY-NC-SA 4.0

To treat the data, you can either convert the .dat file to a spreadsheet (see video in Canvas Module 3 how to!) or, if you have programming skills, you can create a script to plot the irradiance data versus time.

Comparison and discussion of the results

• Plot the Bird model data and SURFRAD measured data for GHI, DHI, and DIF types of irradiance on the same diagram. You should get a pretty close match. You may notice by visually comparing the curves, that even on a clear day, the real sky shows dynamic variations in irradiance in the diffuse component.
• Provide a discussion of the results and comment on the possible discrepancies.

Submitting Your Work

Prepare a written report including the following:

1. Table of input parameters for the Bird model (left side of the Bird spreadsheet)
2. Diagram with irradiance data comparison (Bird model vs. SURFRAD data points)
3. Discussion of results.

Save your report as .docx or PDF and submit to the Lesson 3 Activity - Clear Sky Model dropbox in Canvas.

Grading Criteria

Please see the grading rubric in Canvas

Deadline

See the Calendar tab in Canvas for specific due dates.

Summary

In this lesson, we have learned about the diverse ways in which the atmosphere can interact with shortwave light to affect the solar resource received at the ground by our Solar Energy Conversion Systems. We have observed that the sky has a distinct character derived from air mass source regions, and that the weather has seasonal "fingerprints" that distinguish a single site as multiple unique climate regimes. We further found that a "clear sky" is a fairly complex system of its own, and modeling the clear sky is not trivial. When we finally add clouds to the skies, we see where the real source of solar intermittency stems from. By connecting space and time from Taylor's Hypothesis, we find that we hold additional information on the scales of intermittency to expect in a given locale and for each seasonal climate regime in that same locale.

Do you think that your eyes are great at seeing and measuring light? Surprisingly, your wonderfully adaptive human eyes only capture a tiny fraction (380-780 nm) of the electromagnetic spectrum and cannot reliably distinguish and evaluate the solar resource. In fact, some sources suggest that your bare skin may actually be a better receptor for the shortwave band than your eyes (under no-wind conditions).

Like meteorologists, solar energy specialists have to rely on both ground-based instruments (pyranometers and pyrheliometers) and satellites (such as GOES East and GOES West) to measure sunlight before and after its interaction with the atmosphere. Satellite radiometers measure the intensity of radiation scattered back to space, producing images that reveal clouds, smoke, volcanic ash, and other features that influence surface sunlight. 

In this lesson, we will use the concept of components to break the sky dome and the ground into digestible chunks of surfaces with common emission/absorption/ scattering characteristics - 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 degree of light scattering on a horizontal surface is assessed via the various clearness indices (e.g., k_T, K_T, K-bar_T ). There is a lot to learn!

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

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 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 (maintained by Dr. Frank Vignola). The left image is a LI-COR pyranometer, 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). 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

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 is displayed below on the left, while an Eppley Solar Tracker 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

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 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.
• NOAA's GOES Satellite Server. 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

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

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. 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., 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: $\; \mathrm{MJ} \; \; / \; { \; \; \mathrm{m} \; \; }^{ \; \; 2 \; \; }$) 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.
$$G_d=G_{iso}+G_{cir}+G_{hor} +diffus{e}_{ground}$$$$G_d=\left[ G_d(1-F_1)\frac{1+cos\beta }{2}\right]+\left[ G_d(F_1)\frac{cos\theta }{cos{\theta }_z}\right]+\left[ Gd(F_2)sin\beta \right]+\left[ G_d\rho \frac{1-cos\beta }{2}\right]$$ 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 F₁ (circumsolar radiance), and F₂ can either increase or decrease the contribution of horizon radiance.

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, 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.

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."

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:
   $$I_o=\frac{12\cdot 3600}{\pi }\cdot G_{0,n}\cdot [\frac{\pi }{180}({\omega }_2-{\omega }_1)\sin \varphi \sin \delta +\cos \varphi \cos \delta (\sin {\omega }_2-\sin {\omega }_1)]$$
   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!

Overview

OK, we are now out of the deep end of the class and moving into the frameworks for design and valuation of the solar resource. We will be developing a second major arc through Lessons 5, 6, and 7, working through economic and financial issues. So you should see connectivity among these three lessons.

