PlantPredict Irradiance Optimization
Definitions and Acronyms
Mono-slope: A slope which is uniform and extends forever in one direction.
Row-to-row shading: Shade cast from one horizontal-single-axis tracker onto the next horizontal-single-axis tracker in the array.
Background
Horizontal-single-axis trackers historically have optimized performance by setting their baseline tracking angle to minimize the angle of incidence of incoming beam irradiance [1]. Improvements have been made over time to the baseline tracking angle via various controls algorithms which help the tracker to:
Avoid row-to-row shading on flat terrain [2]
Avoid row-to-row shading on terrain with a mono-slope [3]
Avoid row-to-row shading on variable terrain [4][5]
Another algorithmic improvement to the baseline tracking angle that can be employed is diffuse stow, also known as irradiance optimization. This algorithm improves upon the baseline in diffuse conditions, by reducing the angle of the tracker relative to the baseline tracking angle. This reduction in angle reduces the contribution of beam irradiance to the total plane of array irradiance seen by the module face and increases the contribution of diffuse irradiance. As irradiance conditions tend towards 100% diffuse fraction, the tracker angle tends towards zero degrees.
Historically, irradiance optimization algorithms have over-predicted [4] the gain seen by trackers in the field due to idealization of tracker mechanics. For example, trackers in the real world:
Do not move to new tracker angle set points instantaneously.
Must consume energy for the tracker to move from one position to another position.
Must take take into account the risk of incorrect tracker positioning, due to the fact that the gain from irradiance optimization is asymmetrically low in relation to the gain from baseline tracking during clear sky conditions.
Must take into account uncertainty around sensor/camera spatial and temporal coverage.
Must take into account unknown future weather conditions.
Etc.
The irradiance optimization algorithm implemented in PlantPredict utilizes an irradiance optimization lookup table [6] that can be used for selecting the best tracker angle for maximizing plane of array irradiance, but introduces two new terms which are meant to reduce the ideality and associated over-prediction of the model.
Main Algorithm
The initial step is to create an idealized lookup table which returns the tracker angle which gives the best plane of array irradiance for each timestep. This table must take into account row to row shading if backtracking is specified. The idealized lookup table in PlantPredict is created by calculating the plane of array irradiance for every possible tracker rotation angle, starting at the minimum rotation angle and ending at the maximum rotation angle. Then, at each timestamp, the algorithm selects and saves the rotation angle which gives the highest value for plane-of-array irradiance at that timestep.
For example, at a given location with a tracker which has a maximum rotation angle of 52 degrees and a minimum rotation angle of -52 degrees, PlantPredict will calculate the plane-of-array irradiance for 105 different trackers each with a rotation angle fixed at a given angle for every time-step. At each time-step, the tracker angle which yielded the highest plane-of-array irradiance is returned. The ideal angle for the entire time-series is then stitched together using the best tracker angle for each time-step.
Then the the idealized lookup table can be corrected according to the formula below:
In order to solve for a reduction in plane of array irradiance relative to the plane of array irradiance received from the idealized lookup table approach, while maintaining a physically realistic plane of array irradiance, PlantPredict’s algorithm only modifies the tracker angle setpoint. This modified tracker angle, or the corrected tracker angle, is the weighted-average of the contributions of different angles that a tracker occupy within a given timestamp and must be an angle between the idealized tracker angle and the non-idealized tracker angle depending on two factors, the movement penalty and the hesitation factor.
The movement penalty term represents the amount of time a tracker must spend in transit from the previous rotation angle to the current rotation angle and is a percentage of the total amount of time encompassed by that timestamp. Instead of integrating the transit angles, an average of the previous position and the new position are taken. The movement penalty coefficient is calculated for the user as a function of tracker rotation speed. The calculation is shown in the sub-algorithms section below. If the movement penalty term is set to zero, then the tracker moves instantaneously from one position to the next.
The hesitation factor is an empirical term which represents controls hesitancy to go to the idealized tracker angle due to real world asymmetric risk as well as other non-idealities mentioned in the background section above. If the hesitation factor and the movement penalty terms are set to zero, then the tracker uses only idealized tracker angles.
