Performance modeling of solar module trackers

Abstract

To accurately predict performance under the constraints of available processing resources, the performance of solar trackers at a solar photovoltaic site is modeled. A specific aspect of the present invention involves transposing each bay at a solar photovoltaic site using a terrain-adaptive backtracking schedule that prevents inter-row shading. Furthermore, aspects of the present invention also include simplifying the bay configuration and / or backtracking schedule at a solar photovoltaic site by averaging or selecting representative angles from a plurality of angles, thereby obtaining accurate results while simplifying modeling performance.

Description

Technical Field

[0001] [Priority Claim] This application claims priority based on U.S. Provisional Patent Application No. 63 / 463,224, "MODELING PERFORMANCE FOR SOLAR MODULE TRACKERS", filed in the United States on May 1, 2023, and U.S. Patent Application No. 18 / 651,251, "MODELING PERFORMANCE FOR SOLAR MODULE TRACKERS", filed in the United States on April 30, 2024. The entire contents of these applications are incorporated herein by reference.

[0002] The present invention generally relates to solar trackers, and more particularly to the performance modeling of solar trackers.

Background Art

[0003] Two types of installation systems are widely used for installing solar panels. The fixed-tilt mount structure supports the solar panel at a fixed position. The power generation efficiency of the panel supported in this way can vary greatly throughout the day because the sun moves across the sky and irradiates the fixed panel more or less efficiently. However, the fixed-tilt solar panel mount structure is mechanically simple and inexpensive, and in the case of ground-mounted installations, it can be relatively easily arranged on sloping and / or uneven terrain.

[0004] A single-axis tracker solar panel mounting structure allows for partial tracking of the sun's movement across the sky by rotating the panel around an axis. For example, a single-axis tracker can be positioned with its axis of rotation roughly oriented north-south, allowing the panel to track the east-west component of the sun's daily movement as it rotates around the axis. Alternatively, by positioning the single-axis tracker with its axis of rotation roughly east-west, the panel can be rotated around that axis to track the north-south component of the sun's daily (and seasonal) movement. Solar panels supported by a single-axis tracker can generate significantly more power than comparable panels positioned in a fixed location.

[0005] The amount of grading required to install a short-axis tracking system may reduce the economic efficiency of those single-axis trackers. Furthermore, flaws in the tracker rotation strategy, which dictates how the tracker tracks the sun, may also reduce their efficiency.

[0006] Certain state-of-the-art single-axis trackers are specially designed to reduce or eliminate the need for gradient adjustment by employing special bearings that can accommodate changes in the net angle of the support tube. Solar array sites may have multiple trackers, and each tracker may house multiple bays of solar modules. A bay is a continuous row of solar modules separated by a support, and each bay may have its own normal vector. The variability of the normal vector from bay to bay leads to a relaxation of gradient requirements, which allows solar modules to be installed on uneven terrain. However, this also makes them more susceptible to shadowing caused by the inclination of the cross axis and the intra-tracker axis.

[0007] The basic tracking algorithm used by many trackers is called true-tracking. Its purpose is relatively simple: to minimize the angle of incidence between the normal vector of the solar panel and the incident rays from the sun. Solar panels are placed flat at noon and tilted to face the sun when the sun is low in the early morning and evening. Steep tilting at certain times of day can cast shadows between trackers, resulting in potentially large power losses in a pure true-tracking approach. When one tracker casts a shadow on another, it is often called row-to-row shadowing. This is because a tracker can be considered a row of solar modules, even if there are changes in angle within the tracker itself.

[0008] As a result, a basic backtracking algorithm was developed to improve true tracking. During the morning and late evening hours when shading is likely, the angle of the solar modules is reduced to prevent shading (for example, making the modules more horizontal). These basic backtracking algorithms assume that the tracker is on a perfectly flat plane.

[0009] More advanced backtracking algorithms, known as cross-slope-aware backtracking, take into account that each tracker may have different planes (higher or lower) to the east or west. Since the angle between these two planes, called the cross-axis slope, can extend infinitely, all trackers within the range of each algorithm run will inherit the same cross-axis slope. Cross-slope-aware backtracking may fail to prevent shadows in three ways: Firstly, if the cross-axis slope is not constant across the site and changes, the algorithm may not be able to account for these changes and fail to prevent inter-row shadows. Secondly, if the trackers have different slopes along the tracker axis, the planes of both trackers will not be parallel to each other, which can also cause problems. Finally, even if the slope along the tracker axis is considered, if the slope can change between the posts within each tracker, such an algorithm will only consider the entire sloped tracker. These changes can also cause shadows to fail.

[0010] Preventing shading between rows requires more advanced backtracking algorithms, which must be more terrain-adaptive than those mentioned above. However, advancements in increasingly sophisticated backtracking algorithms may outpace the capabilities of performance modeling programs that model these algorithms. To understand the economics of a solar power site, it is crucial to accurately model the site's performance before or after installation, because knowing the energy generated allows us to determine the return on investment. If the modeled performance may overestimate the energy generated, it could lead to poor investment decisions, such as installing on a substandard site where installation and maintenance costs outweigh the value of the energy gained. If the modeled performance underestimates the energy generated, it could lead to prioritizing other sites with lower performance and overlooking suitable sites.

[0011] Current performance modeling software cannot directly model the performance advantages of operating a horizontal single-axis tracking system employing a terrain-adaptive backtracking strategy on uneven terrain. This is because currently available performance modeling software cannot accurately calculate the rotation angle that individual trackers should be set to in order to avoid shadows between rows. Current complete methods for modeling terrain-following systems, such as modeling the system assuming it is built on flat terrain, overestimate the system's performance. On the other hand, modeling a terrain-following system on uneven terrain using a backtracking algorithm based on standard ground cover underestimates the system's productivity due to shadow losses caused by the terrain. Systems utilizing terrain-adaptive backtracking strategies generate an energy level intermediate between these two extreme cases, but accurately determining this energy level without time-consuming pre-processing, post-processing, or approximations remains an unresolved issue in the industry.

[0012] Horizontal single-axis trackers are typically modeled in performance modeling software as a repeating planar array of tracker columns, where each column is indistinguishable from its neighbor. This simplification leads to performance degradation of the trackers due to shading losses that are not captured by this modeling method. As the solar power industry increasingly constructs sites on uneven ground, horizontal single-axis tracking hardware is evolving to address these challenges. As this new type of tracking hardware evolves, the performance modeling methods and tools used to obtain accurate models of past and future plant performance must also evolve. [Overview of the Initiative]

[0013] Embodiments of the present invention include modeling the performance of solar trackers in a photovoltaic facility in order to accurately predict the performance of solar trackers in a photovoltaic facility, while being subject to constraints on available processing resources. Specific aspects of the present invention include transposing each bay of a photovoltaic facility using a terrain-adaptive backtracking schedule that prevents shading between rows. Further aspects include simplifying the bay configuration and / or backtracking schedule of the photovoltaic facility, such as by averaging or selecting a representative angle from multiple angles. This allows for simplified modeling performance while obtaining accurate results.

