Extraterrestrial, Global, & Tilted Panel Irradiance Simulation

Maximizing photovoltaic (PV) generation requires evaluating how solar geometry and atmospheric extinction translate onto tilted module surfaces. This simulation computes dynamic extraterrestrial normal irradiance (\(G_{0n}\)), solar declination (\(\delta\)), zenith angle (\(\theta_z\)), relative air mass (\(AM\)), horizontal beam and global horizontal irradiance (\(G_b\), \(G_{GHI}\)), and extends the model to quantify direct beam capture on an equator-facing tilted PV surface (\(G_{b,tilted}\)).

Comprehensive Mathematical Model

The calculation sequence links top-of-atmosphere extraterrestrial formulations to clear-sky ground-level attenuation and surface orientation geometry:

1. \(G_{0n} = 1367 \left[1 + 0.033 \cos\left(\frac{2\pi d}{365}\right)\right]\) | 2. \(\delta = 23.5 \sin\left(\frac{360(284+d)}{365}\right)^\circ\) | 3. \(\theta_z = |\Phi - \delta|\)

4. \(AM = \frac{1}{\cos(\theta_z)}\) | 5. \(G_0 = G_{0n} \cos(\theta_z)\) | 6. \(G_b = G_0 \times 0.7^{AM^{0.678}}\) | 7. \(G_{GHI} = 1.1 \times G_b\)

8. **Tilted Beam Irradiance:** \(G_{b,tilted} = G_{bn} \cdot \cos(\theta_z - \beta)\) (where \(G_{bn} = G_{0n} \times 0.7^{AM^{0.678}}\) and \(\beta\) is tilt angle)

Parameter Breakdown:

\(G_{0n}\): Extraterrestrial irradiance normal to the solar beam (\(\text{W/m}^2\)).
\(\delta\): Solar declination angle reflecting seasonal Earth tilt.
\(\Phi\): Geographic latitude angle of the installation site.
\(\theta_z\): Solar zenith angle at solar noon.
\(AM\): Relative optical air mass path length through the atmosphere.
\(G_0\): Extraterrestrial horizontal irradiance.
\(G_b\) & \(G_{GHI}\): Horizontal beam and global horizontal irradiance accounting for clear-sky attenuation.
\(G_{b,tilted}\): Direct beam irradiance intercepted by a PV panel tilted at angle \(\beta\) facing the equator.

Interactive Simulation Panel

Adjust the site latitude, day of the year, and panel tilt angle to analyze how surface orientation optimizes direct beam capture at solar noon.

Latitude Angle (\(\Phi\), in degrees):

Day of the Year (\(d\)): 276 (October 3)

Panel Tilt Angle (\(\beta\), facing equator): 48.75°

Extraterrestrial Normal (\(G_{0n}\))

Declination Angle (\(\delta\))

Zenith Angle (\(\theta_z\))

Air Mass (\(AM\))

Extraterrestrial Horizontal (\(G_0\))

Beam Horizontal (\(G_b\))

Global Irradiance (\(G_{GHI}\))

Tilted Panel Beam (\(G_{b,tilted}\))
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1. Annual Comparison Curve at Solar Noon (Horizontal)

The annual profile below tracks top-of-atmosphere horizontal irradiance versus ground-level global horizontal irradiance across all 365 days.

2. Beam Irradiance vs. Panel Tilt Angle (\(\beta\)) at Solar Noon

This sensitivity curve demonstrates how varying the module tilt angle affects direct beam collection on the selected day of the year, identifying optimal tilt positioning.