In Lesson 6, we will discuss ways to meet the Goal of Solar Energy Design and Engineering: to maximize the solar utility for a client or group of stakeholders in a given locale. We will dig into a short statement, and find a nearly infinite variety of options for design. But first, we need to find out about our clients or stakeholders as "utility maximizers" in Lesson 5; what makes people demand solar energy products, and how easily will they change their minds? Are there any losses or risks that people are avoiding by choosing solar energy goods and services? Essentially, what are the driving forces for people to adopt solar energy?

Solar Energy Economics helps us to establish the following argument: just because one perceives the solar resource to be weak in a region does not mean that it cannot be successful as a technology in that society. The solar resource is ubiquitous, and we make use of it whether we decide to or not. What is interesting for solar energy is that our raw "product'' is the photon. We apply technologies and skilled effort to convert photons into a diversity of goods that society is interested in purchasing.

Figure 5.0. Diagram of Solar Energy Economics

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

The economics of solar technologies helps us to address why we make decisions to use the Sun. We make use of the Sun throughout our lives, but in solar design, we work to develop compelling arguments to the client to increase their marginal demand for the Sun. There is a sense that energy is somewhere between a product and a good in demand by society, and it must be supplied by non-trivial mechanisms, at some cost for the exchange of goods. In order to make marginally (or incrementally) more use of the Sun, we have to learn about the skills to measure and predict the variable phenomenological behavior of solar irradiance as well as the dependence of the variable irradiance on the location of the client in question.

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

• identify the key features of supply and demand for energy systems;
• list the two general motives that shift the value of any commodity;
• list the three specific drivers that will affect the valuation of light as a quantified mineral reserve;
• list the four main factors affecting the price elasticity of demand;
• describe the hypothesis of the energy constraint response for solar energy.

What is due for Lesson 5?

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 5 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.

Energy Supply and Demand

The readily accessible energy that can be used to "do work" in society is still considered a limited natural resource, or good. In economic terms, we would say that many of our useful energy goods are scarce.

As we read in EBF 200, "What is Economics?" Prof. Gregory Mankiw lists seven microeconomic principles. Recall that microeconomics refers to individual economic actors considered as people and firms and their corresponding interactions in markets.

1. People face tradeoffs.
2. The cost of something is what you give up to get it.
3. Rational people think at the margin.

(Watch the following YouTube video of Thinking at the Margin by Prof. Mario Villarreal-Diaz.)

Video: CHAPTER # 2 THINKING AT THE MARGIN (5:26)

• People respond to incentives.
• Trade can make everyone better off.
• Markets are usually a good way to organize economic activity.
• Governments can sometimes improve market outcomes.

In solar systems design, we work to Maximize Solar Utility for the client or stakeholders in a given locale. We will describe the methodologies to do so in the next lesson. But our clients are individuals who are in demand of a solar good. The firms developing or deploying SECSs are supplying access to the solar goods.

• Consumers (clients) can be thought of as "Utility Maximizers;" they want to achieve the highest preference for given goods or service.
• Suppliers (designers/engineers/builders) can be thought of as "Profit Maximizers."

Forms of Energy in Demand

Across the planet, there are non-uniform, ever-increasing demands for energy as thermal heat and electrical power. Light, as electromagnetic radiation, is another form of energy, used as well for visual comfort and indoor activities. The photon can be harvested via a solar energy conversion device. To be clear, photons are ephemeral (flows); they are not collected like fuel in a tank (not stocks).

Energy can be described in terms of sources (as in energy re-sources) and in terms of forms (as in energy trans-form-ations). Think of it this way, an energy source is a resource system, from which we appropriate useful resource units in a given form. Energy is neither created nor destroyed, so if the energy is in a less useful form, we must use an Energy Conversion Device (ECD, not a very technical term, but useful here) to transform one form into a more useful form.

• Thermal (heat)
• Radiant (electromagnetic, light)
• Motion (kinetic)
• Electrical (also called power in the industry)
• Chemical
• Nuclear
• Gravitational

Energy scarcity is partially related to the loss of energy quality with successive transformations. Light happens to be an incredibly high quality of energy, which is then transformed into chemical energy by plants (photosynthesis), or into thermal energy by opaque materials, or kinetic energy via wind, or electrical energy via photovoltaics. (Nuclear and gravitational energy are not linked so directly to radiant energy here.)

