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Summary

3D transposition calculates plane-of-array irradiance on a bay-by-bay basis within a three-dimensional scene, accounting for variations in tracker rotation angle, terrain slope, and tracker axis tilt. This transposition method is automatically invoked when 3D site-level scene modeling is enabled. It uses the pvlib implementation of the Perez transposition model to compute POA irradiance for each tracker bay at each timestamp, incorporating the terrain-corrected bay orientation and site-specific albedo.

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Inputs

NameSymbolUnitsDescription
Tracker Rotation Angleϕ\phidegreesEast-west rotation angle of bay (positive west)
Tracker Axis Tilt Angleα\alphadegreesNorth-south tilt of tracker axis (positive south)
Tracker Azimuthγtracker\gamma_{tracker}degreesAzimuth of tracker axis (0° = north, 180° = south)
Direct Normal IrradianceDNIDNIW/m²Direct beam irradiance perpendicular to sun
Global Horizontal IrradianceGHIGHIW/m²Total irradiance on horizontal surface
Diffuse Horizontal IrradianceDHIDHIW/m²Diffuse irradiance on horizontal surface
Extraterrestrial DNIDNIextraDNI_{extra}W/m²Direct normal irradiance at top of atmosphere
Solar Zenith Angleθz\theta_zdegreesAngle between sun and local vertical
Solar Azimuth Angleγs\gamma_sdegreesSun’s compass direction (0° = north)
Albedoρ\rho—Ground reflectance (0-1)

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Outputs

NameSymbolUnitsDescription
Bay Tilt Angleβbay\beta_{bay}degreesEffective tilt of bay surface from horizontal
Bay Azimuth Angleγbay\gamma_{bay}degreesEffective azimuth of bay surface (0° = north)
POA GlobalEPOAE_{POA}W/m²Total plane-of-array irradiance for bay
POA DirectEdirectE_{direct}W/m²Direct beam component of POA irradiance
POA Sky DiffuseEskyE_{sky}W/m²Sky diffuse component of POA irradiance
POA Ground DiffuseEgroundE_{ground}W/m²Ground-reflected component of POA irradiance

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Detailed Description

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Bay Orientation Calculation

The effective bay orientation (tilt and azimuth) is computed from the tracker rotation angle and axis tilt. The tracker rotation angle ϕ\phi represents the east-west rotation of the bay relative to the tracker axis, while the axis tilt α\alpha accounts for terrain slope in the north-south direction. The bay tilt angle βbay\beta_{bay} and bay azimuth angle γbay\gamma_{bay} are calculated using three-dimensional coordinate transformations that combine the tracker rotation, axis tilt, and tracker azimuth into a single surface orientation. This calculation accounts for:
  • Tracker rotation about the tilted axis
  • North-south terrain slope (axis tilt)
  • East-west terrain slope (implicitly through tracker rotation adjustments)
  • Tracker azimuth offset from true north-south
The transformation yields the effective surface normal vector, from which the bay tilt and azimuth are derived.

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Transposition Model

Once the bay tilt and azimuth are determined, the Perez transposition model is applied to calculate POA irradiance. The Perez model is invoked using the pvlib library’s get_total_irradiance function with the following components: Inputs to Perez Model:
  • Bay surface tilt angle βbay\beta_{bay}
  • Bay surface azimuth angle γbay\gamma_{bay}
  • Solar position (θz\theta_z, γs\gamma_s)
  • Horizontal irradiance components (DNIDNI, GHIGHI, DHIDHI, DNIextraDNI_{extra})
  • Site albedo ρ\rho
Outputs from Perez Model:
  • POA global irradiance EPOAE_{POA}
  • POA direct (beam) component EdirectE_{direct}
  • POA sky diffuse component EskyE_{sky}
  • POA ground diffuse component EgroundE_{ground}
The Perez model accounts for circumsolar and horizon brightening using the clearness and brightness indices, as described in the Perez Model documentation.

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Row-to-Row Variations

In a 3D scene, each tracker bay may have a different terrain slope, causing variations in axis tilt and consequently bay orientation. The 3D transposition method calculates POA irradiance independently for each bay, capturing:
  • Terrain-induced tilt variations across the array
  • Row-to-row differences in angle of incidence
  • Localized albedo effects (if spatially varying albedo is specified)
This bay-by-bay approach enables accurate modeling of performance in complex terrain and ensures that tracker rotation angles from terrain-aware backtracking are correctly translated into POA irradiance.

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Application in 3D Calculations

3D transposition is automatically applied when:
  • 3D Shading is enabled: Row-to-row shading calculations require bay-level POA irradiance.
  • Bifacial Modeling is enabled: Rear-side irradiance calculations require accurate bay orientations.
  • Terrain-Aware Backtracking (TABT) is enabled: TABT produces bay-specific rotation angles based on terrain slope.
For fixed-tilt systems in 3D scenes, the tracker rotation angle is zero and the bay tilt is determined solely by the terrain slope and mounting structure tilt.

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Baseline vs. Rotated Transposition

For comparison and validation, 3D transposition computes two irradiance arrays: Baseline: POA irradiance assuming no tracker axis tilt and no terrain-aware backtracking (flat terrain reference). Rotated: POA irradiance using actual bay rotation angles and terrain slopes (3D scene with TABT). The difference between baseline and rotated POA irradiance quantifies the impact of terrain slope and terrain-aware backtracking on energy yield.

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References

  • Perez, R., Ineichen, P., Seals, R., Michalsky, J., & Stewart, R. (1990). Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy, 44(5), 271–289.
  • Holmgren, W. F., Hansen, C. W., & Mikofski, M. A. (2018). pvlib python: A python package for modeling solar energy systems. Journal of Open Source Software, 3(29), 884.
  • Anderson, K., & Mikofski, M. (2020). Slope-aware backtracking for single-axis trackers. National Renewable Energy Laboratory Technical Report NREL/TP-5K00-76626.