[0014] Further aspects and advantages of this disclosure will be readily apparent to those skilled in the art from the following detailed description. The detailed description shows and describes only exemplary embodiments of this disclosure. As will be understood, other different embodiments are possible, some of their details of which can be modified in various obvious ways without departing from this disclosure. Therefore, the drawings and description are of an exemplary nature and not limiting. [Brief explanation of the drawing]

[0015] [Figure 1] This example shows an all-terrain solar tracker positioned on undulating terrain with a slope that changes angle along its length to follow the natural topography.

[0016] [Figure 2] This shows a perspective view of a solar panel tracker on a sloping, undulating terrain.

[0017] [Figure 3] This shows a cross-sectional view (looking down along the east-west axis) of a solar panel tracker on a sloping, undulating terrain.

[0018] [Figure 4] This shows a cross-sectional view (viewed from above along the north-south axis) of a solar panel tracker on a sloping, undulating terrain.

[0019] [Figure 5] A flowchart showing a raycasting process for determining a backtracking schedule in a solar power generation site array.

[0020] [Figure 6] Showing raycasting performed in two bays where an intersection test is executed in one of the two bays.

[0021] [Figure 7] A flowchart showing a modeling process for determining energy production in a solar power generation site array.

[0022] [Figure 8] A flowchart showing a modeling process for determining energy production in a solar power generation site array.

[0023] [Figure 9] Showing a graph including the rotation angle of an optimized terrain-adaptive backtracking schedule for a tracker and the minimum rotation angle at each time step between trackers.

[0024] [Figure 10] Showing a graph including the rotation angle of an optimized terrain-adaptive backtracking schedule for a tracker and the average rotation angle at each time step between trackers.

[0025] [Figure 11] A flowchart showing a modeling process that utilizes retrotransposition to determine the energy production amount in a solar power generation site array.

[0026] [Figure 12]This flowchart illustrates the modeling process for determining energy output in a photovoltaic site array.

[0027] [Figure 13] This shows a block diagram of a computer system that communicates with a solar panel array.

[0028] [Figure 14] This shows a block diagram of a solar panel control system that communicates with a solar panel array.

[0029] [Figure 15] This shows a histogram model of the north-south torque tube axis tilt in a physically installed solar array bay equipped with a terrain-adaptive tracker.

[0030] [Figure 16] This shows a histogram model of cross-axis tilt in a physically installed solar array bay equipped with a terrain-adaptive tracker.

[0031] [Figure 17] This shows a histogram model of axial tilt mismatch in a physically installed solar array equipped with a terrain-adaptive tracker.

[0032] [Figure 18a] Figures 18a and 18b show graphs comparing the rotation angle and resulting array illumination plane obtained from a backtracking strategy based on a certain range of ground coverage with the rotation angle and array illumination plane based on raycasting. [Figure 18b] Figures 18a and 18b show graphs comparing the rotation angle and resulting array illumination plane obtained from a backtracking strategy based on a certain range of ground coverage with the rotation angle and array illumination plane based on raycasting.

[0033] [Figure 19]This graph compares the array solar radiation receiving surface generated by TRACE with the solar radiation receiving surface generated by retro-transposition and re-transposition using PVSyst.

[0034] [Figure 20] This shows a 3D model of a physically installed solar array with terrain-adaptive trackers that include changes in orientation and angle between stakes.

[0035] [Figure 21] This shows a 3D model of a bay's solar array with a solar position vector, normal plane, and xy plane.

[0036] [Figure 22] This shows a 3D model of a solar array projected onto the normal plane.

[0037] [Figure 23] Figure 22 shows a 3D model obtained by reprojecting the projection shown in Figure 22 onto the xy-plane.

[0038] [Figure 24] Figure 23 shows a 3D model of the reprojected projection, where overlapping polygons (e.g., corners) indicate the shading of the sunlight array.

[0039] [Figure 25] This flowchart illustrates the point-in-polygon process for determining the backtracking schedule of a solar array. [Modes for carrying out the invention]

[0040] The following detailed description should be read with reference to the drawings. In the drawings, the same reference numerals indicate similar components throughout different drawings. The drawings are not necessarily to scale and illustrate selective embodiments, and are not intended to limit the scope of the invention. The detailed description illustrates the principles of the invention by example rather than by limitation. This specification describes several embodiments, adaptations, modifications, alternatives and uses of the invention to enable those skilled in the art to reliably carry out and use the invention.

[0041] In this specification and the appended claims, singular forms such as "a," "an," and "the" are to be considered plural unless the context clearly indicates otherwise. Furthermore, the term "parallel" is to be interpreted as "substantially parallel," including minor deviations from parallel geometry. The term "perpendicular" refers to a direction parallel to Earth's gravity. The term "horizontal" refers to a direction perpendicular to the "perpendicular" direction.

[0042] Figure 1 shows an example of a variable terrain solar tracker device employing support columns 110, a solar panel module support section such as a torque tube extending between the support columns, and a solar panel module 101 supported by the torque tube (solar panel modules directly placed on the torque tube will be referred to as "solar panel modules" below to distinguish them from the "solar panels" included in the pony module 200 described later). Multiple solar panel modules can be placed between each support column, and they may be the same size as each other. The number of solar panel modules between each support column may be the same for the entire tracker, or it may vary depending on the terrain and the spacing of specific support columns.

[0043] This modified version, a variable-terrain solar tracker, is positioned on undulating terrain and features two rotation axes: a first rotation axis positioned along the slope and a second horizontal rotation axis positioned along the flat land on the slope. The angle between the first rotation axis and the second horizontal rotation axis can be, for example, ≥0, ≥5, ≥10, ≥15, ≥20, ≥25, ≥30, ≥35, ≥40, ≥45, ≥50, ≥55, ≥60, ≥65, ≥70, ≥75, ≥80, ≥85, or up to 90 degrees. These examples refer to the magnitude of the angle between the first rotation axis and the second horizontal axis. The angle can be positive or negative.

[0044] Various types of assemblies can be positioned on top of the support column. This depends on the terrain and the positional relationship of the support column to other trackers: straight-through bearing assemblies for inclined planes, flat-ground bearing assemblies for flat ground, row end bearing assemblies for tracker ends, articulated bearing assemblies for terrain angle changes, and drive assemblies positioned at the tracker end or intermediate position for rotational driving of the tracker may be provided.

[0045] For example, both ends of the tracker are rotatably supported by row end bearing assemblies 105 on support columns 110. Tracker sections located on an inclined surface are supported by through bearing assemblies 107, which include thrust bearings that isolate and transmit a portion of the inclined load to the corresponding support columns 110. Tracker sections located on flat ground above the inclined surface are rotatably supported by flat-ground bearing assemblies 115. These assemblies may be conventional through bearing assemblies lacking the thrust bearings described above. The drive system may be a slewing drive system that rotates the solar panel module 101 and solar panels 210 around a first and second rotation axis to track the sun. The solar panel module 101 is supported on a torque tube that is parallel to the rotation axis of the slewing drive system and displaced as needed (e.g., by shifting downward). The torque tube may not be displaced from the rotation axis of the slewing drive system and may be coaxial. An articulated bearing assembly 120 connects the two non-collinear rotation axes and transmits torque between them. Examples of the bearing assemblies 105, 107, and 120 are described in more detail below.

[0046] Other variations of the variable terrain solar tracker 100 include other combinations of bearing assemblies 105, 107, 115, and 120 arranged to accommodate one, two, or more linked rotating axes, which are positioned along terrain having one or more sloped sections and optionally one or more horizontal (flat) sections. By arranging two or more such trackers adjacent to each other, for example in a row, sloped and / or uneven terrain sections can be efficiently filled with single-axis tracking solar panels for power generation.