Lastly, the algorithm ensures that the corrected tracker angles are at least as backtracked as the original backtracking angles in order to ensure no shading losses are introduced.
Sub-Algorithms
The movement penalty coefficient can be determined by the tracker rotation speed and the amount of degrees the tracker must rotate to get from the standard tracking angle to the ideal tracking angle. For example, if the tracker moves at 0.5 degrees per second and the tracker must go from 60 degrees to 0 degrees, then the tracker takes 120 seconds to traverse to target. 120 seconds represents 3.33% of an hourly timestep and therefore the movement penalty coefficient for an hourly timestep is equal to 3.33.
Hesitation Parameter at Different Timesteps
The graphic above shows the difference in global plane of array insolation received by a tracker system with irradiance optimization selected. The timeseries data was sampled from 1 minute data into 5 minute, 15 minutes, 30 minute and 60 minute averages. The hesitation factor was then varied from 0.0 to 1.0 while the tracker movement speed was held constant at 1 degree per second.
Somethings to notice about the model compared to actual tracker algorithms:
Tracker algorithms send move commands from a network control unit to a set of trackers at some interval, for some trackers this interval is 5 minutes, for other trackers it is 15 minutes. This model does not take the movement command interval into account.
In the model, the tracker movement speed is the dominant parameter. Because the tracker movement speed parameter + the hesitation factor cannot exceed 1, sometimes one of the parameters must be reduced. In this case it is always the hesitation factor since the tracker movement parameter is a physical limitation. This effect can be seen in the 1 minute time average where the reduction in annual global plane of array insolation does not decrease linearly with hesitation factor.
Default Values
Selection of Default Values
Default values of 1 degrees per second and a hesitation factor of 0.2 have been chosen because they give the closest results to the measured/modeled results from ATI’s publication [4] which models the effect of diffuse irradiance optimization on operating and theoretical sites.
Some companies may want to change the default values of 0 degrees per second and a hesitation factor of 0 will give the closest results to PVSyst which does not model non-ideal tracker movement.
Version Restrictions
Version 11+
This feature is available.
Version 10-
This feature is unavailable.
The PlantPredict team reworked the tracker angle calculation pipeline in Version 11, switching the coordinate system from left handed to right handed, and also changing the way that surface angles are calculated. Irradiance optimization is built on top of the new pipeline and therefore unavailable for predictions less than or equal to version 10.
References
W. Marion and A. Dobos. 2013. “Rotation Angle for the Optimum Tracking of One-Axis Trackers.” NREL Technical Report NREL/TP-6A20-58891. https://doi.org/10.2172/1089596
E. Lorenzo, L Narvarte, and J Muñoz. 2011. “Tracking and back-tracking.” Progress in Photovoltaics: Research and Applications 19: 747-753. https://doi.org/10.1002/pip.1085
K. Anderson, and M. Mikofski. 2020. Slope-Aware Backtracking for Single-Axis Trackers. United States: N. p., 2020. https://www.nrel.gov/docs/fy20osti/76626.pdf
K. Passow, K. Lee, S. Shah, D. Fusaro, J. Sharp 2022. “Strategies to Optimize and Validate Tracking Performance of Single-Axis Trackers on Diffuse Sites” PVSC 2022
K. Rhee 2023 “Modeling Transposition for Terrain Following Trackers” PVSC 2023 (Pending)
C. D. Rodríguez-Gallegos, O. Gandhi, S. K. Panda and T. Reindl, “On the PV Tracker Performance: Tracking the Sun Versus Tracking the Best Orientation,” IEEE Journal of Photovoltaics, vol. 10, pp. 1474-1480, Sept. 2020, doi: 10.1109/JPHOTOV.2020.3006994.
Reference PDFs
Acknowledgements
Thank you Nicholas Riedel-Lyngskær for providing the study on the effects of the hesitation factor on irradiance optimization model results.
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