---
title: "PV simulators comparison: Irradiance modeling"
slug: "comparison-irradiance-modeling"
description: "Explore how PV simulators model optical chains, including irradiance transposition, bifacial modeling, and shading effects for accurate solar energy predictions."
updated: 2026-08-12T13:24:26Z
published: 2026-08-12T13:24:26Z
canonical: "kb.solargis.com/comparison-irradiance-modeling"
---
> ## Documentation Index
> Fetch the complete documentation index at: https://kb.solargis.com/llms.txt
> Use this file to discover all available pages before exploring further.
# PV simulators comparison: Irradiance modeling
**In this document**
This article compares how the compared PV simulators model the optical chain from solar resource and scene to plane-of-array irradiance: global tilted irradiance (GTI) transposition, bifacial rear-side modeling, horizon shading, and near shading.
### Overview
Irradiance modeling is the optical stage of a PV simulation. It turns solar resource - Global Horizontal Irradiance (GHI), Direct Normal Irradiance (DNI), and Diffuse Horizontal Irradiance (DIF) - and the scene geometry into the irradiance reaching each cell on the front and, for bifacial systems, also the rear of every module. Errors introduced here propagate through the full simulation chain, so the modeling approach is one of the strongest differentiators between simulators.
Two design choices dominate accuracy: the computation method, which is either ray tracing through a full 3D scene or view factors over simplified geometry, and the sky diffuse model, where anisotropic models capture circumsolar and horizon brightening that isotropic models miss. Backtracking algorithms, solar position algorithms, and horizon data sources contribute smaller but measurable differences.
For the test sites, system configurations, versions of the tested software, and statistical methodology shared across the series, see [Setup and test methodology](/v1/docs/comparison-setup-and-test-methodology).
#### Note on Sulov site
The test sites differ in far-field terrain as well as in climate. Sulov is located at 49.16°N in a warm-summer humid continental climate (Dfb), which combines a low winter sun with a high diffuse fraction, and it is the most terrain-affected site in this comparison - see Figure 1. It appears repeatedly below as the extreme case in every stage of the optical chain. Dharan and Las Vegas show moderate terrain influence, while Kadhdhoo, Pretoria, and Yaren are effectively open. For site coordinates and climate zones, see [Setup and test methodology](/v1/docs/comparison-setup-and-test-methodology).
***Figure 1****: The extreme terrain and horizon (grey shading in the background - as seen from the PV array) at the Sulov site. Screenshot from Solargis Evaluate.*
### GTI transposition
GTI transposition converts solar resource (GHI, DNI, DIF) into Global Tilted Irradiance (GTI) on the module surface. It is the first step of the optical chain and the largest single contributor to differences within it. Horizon shading is applied separately, in the next step. Three factors drive the differences between the simulators: the computation method, the sky diffuse model, and the backtracking algorithm.
#### Computation method
Ray tracing follows light paths through a full 3D scene; view-factor methods integrate analytical sky and ground contributions over simplified geometry. Solargis Evaluate uses path tracing (a ray-tracing variant) that samples each cell multiple times. All other simulators use view factors. Ray tracing handles arbitrary geometry, partial shading, and reflections without simplifying assumptions, at higher computational cost.
#### Sky diffuse model
Anisotropic models (the Perez family and its variants) capture circumsolar and horizon brightening better than isotropic models, particularly for tilted surfaces. Default models differ: Perez all-weather (Solargis Evaluate), Perez-Ineichen (PVsyst, SolarFarmer), Perez 1990 (SAM), and isotropic (pvlib, with six user-selectable alternatives). Sky diffuse model selection is the second-largest source of differences in GTI transposition, concentrated in the diffuse component.
#### Backtracking algorithm
Relevant only to single-axis trackers (SAT). Backtracking adjusts tracker rotation in the morning and evening to prevent row-to-row self-shading. Different implementations contribute to tracker-system differences in GTI through the cosine of the angle of incidence on the direct beam. Slope-aware variants (pvlib, SolarFarmer) correct for terrain cross-slope; the Lorenzo-Narvarte-Muñoz formulation (Solargis Evaluate, Solargis Prospect) and the PVsyst proprietary algorithm assume no vertical offset between rows.