[0047] Referring again to Figure 1, as described above, the articulating joint bearing assembly 120 accommodates changes in the direction of the rotation axis along the tracker. In this specification, “articulating joint” refers to a joint that can receive torque on one rotation axis and transmit that torque to a second rotation axis that has a point coinciding with the first rotation axis. This joint is inserted between two rotation rods that transmit torque and allows the second rotation rod to bend away from the first rotation rod, without requiring the first or second rotation rod to bend along its entire length. One such joint available for use in the articulating joint bearing assembly described herein is called a hook joint and is characterized by comprising a forked yoke attached to the first rotation rod, a forked yoke attached to the second rotation rod, and a four-point cross connecting them, thereby transmitting torque from the york ears of the first shaft to the york ears of the second shaft.

[0048] A solar panel array control system may be provided. This system can control the operation of one or more solar panels within a solar array. The operation of one or more solar panels may include the positioning of one or more solar panels. For example, the solar panel array control system may control the orientation of one or more solar panels. The control system may transmit signals to solar panel support structures that can affect the position of one or more solar panels. Articulated joints may be configured to allow the control system to control the position of the solar panels.

[0049] Certain state-of-the-art single-axis trackers are designed to accommodate uneven terrain by being constructed using discontinuous torque tubes held by special bearings. These special bearings can accommodate net angular changes of up to 15 degrees between the support columns. In these trackers, each section of the torque tube to which the solar power modules are connected is called a "bay," and each bay has a unique inclination angle on the torque tube axis.

[0050] Figures 2-4 show a solar panel array at a solar site, including a single-axis tracker and bays. Figure 2 shows two trackers directly adjacent to each other within the solar site array, each extending along or approximately in the north-south direction, with the solar modules extending longitudinally in the east-west direction or approximately in the east-west direction. Angular changes are shown in the bearing assemblies 112 of both trackers. The bearing assemblies 112, positioned on the support 110, can be any of the aforementioned bearing assemblies, such as articulated bearing assemblies. The bays 117 contain a series of one or more solar modules (e.g., 8 or fewer, 10 or fewer, or more than 10 modules) positioned directly adjacent to each other. The bays 117 are enclosed by bearing assemblies 112 and can be positioned on a single torque tube. The solar modules 101 within the single bay 117 have parallel normal vectors and lie on the same plane, even when the torque tube rotates the solar modules. Figure 3 shows a cross-section of the solar site array viewed along the east-west axis. A single tracker with three bays 117 as seen from a solar site array is shown. Figure 4 shows a cross-sectional view of the solar site array in the north-south axis direction. Three trackers of the solar site array are shown arranged in parallel on a sloping ground. The solar modules 101 within bay 117 are tilted away from the horizontal plane. As is clear from the figure, directly adjacent trackers along the east-west axis (i.e., adjacent trackers) may shade each other in their bay 117 depending on the direction of the sun and the cross-axis tilt. All the trackers shown in each of the above figures are mounted on separate column controllers, and all column controllers may be mounted on the same central controller.

[0051] Figure 14 shows an example of a solar panel array control system 150 connected to a solar panel array. The solar panel array control system 150 is capable of communicating with the solar panel array. The solar panel array control system 150 and / or its components (e.g., a central control unit 152 and / or a group control system 154) may include, be included in, or consist of the components of the aforementioned computer system 320 or computer system 320.

[0052] A solar panel array may include one or more solar panel groups 156, each containing one or more solar panel modules 101. A group 156 may include one or more solar panels connected in series, parallel, or any combination thereof. A solar panel group may include a row of solar panels, which may be the tracker 100 described above. The descriptions of rows of solar panels herein may apply to any other arrangement or grouping of solar panels.

[0053] Optionally, each solar panel group has its own group control system 154 (for example, connected to and able to communicate with the group control system 154), and each group control system 154 can control the operation of its own solar panel group 156. When the group control system 154 controls a row of solar panels, it may be called a row controller. Any number of solar panel groups and / or group control systems can be provided. Each group can consist of any number of solar panels. Each group may have the same number of solar panels or different numbers of solar panels. A central control device 152 for controlling the group control systems can optionally be provided.

[0054] The solar panel array control system 150 may include a central control unit 152 and optionally one or more group control systems 154. In some cases, one-way communication may be provided from the central control unit to one or more group control systems. The central control unit may send instructions to one or more group control systems, which may control the operation of the corresponding solar panel groups. In some cases, two-way communication may be provided between the central control unit and one or more group control systems. For example, a group control system may be a group controller that sends data to the central control unit. The central control unit may send commands to the group controller, for example, in response to or based on data received from the group controller. The data from one or more group controllers may optionally include data from one or more solar panels, or data from various sensors that are physically included as part of the solar panel group (e.g., mounted on torque tubes, foundations, bearing assemblies, or other parts of the tracker), data from sensors located physically separate from the solar panel group, and / or data from sensors that are physically or electrically connected to the solar panel group in other ways.

[0055] A solar panel array control system can direct and influence the operation of solar panels, which may include positioning of the solar panels. The control system can influence the orientation of the solar panels. The control system can control the amount of rotation, rotational speed, and / or rotational acceleration of one or more solar panels. The control system can influence the spatial arrangement of the solar panels. The control system can control the amount of translation, translational speed, and / or translational acceleration of one or more solar panels. The control system can influence the operation of the drive mechanism for the solar panel array, for example, by sending a signal to a swivel drive connected to one or each group of solar panels, thereby controlling the orientation of the solar panels. Solar panels are positioned according to one or more factors as described above. A solar panel array control system can influence other operations of solar panels (e.g., on / off switching of solar panels, operational parameters related to the conversion of solar energy to electrical energy, diagnostics, error detection, calibration, and all other types of solar panel operations).

[0056] As one example, a method for optimizing power generation across the entire field of trackers is provided. Operating data for each group of solar panels (e.g., each row) is provided. The descriptions of rows in this specification may apply to any group. This method involves collecting row-level operating data aggregate or partially to determine the operating characteristics of one or more tracker rows. The power generation of each row is measured to determine whether shading is occurring between rows. This method involves analyzing the power generation of the entire field to determine whether power generation can be increased by further optimizing or adjusting the tilt angles of other rows while analyzing shading in a particular row.

[0057] Column-level testing is conducted to determine the impact of shadowing from one or more columns on power generation in adjacent columns. Column-level testing is performed on one or more columns to determine whether it results in optimal power generation or an increase in power generation, assuming optimal orientation. Tracking schedules can be updated to optimize or increase power generation across the entire tracker field or for each individual column. By monitoring column-level power generation and comparing it to weather station reports, it is possible to determine whether solar-tracking or non-solar-tracking operation generates more power. Based on this comparison, the operation that yields higher power generation can be selected.

[0058] Modeling the performance of an array at a solar power site is useful, whether or not the array is already installed. This determination of power generation may include simulations of the array's optical, electrical, and / or thermal performance using a 3D model. Modeling the array at different installation locations allows for the selection of the optimal installation location that provides the best energy performance relative to installation cost. In other words, from multiple candidate sites, the location with the highest energy generation and / or energy generation efficiency relative to installation cost can be selected. After performance modeling is completed according to embodiments of the present invention, the solar power array is physically installed at the selected installation location.