Our society is used to beginning with "concentrated sunshine" (geofuels from stored photosynthesis in coal, oil, and gas), and then transforming the chemical form to the thermal form (hot steam), which is then transformed into the motion form (to spin a turbine-generator) and finally transformed into electrical energy.

Sidenote on Heat and Power

The terms Heat and Power have been adopted by several industries to have a specialized trade meaning.

• Power is electrical energy (as opposed to a rate of energy use), and
• Heat is thermal energy (as opposed to the transfer of energy).

Thus, in the energy industry, we hear about Combined Heat and Power (CHP) for energy conversion systems that provide two useful forms in one system.

Flow vs. Stock Energy Reserves

Stocks and flows exist in nature and in society. We see stocks in business. In nature, a lake is a stock of water, with a river flowing into it. And the Sun is a stock of nuclear fusion yielding a flow of radiant energy.

• Potential: a driving force for flow.
• Flow: a dynamic entity connected to a stock that either supplies or depletes the stock; can be a change in mass, energy, or information with respect to time.
• Stock: an entity that has accumulated over time due to flows; can be stored potential, or a resource system that replenishes itself (like the fusion in the Sun).
• Resource system: often an environmental stock (and could be a human institution).
• Resource units: the flow of a useful resource that a client may appropriate from a resource system.

A resource system is considered renewable if the rate of withdrawal from the stock does not exceed the rate of resource replenishment. In the case of shortwave light, the solar resource system has physical conditions that define an upper limit of flow without disturbing or harming the constitution of the stock. We can't really withdraw sunlight at a faster rate than it comes to us. Hence, sunlight is flow-limited.

A resource system is considered non-renewable if the rate of withdrawal from the stock exceeds the rate of resource replenishment. In the case of geofuels, the process to make them takes 10s-100s of millions of years (and heat/pressure underground), yet the rate of withdrawal can be almost as fast as we want. Hence, geofuels are stock-limited.

The "Quantity" of Light

Compared to what is available on Mars, the quantity of light is abundant on Earth! Even between the Arctic Circles ($\varphi <60°\text{ or }\varphi >-60°$), there is a great abundance of light available to society to do work. As a society, we are not as skilled at transforming light into useful work as we are at transforming fuel into useful work. We are still struggling to frame light as a valued good, especially as it is all around us every day. So, let's take a look at that value structure.

The value of light from the Sun is variable. There is "less" of an energetic resource from the Sun in the annual irradiation budget for Germany than in the US state of Georgia, yet the value of solar power (as electricity) is much higher in Germany than in Georgia. So is the value of the light to the clients relative to the "quantity" of light, or relative to other parameters.

In the mineral economics of commodity goods, the value of the resource units will vary with respect to two general driving forces:

1. demand for the good or service, and
2. cost of alternatives.

If the demand for a good goes up, the value of the resource units will go up. If the cost of an alternative good goes up (like the price of geofuels), then the value of the resource units (like solar) will go up.

Light as a Mineral Resource (Commodity)

An increased demand for a mineral commodity will increase the value, and a high cost of alternative goods will increase the value.

Value and quantity are joint properties here. As such, the "quantity" of a mineral reserve can expand or shrink in response to three main pressures. Solar resources follow the same commodity trend. In the case of the solar resource framed as a type of mineral reserve, the solar reserve is available when it is economically feasible, expanding and contracting in response to the following three pressures. That is to say, there are three levels that open up, or expand, the solar reserve in a given locale.

The value of an unconverted photon is a variable quantity, much like the value of a mineral resource in a geologic formation. Once again, the value of any commodity varies with the demand for the good and the costs of alternatives. The three main drivers that affect the valuation of light as quantified mineral reserve are:

1. increased demand by clients seeking to avoid fuel costs (choosing an alternative to fuel);
2. technological advances that reduce materials costs and/or installation costs;
3. presence of incentives (often government incentives).