#### Methodology comparison
| GTI transposition | Solargis Evaluate | Solargis Prospect | pvlib | PVsyst | SAM | SolarFarmer |
| --- | --- | --- | --- | --- | --- | --- |
| **Solar position algorithm** | PSA (updated to 2050) | PSA (updated to 2050) | Reda and Andreas (2004; updated NREL 2008) | Simplified algorithm | Michalsky (1988) | Reda and Andreas (2004; updated NREL 2008) |
| **Computation method** | Ray tracing | Advanced view factor | View factor | View factor | View factor | View factor |
| **Sky diffuse model** | Perez all-weather | Perez (anisotropic) | Isotropic (default), Klucher, Hay-Davies, Reindl, King, Perez, Perez-Driesse | Perez-Ineichen (default), Hay | Isotropic (Liu 1963), HDKR (Duffie and Beckman 2013, Reindl 1988), Perez (1988, 1990) | Hay, Perez-Ineichen |
| **Backtracking algorithm** | Lorenzo et al. (2011) | Lorenzo et al. (2011) | Anderson and Mikofski (2020), Lorenzo et al. (2011) | PVsyst proprietary | National Renewable Energy Laboratory (NREL) algorithm developed for SAM | Marion and Dobos (2013), Lorenzo et al. (2011), Anderson and Mikofski (2020) |
***Table 1****: GTI transposition modeling comparison per simulator.*
GTI transposition - How does Solargis Evaluate compare
Solargis Evaluate uses ray tracing instead of the view-factor approximation used by every other simulator, capturing partial shading, complex geometry, and reflections directly rather than through simplifying assumptions.
This matters most on single-axis trackers, where the sky model and the computation method disagree most, and where a view-factor shortcut is most likely to diverge from reality.
Solar position algorithm choice makes negligible difference across all six simulators and is not a meaningful factor in simulator selection.
#### Numerical results
Results are computed for the six test sites and four system configurations defined in the [Setup and test methodology](/v1/docs/comparison-setup-and-test-methodology) article.
All three simulators agree closely with Solargis Evaluate on typical front-side GTI: the median bias stays below one percent in every configuration (Figure 2). The difference lies in consistency rather than in central tendency. Fixed-tilt configurations are consistent across all six sites, while tracker configurations spread considerably wider, most visibly in RMSE (Figure 3). Tracker geometry drives this: a tracking array sweeps a far wider range of incidence angles than a fixed plane, and that is where the sky diffuse models diverge most. Dharan and Sulov account for nearly all of the spread, and only in their tracker configurations. At both, RMSE far exceeds bias, indicating differences that change sign through the year and largely cancel in the annual total. On trackers, PVsyst stays the most consistent and SAM shows the widest RMSE tail.
> [!NOTE]
> Solargis Evaluate and PVsyst compute different front-side GTI for the bifacial and monofacial tracker configurations, because the two module types give the tracker table different physical dimensions at the same ground coverage ratio. pvlib and SAM return identical values for both, since their tracker geometry is defined by the ground coverage ratio alone and does not respond to the actual dimensions of the table.
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***Figure 2****: Front-side GTI bias for pvlib, PVsyst, and SAM against Solargis Evaluate, as a percentage of the Solargis Evaluate GTI, by mounting configuration across the six test sites.*
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***Figure 3****: Front-side GTI RMSE for pvlib, PVsyst, and SAM against Solargis Evaluate, as a percentage of the Solargis Evaluate GTI, by mounting configuration across the six test sites.*
**Per-site breakdowns of the GTI front transposition bias and RMSE**
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### Bifacial rear-side modeling
For bifacial modules, rear-side irradiance is calculated separately from the front. Ground albedo, rear-side shading from mounting structures, and the geometry of the scene behind the modules all contribute. Rear-side gain is typically 5 to 15% of the total energy yield for utility-scale bifacial systems, so modeling fidelity directly affects bankable yield estimates.
#### Computation method and scene fidelity
Solargis Evaluate extends its front-side path tracing to the rear side using the same full 3D scene. The view-factor simulators (pvlib, PVsyst, SAM, SolarFarmer) work on simplified 2D representations of regularly spaced rows, with end-of-row and terrain effects neglected. SolarFarmer offers 3D in its cloud version. The 3D approach captures contributions from non-uniform geometry, neighboring objects, and terrain that 2D methods cannot represent.