[0059] However, for the state-of-the-art single-axis trackers described above, most current performance modeling software ignores the angular changes that can occur in each bearing in terrain-following trackers, assuming that each bay has the same angle forward and backward. Furthermore, most software ignores the unique backtracking algorithms required during the operation of terrain-following trackers to avoid power loss due to shading. Some superior software allows the use of custom tracker angles for both the north-south angle of the torque tube axis and the tracker rotation angle. These and similar software, combined with a custom backtracking schedule adapted to the terrain, can accurately model the performance of terrain-adaptive backtracking strategies. This can be done even before plant construction.

[0060] To more accurately model the amount of energy generated by solar tracking systems and prevent overestimation or underestimation by conventional methods, specific tools and techniques have been developed. For example, these tools and techniques may take the form of software programs that generate terrain-adaptive tracker rotation schedules, which can be used to accurately model the performance of terrain-following trackers employing advanced back-tracking strategies. For example, the tracker rotation schedule can be imported into performance modeling software. In performance modeling software programs where users cannot input custom tracker rotation angles, various techniques have been developed to approximate the results.

[0061] When completing a performance model using software that cannot accept custom variable tracker axis tilt angles and custom variable tracker rotation angles, embodiments of the present invention generate a simplified model that can be used to approximate the results of advanced performance modeling tools. Regardless of the modeling tool used, solar power project developers and asset owners may seek more accurate estimates of pre-construction site energy output to make more informed investment decisions.

[0062] Properly modeling a terrain-following single-axis tracker system requires several steps that differ from standard modeling procedures for planar systems. If the system performs backtracking, a time series of rotation angles should be calculated for each tracker, and occlusion between columns should be avoided at every time step. For each bay, a transposed model with a unique normal vector pointing outward from the module surface must be calculated at every time step.

[0063] Reference Model

[0064] Modeling as Flat Ground and GCR-Based Backtracking: Most performance modeling software systems default to modeling the entire solar site as being installed on flat ground. Solar power plants built on uneven terrain can be modeled using performance modeling programs with standard ground cover (GCR) backtracking algorithms. Because this backtracking algorithm does not account for terrain effects, applying a flat ground backtracking algorithm to an uneven site will result in power losses due to shading. Consequently, these models are primarily used as reference examples or for comparison.

[0065] Average Tracker Axis Tilt: Some performance modeling software may not allow input of custom tracker rotation schedules. If tracker axis tilt is adjustable as a variable, an approximation can be made simply by averaging all torque tube axis tilts across the entire site without any other modifications. This allows the system to be modeled as a single repeating tracker array sharing a common tracker axis tilt.

[0066] Commissioned Backtracking: One way to mitigate the shading effect caused by terrain is to set the ground cover rate (GCR) of the site backtracking algorithm to a denser value than the actual tracker spacing. For example, if the trackers are positioned at a ground cover rate of 0.33, setting an artificial ground cover rate greater than 0.33 can reduce the amount of shading that occurs between rows. This method allows the site to maintain all trackers at the same rotation angle as the site plane of the array solar radiation sensor while avoiding shading between rows. To determine an appropriate artificial ground cover rate, a rotation schedule array is generated using a standard ground cover rate-based method. This array starts with the ground cover rate of the actual installation site and is iteratively increased by 1% until the estimated array surface solar radiation falls below a set threshold, indicating that shading is occurring or at risk of occurring. Because standard backtracking algorithms cannot account for east-facing / west-facing surfaces or changes in terrain, some shading may still occur with this method. In an oversimplified model, the contribution of a shaded section to the overall plant phase shift is equal to that of the diffuse component of the incident irradiance alone. This model is intended to very roughly simulate the effect of electrical mismatch along the string.

[0067] Bespoke Transposition Modeling

[0068] According to embodiments of the present invention, the most rigorous method for modeling transposition is to model the transposition individually for each bay within a given solar power site. This is done, for example, after obtaining a backtracking schedule of the rotation angle from the raycasting method (described later). For example, in the case of a 100MW site constructed with discontinuous torque tube trackers (such as a structure in which bearings are provided on support columns to support the inlet and outlet torque tubes and maintain spacing), this corresponds to approximately 36,000 bays. If typical meteorological year time series data is processed at one-hour intervals, this means 315,360,000 calculations. For a 500MW site at one-minute intervals, approximately 94.6 billion calculations would be required. Depending on the available computing power, this method can be used to obtain the most accurate modeling of the power generation obtained from the site. For example, in a solar power site on a slope, a backtracking schedule can be generated by the raycasting method, thereby avoiding shading between rows of trackers. The power generation is then calculated using the backtracking schedule. For example, backtracking schedules can be entered into software tools that fully or nearly fully accept these schedules as input, such as Terabase®'s PlantPredict® and DNV®'s SolarFarmer®. In addition to backtracking schedules, modeling programs may require additional inputs such as global horizontal radiation (GHI), direct normal radiation (DNI), and / or scattered horizontal radiation (DHI).

[0069] Figure 7 illustrates this process. In 305, a terrain-adaptive backtracking schedule is obtained, i.e., a schedule that prevents inter-row shading despite changes in axial and / or transverse slopes across the entire site. This schedule is obtained by the raycasting method described later. In 310, other input values ​​required for the modeling program (such as GHI and DHI) may be obtained. These input values ​​are obtained via a database based on the geographical location of the site or measured by satellites or sensors at the site. Some programs use DNI instead of GHI, or in addition to GHI. In this specification, unless otherwise specified, when GHI is mentioned as an input, it is understood that DNI is used instead of GHI, or in addition to GHI. In 315, the output of the solar site is determined based on the schedule and inputs. This output determination may include simulation of a 3D model of the optical, electrical, and thermal performance of the array using the obtained backtracking schedule. Within this simulation, the global plane of the array (GPOA: the array plane of all solar panels on the site, i.e., the amount of solar radiation received by angled solar panels) can be determined and ultimately used to calculate the total output of the solar power site.

[0070] If a site has an excessive number of trackers / bays and there are constraints on computing resources or the modeling program itself, a simpler approach may be preferable, as shown below.

[0071] Backtracking / rotation schedule and / or axis tilt limitations

[0072] Some performance modeling programs allow custom terrain-adaptive backtracking schedules and GPOAs as input, while others do not. For example, one program might accept custom angles for trackers, but require all trackers to use the same rotation angle and axis tilt. In such cases, even if the same rotation angle and axis tilt are used, simplification is still necessary to obtain reasonably accurate results for terrain-adaptive backtracking.

[0073] Embodiments of the present invention include a method called limit backtracking / rotation scheduling, or limit raycasting. Limit backtracking scheduling can begin by obtaining a schedule of backtracking angles, for example, by tracking the sun in a solar power facility installed on a slope using a raycasting technique to obtain a terrain-adaptive backtracking schedule that does not cause shading between rows. At least for some time of day, particularly in the early morning and evening, the backtracking angles of specific trackers may differ from each other. Figure 9 shows the backtracking angles (e.g., obtained by raycasting) in a solar power site with multiple trackers, and the individual backtracking angles of each tracker corresponding to the individual time steps that make up the terrain-adaptive backtracking / rotation schedule. The x-axis represents time, and the y-axis represents the rotation angle of the tracker. Thin lines represent the individual rotation angles of different trackers, with the most significant differences observed in the morning and evening. As is clear from the figure, the backtracking angles differ significantly between trackers in the morning and evening, and are identical or approximate around noon. The large number of rotation angles within a specific time period may require simplification in some performance modeling programs that lack the capability to model such a large number of individual control trackers.

