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Summary

3D transposition calculates on a -by-bay basis within a 3D scene, accounting for variations in tracker rotation angle 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 when terrain-aware backtracking is enabled.

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Inputs

NameSymbolUnitsDescription
Tracker Azimuthγtracker\gamma_{tracker}degreesAzimuth of tracker axis measured clockwise from north
Standard Rotation Angleϕ0\phi_0degreesTracker rotation angle from baseline tracking algorithm (true tracking or backtracking, no terrain)
Terrain-Aware Rotation Angleϕi\phi_idegreesEast-west rotation angle of bay ii
Tracker Axis Tilt Angleαi\alpha_idegreesNorth-south tilt of tracker axis for bay ii
Bay Lengthwiw_imLength of bay ii (used for weighted averaging)
Global Horizontal IrradianceGHIGHIW/m²Total irradiance on horizontal surface
Direct Normal IrradianceDNIDNIW/m²Direct beam irradiance perpendicular to sun
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 azimuth angle measured clockwise from north
Albedoρ\rho—Ground reflectance (0-1)

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Outputs

NameSymbolUnitsDescription
Transposition Factor (Global)TFPOATF_{POA}—Ratio of 3D to baseline POA global irradiance
Transposition Factor (Beam)TFbeamTF_{beam}—Ratio of 3D to baseline POA beam irradiance
Transposition Factor (Sky Diffuse)TFskyTF_{sky}—Ratio of 3D to baseline POA sky diffuse irradiance
Transposition Factor (Ground)TFgroundTF_{ground}—Ratio of 3D to baseline POA ground-reflected irradiance

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Detailed Description

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Bay Orientation

For each bay ii, bay tilt βi\beta_i and azimuth γi\gamma_i are computed from the tracker rotation angle ϕi\phi_i and axis tilt αi\alpha_i, using pvlib’s implementation: βi=arccos⁡(cos⁡ϕi⋅cos⁡αi)\beta_i = \arccos(\cos\phi_i \cdot \cos\alpha_i) γi=γtracker+arcsin⁡(sin⁡ϕisin⁡βi)\gamma_i = \gamma_{tracker} + \arcsin\left(\frac{\sin\phi_i}{\sin\beta_i}\right)

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Baseline POA

Baseline POA irradiance components (Gbeam,baselineG_{beam,baseline}, Gsky,baselineG_{sky,baseline}, Gground,baselineG_{ground,baseline}) are calculated assuming flat terrain (α=0\alpha = 0) using the standard rotation angle ϕ0\phi_0 and pvlib’s implementation of the Perez model with the All Sites Composite 1990 coefficient set.

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3D POA

POA irradiance components (Gbeam,iG_{beam,i}, Gsky,iG_{sky,i}, Gground,iG_{ground,i}) are calculated for each bay ii using the terrain-aware rotation angle ϕi\phi_i and axis tilt αi\alpha_i, with pvlib’s implementation of the Perez model (same coefficient set).

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4. Transposition Factors

For each irradiance component, the transposition factor is computed for each bay: TFbeam,i=Gbeam,iGbeam,baselineTF_{beam,i} = \frac{G_{beam,i}}{G_{beam,baseline}} TFsky,i=Gsky,iGsky,baselineTF_{sky,i} = \frac{G_{sky,i}}{G_{sky,baseline}} TFground,i=Gground,iGground,baselineTF_{ground,i} = \frac{G_{ground,i}}{G_{ground,baseline}} TFPOA,i=Gbeam,i+Gsky,i+Gground,iGbeam,baseline+Gsky,baseline+Gground,baselineTF_{POA,i} = \frac{G_{beam,i} + G_{sky,i} + G_{ground,i}}{G_{beam,baseline} + G_{sky,baseline} + G_{ground,baseline}}

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Field Average

The transposition factors are averaged across all bays, weighted by bay length wiw_i: TFbeam=∑iwi⋅Gbeam,i∑iwi⋅Gbeam,baselineTF_{beam} = \frac{\sum_i w_i \cdot G_{beam,i}}{\sum_i w_i \cdot G_{beam,baseline}} TFsky=∑iwi⋅Gsky,i∑iwi⋅Gsky,baselineTF_{sky} = \frac{\sum_i w_i \cdot G_{sky,i}}{\sum_i w_i \cdot G_{sky,baseline}} TFground=∑iwi⋅Gground,i∑iwi⋅Gground,baselineTF_{ground} = \frac{\sum_i w_i \cdot G_{ground,i}}{\sum_i w_i \cdot G_{ground,baseline}} TFPOA=∑iwi⋅(Gbeam,i+Gsky,i+Gground,i)∑iwi⋅(Gbeam,baseline+Gsky,baseline+Gground,baseline)TF_{POA} = \frac{\sum_i w_i \cdot (G_{beam,i} + G_{sky,i} + G_{ground,i})}{\sum_i w_i \cdot (G_{beam,baseline} + G_{sky,baseline} + G_{ground,baseline})} A value less than 1 indicates a reduction in that irradiance component due to terrain effects; a value greater than 1 indicates an increase. The calculated field-averaged transposition factors are applied as site-level modifiers to the POA irradiance components computed by the standard transposition model. This allows the main prediction engine to account for terrain effects without requiring bay-level calculations throughout the full simulation.

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References

  • Marion, W. F., & Dobos, A. P. (2013). Rotation Angle for the Optimum Tracking of One-Axis Trackers. NREL Technical Report NREL/TP-6A20-58891.
  • Perez, R., Seals, R., Ineichen, P., Stewart, R., & Menicucci, D. (1987). A new simplified version of the Perez diffuse irradiance model for tilted surfaces. Solar Energy, 39(3), 221–231.
  • 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.
  • pvlib python. Irradiance module source code. https://pvlib-python.readthedocs.io/en/latest/_modules/pvlib/irradiance.html