#### Rear-side structural shading
Torque tubes and rear-side mounting elements block a non-negligible portion of rear irradiance. Solargis Evaluate models torque tubes explicitly with configurable albedo. PVsyst and SolarFarmer apply a structure shading factor. pvlib does not model rear-side obstructions, SAM allows a generic loss factor in place of an explicit model.
#### Loss application to the rear side
Soiling, spectral, and incidence angle modifier (IAM) losses apply to the rear differently from the front. Solargis Evaluate simulates front and rear independently. SolarFarmer omits rear-side soiling and spectral losses, and applies IAM to the rear only in cloud calculations. The other view-factor simulators apply front-side losses to the rear without rear-specific modeling. See [Optical losses](/v1/docs/comparison-optical-losses) for the underlying loss models.
#### Methodology comparison
| Rear-side modeling | Solargis Evaluate | Solargis Prospect | pvlib | PVsyst | SAM | SolarFarmer |
| --- | --- | --- | --- | --- | --- | --- |
| **Computation method** | Ray tracing | Currently not available | pvfactors, infinite sheds | View factor (2D unlimited sheds, 2D unlimited trackers) | View factor (bifacial) | View factor |
| **Scene modeling** | 3D | Currently not available | 2D | 2D | 2D | 2D (desktop), 3D (cloud) |
| **Rear-side shading objects** | Torque tubes | Currently not available | Not considered | Applicable via structure shading factor | Applicable via a generic loss factor | Applicable via structure shading factor |
| **Additional features** | Albedo, shape, and position of torque tubes considered | n/a | n/a | n/a | n/a | Soiling and spectral losses not modeled on rear side; incidence angle modifier (IAM) modeled on rear side only in the cloud version |
***Table 2****: Rear-side modeling comparison per simulator.*
Bifacial rear-side modeling - How does Solargis Evaluate compare
Solargis Evaluate extends the same full 3D ray tracing to the rear side, including explicit torque tube modeling with configurable albedo.
This captures non-uniform geometry and structural shading that the 2D approximations used by pvlib, PVsyst, SAM, and SolarFarmer's desktop version cannot represent.
SolarFarmer's cloud version offers 3D scene modeling but still omits rear-side soiling and spectral losses.
#### Numerical results
Only Solargis Evaluate and pvlib expose the rear-side transposition step on its own, before any rear-side losses are applied. Figures 4 and 5 compare them across the bifacial configurations. PVsyst and SAM report the rear side irradiance only after their own downstream losses. [Detailed results and analysis](/v1/docs/pv-simulators-comparison-detailed-results-analysis#rearside-irradiance-and-bifacial-projects1) article covers all three simulators.
pvlib computes higher rear-side GTI than Solargis Evaluate in all twelve bifacial cases, by +1.6 to +7.8%, and more on trackers than on fixed tilt at five of the six sites. Its RMSE is larger than its bias in every case, so the disagreement varies considerably by site and condition. Measured against rear-side irradiance itself, this is the widest divergence in the optical chain, although rear-side gain is a small fraction of front-side GTI, so its absolute effect on yield is correspondingly smaller. The result is consistent with the 2D infinite-sheds approximation in pvlib being very different compared to the full 3D rear-side geometry that Solargis Evaluate simulates.
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***Figure 4****: Rear-side GTI bias for pvlib against Solargis Evaluate, as a percentage of the Solargis Evaluate rear-side GTI, for the two bifacial configurations across the six test sites.*
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***Figure 5:*** *Rear-side GTI RMSE for pvlib against Solargis Evaluate, as a percentage of the Solargis Evaluate rear-side GTI, for the two bifacial configurations across the six test sites.*
### Horizon shading
Horizon shading is the second step in the optical chain. Far-field terrain blocks direct irradiance below the horizon line and reduces the visible sky for diffuse irradiance. The impact is significant at sites surrounded by mountains, valleys, or building skylines, and negligible at flat open sites.
#### Horizon data source
Solargis Evaluate and Solargis Prospect supply the horizon from an integrated model, post-processed SRTM v4.1 at 90 m resolution. Every other simulator requires the user to import it. Table 3 lists the sources each one accepts.
#### Diffuse irradiance handling
Diffuse irradiance handling is the main methodological differentiator. Solargis Evaluate uses ray tracing per array segment: rays hitting sky use the sky model, rays hitting terrain contribute terrain albedo × GHI. PVsyst applies a linear reduction up to 20° horizon height. SAM integrates over the shaded portion of the spherical dome. pvlib has no built-in diffuse-horizon function — a documented user example reduces GHI to DIF where DNI is set to zero. SolarFarmer does not model the horizon effect on diffuse irradiance.
