# SOLAR SPECTRUM CALCULATOR

This calculator determines the spectrum of the solar radiation intercepted by a PV module under clear-sky conditions.

The user sets the location and orientation of the module, the time of day and year, and the atmospheric conditions for cloudless skies (e.g., preciptiable water vapour, ozone, turbidity). The calculator then determines the direct, diffuse and global components of the spectral irradiance that is incident to the module.

# ALGORITHMS

The calculation of the clear-sky spectrum is based on the SPCTRAL2 algorithm published by Bird and Riordan in 1986 [Bir86]. Next year, we intend to add the SMARTS2 algorithm published by Gueymard [Gue95] to this calculator.

One significant difference between this calculator and SPCTRAL2 is that we give the option of selecting an extraterrestrial spectrum different to that provided in Table I of [Bir86]. When the selected spectrum has a different wavelength interval to the data in [Bir86], the calculator linearly interpolates the other inputs in Table I to find their value at each wavelength of interest. These inputs are the absorption coefficients *α*_{wλ}, *α*_{oλ} and *α*_{uλ}. Interpolating in this way can introduce error in the calculated spectral irradiance.

# PROCEDURE

The calculator first determines the '**Earth–Sun factor**' from the date and time. This factor accounts for the change in intensity that occurs as the distance between the Earth and the Sun varies over the course of a year. The Earth–Sun factor is unity when the Earth is at its average distance from the Sun, as occurs around the 3rd of April and the 1st of October.

The **spectral irradiance of the extraterrestrial spectrum** is then loaded and mapped onto the the desired wavelengths. The extraterrestrial spectrum is the spectrum of sunlight that reaches Earth's outer atmosphere. The 'AM0 spectrum' defines this spectrum when the Earth is at its average distance from the Sun. The calculator therefore multiplies the extraterrestrial spectrum by the Earth–Sun factor to determine the spectral intensity at the date and time of interest. Note that it is also possible to load an extraterrestrial spectrum rather than using the AM0 spectrum.

The calculator then determines the **zenith and azimuth angles** of the Sun relative to the location of the module, where the location is defined by the module's latitude and longitude. This gives the position of the Sun in the sky in the manner followed by the solar path calculator. See the PV CDROM (www.pveducation.org) for a description of these angles.

From the zenith angle, the calculator next determines the **air mass** (AM), also described in the PV CDROM.

With the air mass, the calculator applies the SPCTRAL2 algorithm [Bir86] to determine the **transmission of direct and diffuse light** through the Earth's atmosphere. The atmosphere is defined by (i) the atmospheric pressure, (ii) the turbidity of the atmosphere at 500 nm, (iii) the precipitable water vapour, (iv) the ozone content, and (v) the albedo. The albedo, which represents reflection from the ground, contributes to the intensity of the diffuse light; in SPCTRAL2 and this calculator, the albedo is assumed constant with wavelength.

The **spectral irradiance of the direct and diffuse components** of sunlight is then determined relative to two planes. The first plane is perpendicular to the direction of the direct sunlight; i.e., this first plane directly faces the Sun. This plane gives the maximum spectral intensity for direct light.

The second plane of interest is the **plane of an installed module**. This plane is defined by the module's tilt and azimuth angles. The direct irradiance incident to the module is then given by cos(*θ*) multiplied by the direct irradiance to the perpendicular plane, where *θ* is the angle between the plane of the module and the perpendicular plane. The diffuse light is calculated by a more complicated formula [Bir86].

Having calculated the spectral irradiance, the calculator then integrates this spectrum to calculate (i) the **power density**, and (ii) the equivalent **photon current** incident to two planes. Generally, it is only relevant to compute these values over the wavelength range of relevance to the solar cell, i.e., at wavelengths that can be absorbed by the cell and converted into electric current. One can set the wavelength limits on the Options tab.

The calculator plots a variety of spectral outputs and all can be downloaded from the 'Export as Excel file' function.

# DEFINITIONS

**Direct** irradiance refers to sunlight that is not scattered by the atmosphere.

**Diffuse** irradiance refers to sunlight that is scattered by the atmosphere.

**Global** refers to the sum of the direct and diffuse sunlight.

**AM1.5g** is a spectrum widely used by the photovoltaic community. It is defined by an IEC international standard [IEC08], where it represents the global irradiance when the Earth–Sun factor is 1, the extraterrestrial spectrum is the AM0 spectrum also defined in the IEC standard, the air mass is 1.5, atmospheric pressure is 1013.25 mb (i.e., sea level), turbidity at 500 nm is 0.084, precipitable water vapour is 1.4164, ozone content is 0.3438 atm-cm, CO_{2} concentration is 370 ppm, a rural aerosol model is used assuming no pollution, the plane of incidence is tilted at 37°, the albedo is wavelength-dependent and representative of light-bare soil, and the integrated irradiance is scaled to give 1 kW/m^{2}. Many of these inputs can be inserted into this calculator and the resulting spectrum is similar but not exactly the same as the IEC international standard.

Visit our spectrum library to download the actual AM1.5g spectrum.

# REFERENCES

| |

[Bir86] | R.E. Bird and C. Riordan, "Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the Earth's surface for cloudless atmospheres," *Journal of Climate and Applied Meteorology*, **25**, pp. 87–97, 1986. |

[Bla01] | M Blanco–Muriel, D.C. Alarcón–Padilla, T. López–Moratalla and M. Lara–Coira, "Computing the solar vector," *Solar Energy*, **70** (5), pp. 431–441, 2001. |

[Gue95] | C. Gueymard, "SMARTS2, A simple model of the atmospheric radiative transfer of sunshine: Algorithms and performance assessment," 1995. |

[IEC08] | IEC International Standard 60904-3, Edition 2.0 2008-04, "Photovoltaic devices – Part 3: Measurement principles for terrestrial photovoltaic (PV) solar devices with reference spectral irradiance data," 2008. |

[Mic88] | J.J. Michalsky, "The astronomical almanac's algorithm for approximate solar position (1950–2050)," *Solar Energy*, **40** (3), pp. 227–235, 1988. |

[Wal78] | R. Walraven, "Calculating the position of the Sun," *Solar Energy*, **20** (5), pp. 393–397, 1978. |

# FEEDBACK

Please email corrections, comments or suggestions to support@pvlighthouse.com.au.