[0074] Figure 8 shows an embodiment of the present invention, represented as an extensive process for simplifying modeling. In 405, a first rotation schedule is obtained, which includes the rotation angle of each tracker installed at the solar site at each time step. The first rotation schedule is obtained by the raycasting method described above. This first rotation schedule may provide better power generation performance than the second rotation schedule described later, when used by the trackers at the associated solar site, but it may be difficult or impossible to model depending on the performance modeling program used.

[0075] In step 410, a desired rotation angle is determined for each time step. The desired rotation angle may be the minimum rotation angle in the first rotation schedule considered for each time step. In Figure 9, the dark line represents the minimum rotation angle (meaning the minimum absolute value of the angle) for any given time step. In contrast to the rotation angles of all trackers in the first rotation schedule, there may be only one desired rotation angle for each time step.

[0076] In 415, a second rotation schedule can be created using a desired rotation angle. For example, the minimum rotation angle at each time step can be used to simplify the modeling. All trackers in a site can be set to this minimum rotation angle (i.e., the most backtracked angle) at each time step of the second rotation schedule. This is useful for simplifying the modeling because all trackers will have the same rotation angle, but it is advantageous for improving modeling accuracy as it does not cause occlusion. For example, if a site has three trackers and the optimal rotation angles calculated at a certain time step are 10 degrees, 12 degrees, and 15 degrees, then if the site is set to backtracking limited schedule mode, all three trackers will be set to 10 degrees. Alternatively, the desired rotation angle can be the average of all rotation angles (of the first rotation schedule) at that time step. Figure 10 illustrates this concept and is similar to Figure 9, but differs in that the thickest line represents the average rotation angle instead of the minimum rotation angle. There may only be one average rotation angle for each time step.

[0077] In 420, this simplified second rotation schedule allows for a more manageable modeling of solar panel output at a solar power site. For example, a performance modeling program can model the entire solar power site as a single array of trackers, all of which can be set to rotate at either a minimum rotation angle or a calculated average angle (selected as needed). In this way, even a performance modeling program with strict modeling constraints, such as forcing a single angle for all trackers in the site, can obtain reasonably accurate results for a terrain-adaptive backtracking solar power site.

[0078] Limit backtracking schedules can be used to model terrain-adaptive backtracking strategies for ganged trackers. A solar power site can be divided into groups of ganged trackers. Each set of ganged trackers is set to a separate limit backtracking schedule group. Each group tracks independently of the others based on its own limit backtracking schedule. In other words, each ganged tracker is set to its own unique minimum rotation angle at each time step, so different ganged trackers may have different minimum rotation angles at the same time step. This allows for finer control while maintaining the efficiency of the limit backtracking schedule.

[0079] Furthermore, or in addition to or instead of simplifying the rotation angle, it is also possible to use the calculated average of the torque tube axis angles of all trackers as the tilt angle. This average tilt angle becomes the input tilt angle to the performance modeling program, thereby forcing the entire solar site to be modeled as identical trackers with the same tilt angle. Alternatively, it is possible to keep the axis tilt angles of all trackers in the same group horizontal.

[0080] Retro-transposition

[0081] Many performance modeling programs use global horizontal irradiance (GHI) and diffuse horizontal irradiance (DHI) as inputs, but some modeling programs may allow GPOA as an additional or alternative input.

[0082] In certain situations, the GPOA of a plant or site is calculated or measured externally. For example, a sensor measuring the site's GPOA may be installed on-site at a physically installed solar power site. When the GPOA is imported into a performance modeling program, some of these programs convert it back to GHI and DHI. This is because programs such as PVSyst® always start their calculations from GHI and DHI. The converted GHI and DHI are then converted back to obtain a new GPOA (potential value) that is actually used in the simulation model to calculate the site's energy. However, the results of this inversion and reconversion process depend heavily on the underlying conversion model and the assumed rotation angle. PVSyst uses the Hay model for inversion, and the backtracking schedule specified by PVSyst may be a standard GCR-based schedule rather than a desirable terrain-adaptive backtracking strategy (such as one obtained from raycasting). A lack of choice or the use of potentially undesirable model backtracking schedules can lead to inaccurate results in performance modeling. Instead of importing an external GPOA, importing modified or adjusted GHI and DHI yields more accurate results regarding the behavior of terrain-adaptive backtracking. After conversion by the modeling software, the GHI and DHI should be adjusted so that the final GPOA used in the simulation actually matches, or substantially matches, the GPOA of the tracker employing a terrain-adaptive backtracking strategy, even if the modeling program uses a GCR-based schedule. The modified GHI and DHI can be computed externally by retro-transposing. Figure 11 illustrates this process.

[0083] In step 505, the external GPOA of the solar array at the installation site is obtained. The external GPOA may be obtained, for example, by physical measurements using sensors at the installed solar site with a terrain-adaptive backtracking strategy, or by calculating it from the measured GHI·DHI of the site and the terrain-adaptive backtracking schedule used by the on-site tracker.

[0084] In 510, a GCR-based backtracking / rotation schedule is obtained. For example, a performance modeling program may provide and / or enforce a standard GCR-based backtracking angle schedule.

[0085] In 515, the schedule and external GPOA are inversely transformed. For example, this external GPOA can use an external program with the pvlib_gti_dirint function, which utilizes the Perez transform and a standard GCR-based backtracking angle schedule. This allows the external program to inversely analyze the GHI and DHI required to obtain the same amount of planar array solar radiation as a terrain-adaptive backtracking strategy in a GCR-based backtracking simulation. While this adjusted GHI and DHI do not necessarily represent the physical and / or exact GHI and DHI of the relevant solar site, inputting them into the performance modeling program in 520 can lead to the calculation of a final GPOA that matches or substantially matches the site's external GPOA (GPOA calculation may involve running simulations using a 3D model of the array). This accurate, or more accurate, GPOA can be obtained even if the performance modeling software forces a GCR-based backtracking schedule that differs from the terrain-adaptive backtracking schedule used or desired for the solar site. As a result, the performance of sites using terrain-adaptive backtracking schedules can be more accurately modeled in programs where such schedule inputs are not permitted, and / or programs that do not adequately utilize the measured GPOA of the site. Consequently, in 525, performance modeling programs can use this more final and accurate GPOA to appropriately determine the accurate, or more accurate, output of the solar site.

[0086] Average transformation

[0087] Depending on the size of the solar power site and the number of bays, some performance modeling software may not have the capability to calculate the GPOA for the number of bays required to apply a custom method to the entire site. In this case, if the POA calculated externally can be imported into the modeling software, the total POA for the entire site can be calculated by using the modeling software to obtain the POA for each bay individually. For example, the POA can be determined using the backtracking schedule and / or the bay normal vector, the solar normal vector, and solar irradiance. Once the POA for each bay is calculated, a weighted average can be created using weights corresponding to the number of modules in each bay. Alternatively, the POA for each bay can be obtained by means other than modeling software, such as when the calculation is simple enough that modeling software is not required. In either case, the resulting total POA (e.g., GPOA) can be input into the modeling software. This process can be performed at each time step of the backtracking schedule.