#### Direct irradiance handling
All simulators set DNI to zero below the horizon. PVsyst additionally weights DNI when the sun crosses the horizon within an hour and SolarFarmer scales DNI for partial crossings. These refinements matter at coarse hourly time steps only.
#### Methodology comparison
| Horizon shading | Solargis Evaluate | Solargis Prospect | pvlib | PVsyst | SAM | SolarFarmer |
| --- | --- | --- | --- | --- | --- | --- |
| **Horizon data source** | SRTM v4.1 (90 m) postprocessed by Solargis, user-imported GEOTIFF | SRTM v4.1 (90 m) postprocessed by Solargis | Imported from any source, PVGIS import function | Direct import: PVGIS, Meteonorm, SolarAnywhere API File import: PVsyst, CSV, Meteonorm | Imported (PVsyst, SolarPathFinder, SunEye), shading tables, 3D scene editor | Generated from digital terrain model; SolarFarmer file; Meteonorm; PVsyst; manual input |
| **Horizon editor** | Available | Available | Editable in Python code | Available | Not available | Available |
| **Direct irradiance handling** | Per array segment; DNI ray traced against horizon | Hard shade contours | DNI set to 0 below horizon | DNI set to 0 below horizon, hourly weighted DNI at crossings | Hourly direct shading table | DNI set to 0 below horizon, or scaled for partial crossings |
| **Diffuse irradiance handling** | Sky brightness from ray-traced direction, terrain albedo × GHI for horizon hits | View factor with sky model | GHI set to DIF when DNI = 0 | Linearly decreasing by horizon height (0 above 20°) | Integration over shaded spherical dome | Not modeled |
***Table 3****: Horizon shading modeling comparison per simulator.*
Horizon shading - How does Solargis Evaluate compare
Solargis Evaluate's built-in horizon database removes the need to source and import horizon data — PVsyst, SAM, and SolarFarmer all require importing it from an external tool.
Solargis Evaluate calculates diffuse horizon shading with ray tracing against the actual sky model, while PVsyst applies a linear approximation, pvlib has no built-in method for this at all, and SolarFarmer does not model the diffuse horizon effect at all.
At most sites this makes little practical difference, but at sites with material far-field terrain, such as Sulov in this comparison, the gap becomes substantial.
#### Numerical results
Horizon shading loss can be compared only for Solargis Evaluate, pvlib, and PVsyst, because SAM does not separate horizon shading from near shading. At the flat and near-flat sites the three agree closely, and horizon shading is not a meaningful source of disagreement (Figures 6 and 7). Sulov changes that sharply, with Las Vegas a milder version of the same effect. There the methodological gaps described above surface directly in the results: pvlib, which has no diffuse-horizon treatment, computes a smaller horizon loss than Solargis Evaluate in 23 of the 24 cases, while the linear approximation in PVsyst computes a larger one in 22 of 24. Solargis Evaluate sits between the two at every site (Figure 6) The two also differ in where the error settles. PVsyst diverges most on trackers, whereas the largest systematic offset for pvlib falls on fixed tilt; its tracker errors are far larger at time-step level but cancel across the year.
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***Figure 6****: Horizon shading loss bias for pvlib and PVsyst against Solargis Evaluate, as a percentage of the front-side GTI entering the step, by mounting configuration across the six test sites.*
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***Figure 7:*** *Horizon shading loss RMSE for pvlib and PVsyst against Solargis Evaluate, as a percentage of the front-side GTI entering the step, by mounting configuration across the six test sites.*
**Per-site breakdowns of the horizon shading loss bias and RMSE**
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### Near shading
Near shading is the third step in the optical chain. It covers shadows cast by mounting structures, neighboring arrays, terrain close to the plant, and other site objects (buildings, trees, balance-of-plant equipment). Partial shading of a string creates disproportionate electrical losses, so for sites with significant near-shading exposure the choice between geometric-only and electrically aware models is material. Scene fidelity bounds the result: the [scene modeling capabilities](/v1/docs/comparison-solar-data-and-system-config#scene-modelling) of each simulator set what its near shading calculation can represent.
