Extraterrestrial, Global, & Tilted Panel Irradiance Simulation

Evaluating photovoltaic (PV) system performance requires modeling both solar geometry and energy conversion efficiency under realistic operational conditions. This simulation integrates top-of-atmosphere extraterrestrial dynamics, clear-sky atmospheric attenuation, tilted surface beam capture, and electrical power generation metrics based on module physical characteristics and Standard Test Conditions (STC).

Comprehensive Mathematical Model

The calculation sequence links solar orbital geometry, clear-sky transmission models, and photovoltaic conversion efficiency equations:

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. \(\theta_z = |\Phi - \delta|\)

8. **Tilted Beam Irradiance & Power:** \(G_{b,tilted} = G_{bn} \cdot \cos(\theta_z - \beta)\) | \(P_{\text{electric}} = G_{b,tilted} \times A \times \eta\)

Parameter Breakdown:

\(G_{0n}\): Extraterrestrial irradiance normal to the solar beam (\(\text{W/m}^2\)).
\(\delta\): Solar declination angle governing seasonal variations.
\(\Phi\): Geographic latitude angle of the site.
\(\theta_z\): Solar zenith angle at solar noon.
\(AM\): Relative optical air mass path length.
\(G_{GHI}\): Global horizontal irradiance.
\(G_{b,tilted}\): Direct beam irradiance intercepted by an equator-facing tilted panel.
\(\eta\) & \(P_{\text{electric}}\): Module conversion efficiency derived from STC and resulting instantaneous electrical power output.

Interactive Simulation Panel

Configure the site latitude, day of the year, panel tilt angle, rated power, and surface area to analyze instantaneous irradiance capture and electrical energy extraction.

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

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

Panel Tilt Angle (\(\beta\), facing equator): 49.0°

Panel Rated Power (\(P_{\text{rated}}\) in W):

Panel Surface Area (\(A\) in \(\text{m}^2\)):

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

Declination Angle (\(\delta\))

Zenith Angle (\(\theta_z\))

Air Mass (\(AM\))

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

Tilted Panel Beam (\(G_{b,tilted}\))
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Panel Efficiency (\(\eta\))

Extracted Electric Power (\(P_{\text{electric}}\))

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.