[0088] For example, if you have a tracker for a 3-bay solar power site, with 1 module, 2 modules, and 5 modules in each bay, the tracker's POA can be averaged as follows: GPOA = 1 / 8 × POA1+ 2 / 8 × POA2+ 5 / 8 × POA3 Here, POA1 represents the planar array solar irradiance of bay 1, POA2 represents the planar array solar irradiance of bay 2, POA3 represents the planar array solar irradiance of bay 3, and GPOA represents the plant / site weighted average planar array solar irradiance. In other words, the POA of each bay is weighted based on the ratio of the number of modules in that bay to the total number of modules in the site, and the site's POA is the sum of the weighted values ​​of each bay. This method is called averaging at the plant level because, in this case, there is only one tracker in the plant. Using this method, an intermediate approximation is possible between modeling the individual transformations of each bay and modeling the entire plant as flat. By employing different averaging strategies based on this method, even more intermediate models can be created. For example, if the modeling software in question supports input of multiple array surface solar irradiance time series data, the model can be further subdivided by averaging at the inverter level, the maximum power point tracker level, the tracker level, and even the string level. That is, a solar site consists of multiple solar arrays, and each array consists of one or more modules. Each solar array can be selected as all modules connected to an individual inverter, all modules constituting an individual tracker or bay, or all modules constituting an individual string (which may include multiple strings, such as two strings where bays are physically adjacent). Following the above technique, multiple "GPOAs" can be obtained for each solar array. These GPOAs can be used for performance modeling to calculate the power generation of a solar site. For example, they can be input into performance modeling software that models the power generation of a solar site based on inputs from multiple array faces. If further subdivision is desired without implementing special modeling techniques, it should be assumed that the model accuracy will improve accordingly with each step down of averaging. The averaging transformation can be created using pvlib (a performance simulation tool for solar power systems). The averaging transformation may underestimate the plant's mismatch losses, which may result in the modeled energy being higher than the actual energy.

[0089] Figure 12 shows an embodiment of the invention described above. In 605, the transposition of individual bays (or any other array of modules) is obtained. In 610, the weighted average global plane (GPOA) of the array is obtained as described above. In 615, the amount of power generated is determined based on the weighted average GPOA, for example by inputting the GPOA into a performance modeling program.

[0090] As described above, raycasting can be used to obtain an optimal backtracking schedule adapted to a solar power site installed on a slope. This prevents shading between rows of adjacent trackers. Obtaining this backtracking schedule via raycasting helps ensure that the results are as accurate as possible to actual performance, even after subsequent simplifications performed for performance modeling.

[0091] To begin the raycasting process, it is necessary to obtain elevation-encoded location points for a specific solar array installation site. These points describe a series of rectangular polygons. Each rectangular polygon encloses a contiguous group of solar modules that share a common plane and have parallel normal vectors. For example, each rectangular polygon may enclose one bay. A tracker may consist of multiple solar module bays. Each bay is a group containing one or more solar modules. Each bay can be positioned on a torque tube. Each bay is between two bearings and / or foundations, allowing for angular changes between bays. This angular change is either in the north-south direction or the east-west direction.

[0092] After the solar angle is determined for the highly encoded position points, a true tracking angle schedule is created for each tracker.

[0093] The true tracking angle is obtained by maximizing the collected irradiance by minimizing the angle of incidence relative to the solar module normal. Single-axis trackers are not typically oriented directly towards the sun (e.g., the sun is to the south of the tracker). Therefore, to minimize the angle of incidence of sunlight, the solar module normal is matched to a projection onto a plane swept across the entire range of motion of the solar module normal by the sun's position. This matched solar module normal is the tracker's true tracking angle, and its variation throughout the day generates the angle schedule.

[0094] Using only these true tracking angles could lead to significant power loss due to adjacent tracker solar modules shading each other. By obtaining backtracking angles, trackers can avoid shading while tracking as faithfully as possible to the true tracking angle. These backtracking angles are obtained through raycasting.

[0095] By using a true tracking angle schedule, the orientation of the sun relative to each rectangular polygon (i.e., each solar module bay) can be determined. This schedule includes the true tracking angle for each time step over the target period (e.g., an entire day, an entire month, an entire year).

[0096] To begin the raycasting process, it is necessary to obtain location points with height information for a specific solar array installation site. For example, a 3D shape can be constructed using a tracker layer drawn in CAD, and highly encoded location points can be obtained from this construction. These points describe a series of rectangular polygons. Each rectangular polygon encloses a continuous group of solar modules that share a common plane and have parallel normal vectors. For example, each group of rectangular polygons may form a cuboid enclosing a bay. Alternatively, the highly encoded location points may form any polyhedron that is not necessarily a cuboid. The tracker may consist of multiple solar module bays. Each bay may be a group containing one or more solar modules. Each bay may be located on a torque tube. Each bay may be located between two bearings and / or foundations that allow for angular changes between bays (either north-south or east-west). Each bay extends beyond the two bearings and / or foundations and may be defined by the length of a section of the torque tube with start and end points at different inclination angles from the specified bay.

[0097] After the solar angle is calculated for the highly encoded position points, a true tracking angle schedule is created for each tracker.

[0098] The true tracking angle is obtained by maximizing the amount of solar radiation collected by minimizing the angle of incidence relative to the solar module normal. Single-axis trackers are not typically oriented directly towards the sun (e.g., the sun is to the south of the tracker). Therefore, to minimize the angle of incidence of sunlight, the solar module normal is aligned with the projection of the sun's position. This projection is formed on the plane swept by the solar module normal across its entire range of motion. This aligned solar module normal is the tracker's true tracking angle, and its variation throughout the day generates the angle schedule.

[0099] These true tracking angles alone can lead to an undesirable phenomenon where adjacent tracker solar modules block each other's light when the sun is low in the sky in the morning or evening, resulting in significant power loss. By obtaining backtracking angles, trackers can avoid blocking each other while still tracking as faithfully as possible to the true tracking angle. These backtracking angles can be obtained through raycasting.

[0100] By using a true tracking angle schedule, the orientation of the sun relative to each rectangular polygon (i.e., each solar module bay) can be determined. This schedule includes the true tracking angle at each time step throughout the target period (e.g., an entire day, an entire month, an entire year).

[0101] To begin raycasting, we directly (e.g., computationally) trace the light from the light source, the sun, to each bay. In the simplest implementations of inverse ray tracing programs, such as those used in the film and video game industries, the ray starts at the "camera," passes through pixels on the screen into the scene, and is ultimately traced towards the light source. Since a realistic image is not always necessary to determine whether shadows are cast by direct sunlight, we can exclude the camera and screen objects from the problem and trace the light from the light source (sun) rather than tracing towards the light source. First, we select a specific starting tracker to define the direction of the generated ray. The starting tracker may be the westernmost or easternmost tracker in the entire array of trackers on the site. The starting tracker may be the tracker on the opposite side of the sun, or the tracker furthest from the sun in the array. As a first example, if the sun rises in the east in the morning, we can select the westernmost tracker as the starting tracker. Alternatively, the starting tracker does not have to be the furthest from the sun; it could be the closest tracker to the sun, or a tracker that is neither the closest nor the furthest from the sun.