#### Scene object support
The range of objects a simulator can place in the scene bounds what its near shading calculation can represent. Solargis Evaluate and SolarFarmer support the broadest sets; Solargis Prospect and pvlib handle only inter-row shading of regular layouts. Details are shown in Table 4.
#### Computation approach
Solargis Evaluate uses the same 3D path tracing as the GTI transposition step, combining self-shading, terrain, and object shading in a single calculation.The view-factor simulators compute the same shading through geometric view factors over simplified geometry, and treat self-shading and object shading as separate calculations.
#### Electrical mismatch
PVsyst and SolarFarmer combine linear (geometric) shading with an electrical mismatch model that captures the disproportionate string-level power loss when a few cells are shaded. Note that in this comparison, the electrical effects are accounted for in the [DC conversion simulation step](/v1/docs/comparison-electrical-modeling-dc-side#dc-conversion). SAM separates external (object) and self (inter-row) shading. Solargis Evaluate handles electrical effects in the downstream electrical simulation step (see [Electrical modeling of the DC side](/v1/docs/pv-simulators-comparison-electrical-modeling-of-the-dc-side)), and does not need to approximate the mismatch, because it simulates each cell optically and electrically.
#### Methodology comparison
| Near shading | Solargis Evaluate | Solargis Prospect | pvlib | PVsyst | SAM | SolarFarmer |
| --- | --- | --- | --- | --- | --- | --- |
| **Shading objects supported** | Shading objects, shading lines, restricted areas, arrays, inverters, transformers, high-voltage transformer station, grid connection | Arrays only | Arrays only | 2D shapes, 3D shapes, buildings, ground objects, arrays | Active area, box, cylinder, roof, tree | Imported 3D models (COLLADA) Pre-defined editor objects: box, cylinder, wind turbine, tree, building, arrays, regions, restricted regions |
| **Computation approach** | Ray tracing, direct and diffuse handled separately Self-shading, terrain, and object shading combined | Inter-row shading for regular layouts | Inter-row shading for regular layouts | Linear shading (geometric) plus electrical shading (mismatch effects on cells, modules, strings) | Separate modeling of external shading (objects) and self-shading (inter-row) | View factors for direct and diffuse, electrical mismatch |
| **Bifacial systems** | Front and rear sides simulated separately | Not applicable | Near shading not modeled on the rear side | Single side | Single side | Single side |
***Table 4****: Near shading modeling comparison per simulator.*
Near shading - How does Solargis Evaluate compare
Solargis Evaluate's per-cell optical and electrical resolution means it does not need to approximate string-level mismatch from partial shading.
PVsyst and SolarFarmer both require a separate electrical mismatch correction precisely because they lack this resolution.
Solargis Evaluate and SolarFarmer support the broadest range of shading objects (imported 3D models, terrain, balance-of-plant equipment).
Solargis Prospect and pvlib model only inter-row shading of regular layouts, which fits their role as fast, simplified tools but limits them at sites with irregular layouts or nearby obstructions.
#### Numerical results
Near shading losses agree closely across the simulators at most sites, with median differences well under one percent of the incoming irradiance (Figures 8 and 9). PVsyst stays closest to Solargis Evaluate. Divergence concentrates at Sulov, and to a lesser degree at Las Vegas and Dharan, where terrain near the plant contributes to the shading calculation. Fixed-tilt configurations are not uniformly more aligned than trackers: at Las Vegas all three simulators diverge more on fixed tilt than on trackers, and the largest RMSE recorded for pvlib in this stage is a fixed-tilt case at Sulov. SAM shows the widest spread of the three, although part of that follows from a difference in definition rather than in modeling.
> [!NOTE]
> SAM does not separate horizon shading from near shading. Its near shading loss is measured from nominal irradiance rather than from irradiance after horizon shading, so it also contains the horizon loss that pvlib and PVsyst report separately in Figures 6 and 7. This inflates SAM's near shading bias at every site and accounts for much of its extreme values at Sulov. Read SAM's results in Figures 8 and 9 as horizon and near shading combined.
