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Summary

The DC Field 3D Shading algorithm is a legacy ray-tracing approach that calculates shading within individual DC fields. This method uses shadow volume construction and polygon-polyhedron intersection testing to determine shaded fractions for each module. The algorithm is limited to single DC field geometries and is computationally intensive, primarily used for DC field-level validation in earlier versions of PlantPredict.

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Inputs

NameSymbolUnitsDescription
Sun Position Vectors⃗\vec{s}—3D unit vector pointing from origin to sun
Module Vertices—m3D coordinates of module corner points (4 vertices per module)
Array Dimensions—mRow spacing, module dimensions for clipping plane calculation
Solar Zenith Angleθz\theta_zdegreesAngle from vertical to sun position
Solar Azimuth Angleγs\gamma_sdegreesCompass direction of sun position

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Outputs

NameSymbolUnitsDescription
Shaded Fraction per Modulefshadedf_{shaded}—Fraction of module area in shadow (0-1)
Shadow Polygon Vertices—mCoordinates defining shadow boundaries on receiver surface

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Detailed Description

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Shadow Volume Construction

For each occluder module, the algorithm constructs a 3D shadow volume:
  1. Define Module Polygon: Extract 4 corner vertices of the occluder module
  2. Project Rays: Cast rays from each vertex along the sun vector direction
  3. Extend to Clipping Plane: Extend rays to a far clipping plane scaled by array dimensions
  4. Form Polyhedron: Connect original vertices to projected vertices to form a closed 3D shadow volume
The shadow volume represents the region of space that is occluded from direct sunlight by the module.

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Occlusion Testing

For each receiver module, the algorithm tests for intersection with shadow volumes from upstream modules:
  1. Intersection Test: Determine if receiver module polygon intersects any shadow volumes
  2. Shadow Polygon Calculation: For intersecting volumes, calculate the shadow polygon vertices on the receiver surface
  3. Area Computation: Compute the area of the shadow polygon

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Shaded Fraction Calculation

The shaded fraction is the ratio of shadow area to total module area: fshaded=AshadowAmodulef_{shaded} = \frac{A_{shadow}}{A_{module}} where AshadowA_{shadow} is the area of the shadow polygon intersection and AmoduleA_{module} is the total module area.

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Application to Irradiance

The shaded fraction is applied to beam irradiance: Ibeam,shaded=Ibeam,POA×(1−fshaded)I_{beam,shaded} = I_{beam,POA} \times (1 - f_{shaded}) Diffuse shading is handled separately using view-factor methods (Schaar-Panchula model).

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Algorithm Characteristics

  • Complexity: O(N2)O(N^2) where NN is the number of modules, as each module must be tested against all potential occluders
  • Scope: Limited to single DC field geometry; does not support site-wide calculations
  • Use Case: Primarily used for DC field-level validation and legacy compatibility

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References

  • Deline, C., Sekulic, W., Stein, J., Barkaszi, S., Yang, J., & Kahn, S. (2014). Evaluation of maxim module-integrated electronics at the DOE Regional Test Centers. Proceedings of the IEEE 40th Photovoltaic Specialist Conference, 3259–3264.