Let us compare the way in which light is valued with the way that a metal ore (in this case, zinc) is valued. An ore is an unrefined rock composed of minerals, which contains a raw metal that is valued, but which must be processed to access that metal. In our reading from the USGS Commodity Statistics, Appendix C, we see that an entire lexicon has been developed for classifying mineral resources. (This site as a whole is also an excellent public resource for evaluating mineral reserves from the US perspective.) We have since classified geofuels as "minerals" in the commodity perspective. So, why not extend the concept outward to the commodity of light, and the derived goods and services?

The following terms are within the textbook reading, and were developed from the U.S. Geological Survey Circular 831, Principles of a Resource/Reserve Classification for Minerals (1980). Note the difference among a resource, a reserve base, and a reserve.

• Resource: material or energy source occurring natively in or on the Earth, with a form, concentration, and quantity such that economic collection and/or conversion of that commodity is currently or potentially feasible. (We could apply this to light, right?)
• Identified Resources: specific resources where the location, grade, quality, and quantity are known from specific meteorological evidence, or where the resource has been estimated. Identified solar resources encompass regions that are economic, marginally economic, and sub-economic. As a reflection of the degrees of meteorological confidence, the economic divisions can be subdivided into components of measured, indicated, and inferred.
• Reserve Base: an identified resource meeting minimum criteria related to a specified solar energy conversion technology practice currently employed to convert to useful work.
• Reserve: the portion of the reserve base that can be economically converted at the time of determination (the locale).

Figure 5.1 The potential valuation of the solar resource in a given locale, but framed as a mineral resource, in accordance with USGS commodities structure for mineral resources

Click Here for a text alternative to Figure 5.1

A table shows a two-axis categorical relationship between knowledge of the solar resource and the ability to economically exploit the resource.

On the first axis, three categories describe decreasing levels of knowledge of the resource: “Measured” (measure a few ground sites well), “Indicated” (satellite mapping of resources) and “Inferred” (geospatial mapping by interpolation). The combination of Measured and Indicated resources are termed “Demonstrated,” while all three categories together are termed “Identified Solar Resources.”

The second axis also contains three categories, which describe decreasing levels of economic return from the resource. “Economic” resources are described with the terms: fuel costs are high/annual resource is high/incentives exist/solar tech costs dropping. “Marginally Economic” resources are described with: fuel costs exist/resource is significant/solar tech costs dropping. “Subeconomic” resources can be described by: fuel costs very low/resource may be significant (or not).

Intersections between these category axes are described with text labels. Reserves are shown at the intersection of Demonstrated and Economic resources, while Inferred and Economic resources are termed Inferred Reserves. Marginal Reserves and Inferred Marginal Reserves occur for Marginally Economic resources that are Demonstrated and Inferred, respectively. Demonstrated Subeconomic Resources and Inferred Subeconomic Resources are the last two labelled combinations, and are self-explanatory. An example of Demonstrated Subeconomic Resources is given as those occurring beyond the arctic circle. Arrows and text indicate that as the Reserves move from Economic to Marginally Economic to Subeconomic, the reserve base is expanding. A final category of resource is listed separately from the main table with the heading “Other Occurrences,” and lists non-conventional and low-grade light sources.

A final text box is shown separate, but alongside the table, which describes Cumulative Production of the resource as exponential growth with doubling deployed production every 1-2 years.

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

Elasticity of Demand

In economics, the measured response (in the market) of how the quantity of a product in demand is changed by the incremental change in the price of that product is termed price elasticity of demand. The demand is considered elastic if a small change (like a decrease) in price leads to people demanding more of the product. The demand in considered to be inelastic if a large change (again, a decrease) in price does not lead to people demanding more of the product. The elasticity of demand for solar power will depend on a few general rules, and we will try to contain our examples to solar scenarios for a client or group of stakeholders.

Criteria for Elasticity

The price of PV just changed. What do you do? Do you go out and invest in a PV system for your roof, or do you wait and see? Clients and consumers (us too!) are influenced by several criteria. The four main factors affecting the price elasticity of demand are:

1. availability of close substitutes;
2. whether the form of energy is a necessity or luxury;
3. how large a share of a consumer's income the good will consume; and
4. the time horizon over which the change occurs.