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***Figure 8****: Near shading loss bias for pvlib, PVsyst, and SAM against Solargis Evaluate, as a percentage of the front-side GTI entering the step, by mounting configuration across the six test sites.*
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***Figure 9****: Near shading loss RMSE for pvlib, PVsyst, and SAM against Solargis Evaluate, as a percentage of the front-side GTI entering the step, by mounting configuration across the six test sites.*
**Per-site breakdowns of the near shading loss bias and RMSE**
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### Further reading
#### Solargis resources
- "[Argus optical simulation overview](/v1/docs/argus-optical-simulation-overview)": Solargis
- "[Comparison setup and test methodology](/v1/docs/comparison-setup-and-test-methodology)": Solargis
- "[Solar data and system setup](/v1/docs/comparison-solar-data-and-system-config)": Solargis
#### Solar position algorithms
- "[The astronomical almanac's algorithm for approximate solar position (1950-2050)](https://www.researchgate.net/publication/222131147_The_Astronomical_Almanac's_algorithm_for_approximate_solar_position_1950-2050)": Michalsky, J. J.
- "[Computing the solar vector](https://www.sciencedirect.com/science/article/abs/pii/S0038092X00001560)": Blanco-Muriel, M., Alarcón-Padilla, D. C., López-Moratalla, T., Lara-Coira, M.
- "[Solar position algorithm for solar radiation applications](https://docs.nlr.gov/docs/fy08osti/34302.pdf)": Reda, I., Andreas, A.
- "[Updating the PSA sun position algorithm](https://www.researchgate.net/publication/347191016_Updating_the_PSA_sun_position_algorithm)": Blanco, M. J., Milidonis, K., Bonanos, A. M.
#### Sky diffuse and transposition models
- "[Evaluation of models to predict insolation on tilted surfaces](https://www.sciencedirect.com/science/article/abs/pii/0038092X79901105)": Klucher, T. M.
- "[Calculations of the solar radiation incident on an inclined surface](https://pvlib-python.readthedocs.io/en/stable/reference/generated/pvlib.irradiance.haydavies.html)": Hay, J. E., Davies, J. A.
- "[Calculation of solar irradiances for inclined surfaces: Validation of selected hourly and daily models](https://www.researchgate.net/profile/Meer-Zafarullah-Noohani/post/calculation_of_solar_radiation_on_a_surface/attachment/5f87eef57600090001ee7e4b/AS%3A946791335878656%401602744053204/download/Calculation+of+solar+irradiances+for+inclined+surfaces+Validation+of+selected+hourly+and+daily+models.pdf)": Hay, J. E.
- "[A new simplified version of the Perez diffuse irradiance model for tilted surfaces](https://www.sciencedirect.com/science/article/abs/pii/S0038092X87800312)": Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D.
- "[The development and verification of the Perez diffuse radiation model](https://www.researchgate.net/profile/Richard-Perez-2/publication/236547906_The_development_and_verification_of_the_Perez_diffuse_radiation_model/links/5deabbcb299bf10bc3464a32/The-development-and-verification-of-the-Perez-diffuse-radiation-model.pdf)": Perez, R., Stewart, R., Seals, R., Guertin, T.
- "[Modeling daylight availability and irradiance components from direct and global irradiance](https://www.sciencedirect.com/science/article/abs/pii/0038092X9090055H)": Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R.
- "[Diffuse fraction correlations](https://www.sciencedirect.com/science/article/abs/pii/0038092X9090060P)": Reindl, D. T., Beckmann, W. A., Duffie, J. A.
- "[All-weather model for sky luminance distribution](https://www.sciencedirect.com/science/article/abs/pii/0038092X9390017I)": Perez, R., Seals, R., Michalsky, J.
- "[Solar engineering of thermal processes](https://www.mechfamily-ju.com/storage/images/files/file_1731558700SHla9.pdf)": Duffie, J. A., Beckman, W. A.
- "[A continuous form of the Perez diffuse sky model for forward and reverse transposition](https://www.sciencedirect.com/science/article/pii/S0038092X23007272)": Driesse, A., Jensen, A., Perez, R.
#### Backtracking algorithms
- "[Tracking and back-tracking](https://scispace.com/pdf/tracking-and-back-tracking-4996bzrza0.pdf)": Lorenzo, E., Narvarte, L., Muñoz, J.
- "[Rotation angle for the optimum tracking of one-axis trackers](https://digital.library.unt.edu/ark:/67531/metadc838269/)": Marion, W. F., Dobos, A. P.
- "[Slope-aware backtracking for single-axis trackers](https://docs.nlr.gov/docs/fy20osti/76626.pdf)": Anderson, K., Mikofski, M.