[0102] This start tracker can generate a pair of rays for each bay within the tracker. To reduce total computation time, each ray can be defined by a starting point corresponding to a bay corner and a direction corresponding to a unit vector coming from the direction of the sun. At a minimum, two rays can be generated from the sun toward each bay, directed toward the two upper corners of that bay (for example, the northern and southern corners furthest from the ground vertically if the solar module is tilted at an angle greater than 0 degrees). These two rays alone, generated toward the upper corners, can determine shading with reasonable accuracy, if not perfect, saving processing time compared to generating many rays. If neither of these two rays hits the bay behind the generation bay, it is unlikely that any other rays generated toward the start tracker will shade the bay behind the start tracker. Therefore, these two rays indicate that shading is unlikely to occur. If either ray hits, the ray passing between them will also hit, allowing shading to be determined without generating more than two rays. This optimization eliminates the need to generate rays at the bottom two corners of the generation bay. However, this is not a requirement, and any number of rays, from two to several million, can be generated for each bay. For example, the top edge of bay 4 can have between two and sixteen rays, between 256 and 65,536 rays. More rays require more computational power and time, but allow for a more reliable determination of whether or not shading occurs. Even when generating more than two rays, it is possible to generate one ray at each top corner and additional rays at the top edge of the bay between the top corners. However, this is not a requirement, and rays may also be generated at other edges of the bay or inside the bay outside the edges.

[0103] The generated rays are created in the sense that they take the limit of the rays approaching the corner of the generation bay. In a physical sense, depending on quantum theory, these rays may be partially blocked in reality, but in a classical sense they are not blocked and they graze the corner of the generation bay and proceed to the bay behind the generation bay.

[0104] When rays are generated toward a generation bay, their trajectories are known in relation to bays behind the generation bay. These bays may be on trackers directly adjacent to the generation bay's tracker, or they may be on the opposite side of the sun from the generation bay. These bays are important because they may be shaded by the generation bay. In other words, because they are located within the "field-of-view" of the generation bay, rays generated toward the generation bay may potentially intersect with these other bays (hereinafter referred to as field-of-view bays). An intersection check is performed on these field-of-view bays. If a generated ray intersects with a field-of-view bay, the intersection check is positive. A positive intersection check means that the generation bay is occluding the field-of-view bays at that time step.

[0105] Figure 6 shows the intersection of a ray 130, generated toward a first bay 117 (top of the page) that is tilted away from the horizontal plane, and a second bay 117 (bottom of the page). The axes represent the three dimensions of the bays and the positions of the rays. The sun (not shown), which the ray 130 is tracking, is located at the top of the page. The ray 130 is tracked toward one of the upper corners of the first bay 117 and grazes that corner (the direction of gravity is to the right on the page). The ray 130 intersects the second bay 117. A positive result of this intersection test means that the first bay 117 is blocking the second bay 117 when the first and second bays 117 are in this angular arrangement.

[0106] Therefore, the generating bay tracker, the occluding bay tracker, or both trackers can be backtracked by a predetermined amount (e.g., 1-5 degrees, 1-3 degrees, or 1 degree). Backtracking may occur after testing all generating bays within a single tracker, or after testing the first generating bay and / or each generating bay within a single tracker. Backtracking means tilting the solar panel to a flat or horizontal position (e.g., nearly parallel to a level ground or nearly parallel to a direction perpendicular to Earth's gravity). Both trackers may be backtracked by the same amount, or by different amounts. In embodiments of the present invention, after both trackers have been backtracked, the residual occlusion determination by raycasting described above is repeated until there is no more occlusion. Therefore, new rays are generated on the backtracked generating bays, and cross-tests are performed on the backtracked in-field bays. If occlusion still exists, the trackers for both bays are backtracked again by a predetermined amount. This ray tracing and backtracking cycle is repeated until the generating bays no longer occlude any in-field bays.

[0107] Rays generated by a generation bay may undergo intersection testing with multiple bays within the field of view, depending on the number of bays present within the generation bay's field of view. Due to terrain and other factors, in certain installation locations, each bay within a tracker may not perfectly coincide with a bay in an adjacent tracker; this discrepancy is referred to as the east-west cross axis. The northernmost and southernmost points of the generation bay define the field of view of the generation bay (for optimization purposes, the field of view is defined restrictively here). Adjacent bays located behind the generation bay, whose northernmost or southernmost point lies within the generation bay's field of view in the cross axis direction, are considered relevant in-field bays for intersection testing. For example, this applies when the southernmost point of the first adjacent bay lies between the northernmost and southernmost points of the generation bay, and the northernmost point of the second adjacent bay lies between the northernmost and southernmost points of the generation bay. Even if the northernmost point of the first adjacent bay is not between the northernmost and southernmost points of the generated bay, and the southernmost point of the second adjacent bay is not between the northernmost and southernmost points of the generated bay, both the first and second adjacent bays are considered in-sight bays and are subject to cross-testing.

[0108] If accuracy is prioritized over calculation speed and / or simplicity, the definition of the field of view can be extended beyond the range shown above. For example, the field of view of a generation bay can include not only adjacent bays within the northernmost and southernmost points in the cross axis direction, but also all bays adjacent to adjacent bays in the axis direction (i.e., on the same tracker as the adjacent bay). Therefore, the crossover test described later can be performed not only on the adjacent bays of the generation tracker, but also on additional bays adjacent to those adjacent bays. This definition of the field of view can be further extended to include even more bays. For example, the field of view of a generation bay may include not only adjacent bays and the bays adjacent to those adjacent bays, but all bays within the adjacent bay's tracker. Specifically, the field of view can include all bays within the adjacent tracker, and all bays adjacent to the adjacent tracker located on the opposite side of the generation bay's tracker from the generation bay's tracker. For example, the field of view can include all bays within the solar site except for the bays within the generation bay's tracker and bays within trackers closer to the sun than the generation tracker (e.g., closer to when measured considering only the east-west direction). Each of these bays within the field of view may be cross-tested by the generation bay, as described later.

[0109] Figure 5 shows the raycasting method in flowchart form. In step 205, module location points are obtained. A solar module site, which is either physically installed at a physical site or virtually constructed and modeled, is selected for raycasting. The site may be an array of solar modules. The array contains solar module trackers, each tracker may have multiple solar module bays, and each bay may have one or more solar modules. Highly encoded location points of the solar modules in the site are obtained. This may include obtaining location points for all bays of all trackers in the site, or location points for only some of the solar modules in the site. Each of these location points may describe a series of rectangular polygons. Each rectangular polygon encloses and / or represents a bay in a tracker.

[0110] In step 210, obtain the true tracking angle schedule. Once the highly encoded location points of the site are known, the true tracking angle schedule can be obtained. The schedule may include the angles of some or all of the bays and / or trackers at each time step. The schedule may consist of equally spaced, uniform time steps. Time steps can be, for example, 5-minute intervals and can span at least one day, one week, one month, or one year. Of course, the time steps and spans can be any time interval, and the time steps themselves may be non-uniform. For example, more important time periods of the day may have finer intervals than other time periods.

