How Radiation and Energy Distribution Work in Solar PV

The sun is a constant source of energy with an approximate age of 6,000 billion years, and it will last at least 5,000 billion years more. It provides a broad range of energy, primarily concentrated around the visible and infrared regions.

The power of the sun has been used successfully by humanity to its benefit. Two of the many applications are the production of electricity starting from light (photovoltaics) and heating through solar collectors. Solar collectors transform solar radiation into heat and transfer that heat to a medium (water, heat-transfer fluid, or air).
The first article in our series on solar PV introduced the history and relevant background of the photoelectric effect and how it became such a major player in power. This article focuses on photovoltaic applications and solar radiation.

 

The Sun’s Stats

The sun is a star. It is a vast, spinning, glowing sphere of hot gas. The sun is just like the stars that are seen in the night sky, although it appears so much bigger and brighter because of the earth’s short distance to it — a mean distance of 1.49 · 10⁸ km.

The sun's internal temperature is in the range from 8 to 40 · 10⁶ K and the specific density ranges from 80 to 100 g/cm³. Such high temperatures and pressures drive a continuous nuclear fusion process that releases a tremendous amount of energy estimated in 384.6 yottawatts (3.846 · 10²⁶ watts) in the form of light and other modes of radiation.

The temperature and characteristics of the solar surface are such that the radiation coming from it has a spectral distribution very similar to a black body at a temperature of approximately 5762 K.

 

Key Terms Related to Solar Radiation

This article is getting crowded with numbers and units, so it’s time to define some of the key terms related to solar radiation before continuing.

 

Solar Constant and Total Radiant Energy

Solar constant and solar spectral irradiance describe solar radiation.

The solar constant is the amount of total radiant energy received from the sun per unit time, per unit area exposed normal to the sun's rays, at the mean sun-earth distance at the outer layer of the earth's atmosphere. The mean value of the solar constant accepted by the space community is 1366.1 W/m², with a maximum of 1412.5 W/m² at the perihelion and a minimum of 1321.7 W/m² at the aphelion.

 

Irradiance and Solar Energy

Irradiance is the power of solar radiation per unit of area, expressed as W/m².

Irradiation or solar energy is the solar power accumulated over time, expressed as J/m² or Wh/m². The higher the irradiance, the more energy is generated.

In the PV industry setting, the term irradiation is not conventional. Yet, broadly used are irradiance and insolation.

Insolation = Irradiation

Solar spectral irradiance finds and shows the distribution of solar radiation over wavelengths. The measure of radiation, in the spectral distribution, is in terms of the amount of energy falling per second (W) per unit area (m²) in each band of 1 µm wavelength.

 

Air Mass and Air Mass Zero

Air Mass (AM) is the path length which light takes through the atmosphere standardized to the shortest possible path length (i.e., when the sun is directly overhead or Zenith). The AM quantifies the reduction in the power of light as it passes through the atmosphere. When the sun comes closer to the horizon, its light passes through more air.

Beyond the earth's atmosphere, AM = 0. For Zenith angles θ_z ∈ [0°,70°] at the sea level, to a close approximation, AM = 1/cos θ_z. . When the sun is at the Zenith, θ_z = 0 and AM = 1 at Zenith angle θ_z = 48.19° AM = 1.5.

Air mass zero refers to a spectrum measured in the absence of the earth's atmosphere.

The terminology involved in the PV industry is quite abundant and not always easy to understand. We recommend, for those interested in delving into this topic, put an eye on ASTM E-772 Standard Terminology of Solar Energy Conversion.

 

Peak Sun Hours and Calculating Solar Radiation

The testing of solar modules is for maximum output at an irradiance of

1 kW/m²

Then, it is practical to define the peak sun hour (PSH) as the number of hours/day required for a hypothetical solar radiation of 1 kW/m² to produce the same energy that is received from the sun in the site considered. So

1 PSH = 3.6 MJ/m² =1 kWh/m²

In other words, one hour is required by an irradiance of 1 kW/m² to accumulate energy or irradiation of 1 kWh/m².

The following figure shows, in red, the sun's radiation along a typical day for 14 hours approximately.

 

Figure 1. The sun’s radiation on a typical day. Image courtesy of Ingeniería Energética, Cuba.

 

The area below the red curve represents the total energy received during that day. The rectangle, in yellow, contains the same energy but receiving 1 kW/m² continuously for nine hours approximately. The result is nine peak sun hours. Note that 1 PSH is not equivalent to an actual hour of sun radiation.

 

Why is Understanding Energy Distribution in the Solar Spectrum so Important?

Total radiation energy is not enough for characterizing solar cells. Solar cells are also spectrally sensitive.

For practical applications in the utilization of solar energy, detailed knowledge of solar irradiance at ground locations is needed. The design and strength of solar panels, accurate estimates of the output of solar cells, operation, and fatigue of coatings, finishings, adhesives, and sealants, require the knowledge of the amount of energy available from the sun, its spectral distribution, and natural variations. Some types of solar cells may have excellent performance at short wavelengths, while others may excel at long ones.