First, one evaluates the availability of close substitutes for the particular SECS of interest. If the desired useful energy form or technology has many available close substitutes, then it will be easier for clients/stakeholders to switch among goods for the same desired feature, and the demand will tend to be elastic.

Next, we ask, is the energy form a necessity or a luxury? Our electricity from the coal/nuclear power plant is typically a necessity right (and thus inelastic)? Is there anything about residential PV that seems to be a luxury to families? When did mobile phones stop being a luxury and become a necessity in modern society?

What share of income can an individual or firm (as clients) devote to paying off a loan for solar technologies or directly purchasing a SECS? If a SECS consumes a large share of my income, what tradeoffs will I need to consider (what will I have to give up in return)?

Finally, when making decisions for energy systems, we must consider the time horizon, or the period of evaluation. For energy consumers, when the cost of energy (in dollars per kilowatt-hour, $/kWh) goes up briefly (on the order of hours or days, or for one month) there's not much that they can do to respond. As such, the price elasticity of demand is said to be inelastic for shorter time horizons. In contrast, when the period of evaluation is framed in terms of decades, as is done for PV systems that have productive life cycles of 30-50 years, then the client perspective can shift and become more elastic. When you buy a house, you're in it for the long-term, right? Similar thinking with SECSs.

Video Perspectives

And now for two short perspectives on the Price Elasticity of Demand to complement the reading. Please watch the following two videos: "Episode 16: Elasticity of Demand" by Dr. Mary J. McGlasson, and "Elasticity - Characteristics that determine elasticity" (Dr. McGlasson is an economics faculty at the Chandler-Gilbert Community College.) I want you to think about solar energy and the resource units derived from the conversion of shortwave light.

Video: Episode 16: Elasticity of Demand (9:33)

Video: Elasticity - Characteristics that determine elasticity (1:46)

Hypothesis of the Energy Constraint Response

When fuels (geofuels, biomass) are effectively:

• accessible,
• unconstrained, and
• inexpensive,

light and the associated Solar Energy Conversion Systems are not perceived as a viable alternative. Light is framed as diffuse and insufficient to do work.

However, when fuels are:

• constrained, or
• inaccessible,

then light and the associated Solar Energy Conversion Systems are counter-interpreted as ubiquitous and vast, and capable as a viable alternative.

Fuel Constraints

Our energy use in society is coupled to the locale and to our comfort expectations. Energy use is also coupled to the availability of inexpensive fuel resources. The four main factors constraining fuels are described below:

1. physical inaccessibility due to regional resource depletion (e.g., deforestation) or supply chain disruptions (e.g., oil embargo),
2. exceptionally high demand for fuels that outstrips supply,
3. fuels being accessible, but only at high risk to the community, and
4. fuels constrained by socially restraining policies, regulations, and laws.

Lesson 5 Discussion in Yellowdig!

In this lesson we have been discussing the value of goods in an economic sense. The tendency in the public is to judge the value of a solar technology in a given locale based on metrics (perceived or measured) of the quantity of light (MWh). But I would like you to consider an alternate valuation system related to the value of a mineral resource.

So, this week discuss the following questions in Yellowdig:

Another topic in this lesson that deserves some discussion is the hypothesis of energy constraint response. You already had a chance to review your locale sunlight resource and perception earlier in this class, so do you see any evidence of this hypothesis being true for the area you live in?

You can review the following information to develop your conclusion on this topic:

Do you think that the above observations support or disprove the hypothesis of the energy constraint response? I would be curious to hear your opinion.

When thinking about the solar resource in an economic framework, try to be objective and describe the conditions that you observe around you, rather than what you think "ought" to be happening. Most of us have not really framed the solar conditions in rational terms. If you have conflicting ideas about light and irradiance from your own background, feel free to discuss those and see what others think.

Tagging

When you create a post in the Yellowdig discussion space, you are required to choose a topic tag. For Lesson 5 discussions, please use these tags:

You can tag your post with one or several topics at the same time (just be sure to address all those in your post). All posts and contributions you create are added up to one score at the end of the week.

Importance of interaction

Yellowdig tip: Post early in the study week - that way you have higher chance of generating interest and traffic on your post, which gets you points!