ASTM-E-90 vs. Wehrli ETR Spectrum

In the year 2000, the American Society for Testing and Materials (ASTM) developed an air mass zero reference spectrum for use by the aerospace community. The base of  ASTM E-490 solar spectral irradiance is data from satellites, space shuttle missions, high-altitude aircraft, rocket soundings, ground-based solar telescopes, and modeled spectral irradiance. The integrated spectral irradiance conforms to the value of the solar constant.

The following graphs compare the World Meteorological Organization (WMO) Wehrli extraterrestrial (ETR) spectrum to ETR ASTM E-490.

 

Figure 2. A comparison of ETR ASTM E-490 to Verhrli WMO. Image courtesy of NREL.

 

Figure 3. Another view of the comparison between ETR ASTM E-490 to Wehlri WMO. Image courtesy of NREL

The axis of abscissas stands for the range of wavelengths in the solar spectrum (measured in micrometers). The axis of ordinates denotes the amount of power (watts) in each micron-wide band of a wavelength falling on each square meter just outside of the earth's atmosphere.

Over 96% of the sun's energy is in the wavelength range of 0.27 µm to 2.6 µm. Going up to 4.0 µm increases the amount of energy to 99%. This spectral sector is accountable for all life processes as well as for the forging of climate and weather. Energy entering the earth begins in this zone. The sector 0.4 µm to 1.1 µm is pivotal for photovoltaic conversion. For thermal conversion systems, it is crucial the energy distribution in the region 0.3 µm to 4.0 µm.

 

Solar Radiation in the Earth’s Atmosphere

At the upper reaches of the atmosphere, the energy density of solar radiation is approximately 1366.1 W/m².  Only a portion of the energy radiated by the sun into space strikes the earth: one part in two billion. Yet this amount of energy is enormous. Simply put, the earth reflects about 30 percent of the radiant energy into space.

After entering the atmosphere, solar radiation undergoes two phenomena: dispersion and absorption. Dust particles in the air and clouds disperse a part of the incident radiation while the atmosphere components absorb another fraction. Ozone (Oɜ), in the upper layers, consumes a large part of UV radiation. Land and oceans absorb about half of the radiant energy.

Radiation dispersion generates two components:

1. Direct irradiance when solar rays do not undergo any direction change.
2. Diffuse irradiance when rays come from all directions.

The PV industry also uses the terms direct and hemispherical (i.e., direct beam plus diffuse sky) spectral solar irradiance. It also defines four different types of irradiance:

1. Direct Normal
2. Global Horizontal
3. Diffuse Horizontal
4. Global Tilted

Energy Spectra and the ASTM

In the USA, the American Society for Testing and Materials (ASTM) G-173 spectra     (Reference Air Mass 1.5 Spectra (solar Zenith angle θz = 48.19°S)) represents terrestrial solar spectral irradiance on a surface of specified orientation under one and only one set of specified atmospheric conditions.

The PV industry, in conjunction with the ASTM and government research and development laboratories, developed and defined two standard terrestrial solar spectral irradiance distributions. See also ASTM International.

The software SMARTS2 Simple Model for Atmospheric Radiative Transmission of Sunshine, developed by Dr. Christian Gueymard, models the spectra.

The air mass zero (AM0), or extraterrestrial spectrum used to generate the terrestrial reference spectra — also developed by Dr. Gueymard — is a synthesis of several AM0 data sets. The spectrum used in conjunction with SMARTS2 to produce the reference spectra is not the air mass zero spectrum in ASTM E-490, as there are slight differences in bandpass and spectral resolution for the two spectra.

 

Figure 4. Graph of Reference Spectra. Image courtesy of ASTM

 

Solar Radiation Data from Around the World

For PV projects, there are plenty of sites on the web that provide useful solar radiation data around the world. Three popular sites include:

1. NREL Photovoltaic Research, located in the USA. Data may be found in the RE Atlas.
2. PVGIS Photovoltaic Geographical Information System, for Europe and Africa. Data is available by country.
3. Global Solar Atlas, for world-wide information. Data is available from the World Bank Group.

 

Calculating PSH: an Example

Let’s calculate the number of PSH in a location with an irradiation of 4.8 kWh/m² per day.

The solution is simple enough. Another way of seeing this problem is to ask how many hours are required in a hypothetical irradiance of 1 kW/m² during a day to produce 4.8 kWh/m². The answer for that day is:
 
(4.8 kWh/m²) / (1 kW/m²) = 4.8 h

 

Reviewing Key Terms

The sun is a readily available source of energy. Finding a cost-effective way to harness its energy provides a key energy source. It is essential to consider the climatic and geographical parameters of the region studied.

Solar cells are not only intensity responsive but also frequency sensitive. For this reason, knowing the light spectrum is focal.

Several radiation spectra have been published and are updated as required. The energy of solar radiation is very high, but it lessens through the atmosphere allowing life on earth. Published tables and maps show radiation data for solar applications.