[0111] In section 215, you select a time slot for the test. This time slot is chosen from the true tracking angle schedule. This selection can be done sequentially. For example, when starting the test, you can choose the earliest time slot in the timeline. Generally, the next time slot you choose for the test will be the next untested time step in the schedule. Of course, this is not mandatory, and you can choose any time slot for testing depending on the time slot you are particularly interested in.

[0112] In step 220, select a spawning tracker (also referred to as the start tracker in this description). A spawning tracker is defined as a tracker containing a generation bay that generates rays for raycasting. At the start of testing, you can select a spawning tracker from either the east or west end (e.g., the westernmost or easternmost tracker). Otherwise, the spawning tracker is selected from untested trackers directly adjacent to the last tested tracker (e.g., untested in the current timestep). Alternatively, in at least part of this method, you can select non-tracker objects such as trees, rocks, or inverters as alternatives to spawning trackers, and model the effects of non-tracker objects obstructing adjacent bays as described below.

[0113] In step 225, a spawning bay is selected from the spawning tracker. If no other bays in the spawning tracker have been tested yet, the spawning bay is selected from the northernmost or southernmost bay. If any bay in the tracker has been tested, the next spawning bay is selected from an untested bay directly adjacent to the last tested bay (e.g., untested in the current time step). For example, the northernmost bay can be selected at the start of testing, and the southern bay directly below it can be selected as the test target after testing is complete.

[0114] In step 230, raycasting is performed on the selected generation bay. This involves projecting at least two rays from the sun towards the upper corner of the bay, as previously mentioned.

[0115] In step 235, the generated ray is used to determine crossover with at least one adjacent bay adjacent to the generation bay. The adjacent bay may be a tracker directly adjacent to the spawning tracker in the lateral direction. The adjacent bay may also be on the opposite side of the sun in the lateral direction. If at least a portion of the adjacent bays are directly adjacent to the generation bay, multiple adjacent bays are tested. The next part of the method depends on the result of the crossover test. If the crossover test is positive, proceed to step 240 and backtrack at least one of the involved trackers. For example, it is possible to backtrack both the generation tracker and the adjacent tracker that showed a positive crossover test. In embodiments of the present invention, only one of the generation tracker and / or adjacent tracker may be backtracked. This backtracking involves rescheduling so that the final angles of the generation tracker and / or adjacent tracker are replaced with the true tracking angle or previous angle associated with the relevant time step. In any case, after backtracking, proceed again to step 230 and project the ray towards the (backtracked) generation bay. Again at 235, intersection testing of these newly generated rays is performed against the (backtracked) adjacent tracker. This process may be repeated until the (iteratively backtracked) adjacent tracker returns a negative result in intersection testing with rays generated toward the (iteratively backtracked) generation bay.

[0116] If an adjacent tracker returns a negative cross-test, 250 determines whether there are any untested bays in the spawning tracker, i.e., bays that have not yet generated rays at this particular time step in the true tracking schedule. If so, the process proceeds to 225, where the next spawning bay is selected. Spawning bays can be selected sequentially as described above, or arbitrarily from any remaining untested bays.

[0117] If there are no untested bays remaining in the spawn tracker, step 255 determines whether there are any untested trackers across the entire solar array site. That is, it determines whether there are any trackers in that bay that have not yet been raycasted at this particular time step in the schedule. If so, proceed back to 220 and select the next spawn target tracker as described above. If not, proceed to 260 and determine whether there are any untested time steps in the true tracking angle schedule (i.e., time steps in the site where no bays have been raycasted). If so, select it at the next test target time step 215 in the schedule (e.g., the time step immediately following the most recently tested time step). If not, terminate the process.

[0118] Because ray tracing is a time-consuming process, several techniques can be implemented to solve the problem in a reasonable amount of time. These techniques include reducing the amount of cross-testing required by selecting only reasonable objects that are likely to block direct radiation, and parallelizing the ray tracing process. For example, multiple instances of the technique shown in Figure 5 can be run simultaneously on multiple processors or multiple computers. For instance, a solar power site can be divided into zones, and the technique in Figure 5 can be run in parallel in each zone.

[0119] Thus, by using raycasting at a solar power site with a predetermined tracking angle schedule, it may be possible to obtain a modified tracking angle schedule that increases power generation beyond the predetermined schedule. These methods used to increase power generation are particularly advantageous compared to conventional methods because they can be applied to hypothetical solar tracking equipment sites that have not yet been constructed, allowing for a more accurate determination of the power generation of a particular site before deciding on the potentially high investment of installing solar tracking equipment at the site.

[0120] Alternatively, or in addition to, raycasting, methods for obtaining a backtracking schedule include using point projection onto a plane and point-in-polygon tests to discover and reduce / remove shading. Figure 25 illustrates this process.

[0121] In step 805, the model shape of the solar site is defined by 3D points representing the trackers and bays that make up the solar array, and their initial rotational orientations at a given time. Each tracker, bay, and / or module within a tracker / bay can be a polygon defined by four vertices (determined, for example, by the elevation-coded position point described above in relation to raycasting). The trackers are positioned with spacing and orientation adjustments relative to each other, similar to a physical site, as if they were placed on the undulating terrain of a physical site (e.g., including axial and / or cross-axis inclinations).

[0122] This model represents the xy-plane, the solar position vector, and the plane normal perpendicular to the solar position vector. The solar position vector is determined by the position of the sun (azimuth and zenith angles) at a given time and a selected point, and can be extended to any point between and / or passing through both points. The selected point is located on or near the solar array and may be set on the xy-plane. The plane normal to the solar position vector can be modeled at any point on the solar position vector up to any distance from the selected point. For example, the selected point and / or the normal plane can be located at a distance from zero to twice the longest side of the solar array.

[0123] In step 810, the solar array is projected onto the normal plane to form a first projection. This allows for the identification of locations where module overlap occurs within the solar array as viewed from the sun's perspective. This projection flattens the 3D points representing the trackers and bays that make up the solar array onto the normal plane, although at this stage, the x, y, and z coordinates may remain non-zero in the first projection.

[0124] In 815, the first projection is reprojected onto the xy-plane to form the second projection. In the second projection, the calculation can be simplified by setting the z-coordinate of all points to zero.

[0125] In the 820 system, polygon interior point determination is performed using z-depth information from the solar array configuration. The z-depth information is obtained from the position of the sun and indicates the direction from which the shadow falls. For example, if the trackers are arranged in an approximate north-south direction and the sun is west of due south, the polygon interior point determination starts with the westernmost tracker and checks whether it is occluding the adjacent tracker to the east. The system moves sequentially from west to east along the trackers, checking for occlusion in each tracker pair. If the sun is in the east, the system starts with the easternmost tracker and its adjacent tracker to the west, and checks sequentially from east to west.

[0126] Polygon interior point determination can be performed on the vertices of a tracker / bay polygon, or on any point in the polygon (e.g., any point between vertices on the sides of the polygon). If the polygon interior point determination is positive, it indicates that a bay located at a vertex of an adjacent polygon is causing inter-column occlusion for that adjacent bay.

[0127] If occlusion is detected, backtracking can be performed on one or more unprojected trackers / bays in the 3D solar array. That is, the unprojected polygons representing the trackers / bays are rotated to position at least one of them in the array at the new angle. Backtracking is performed in units of less than one degree. For example, if it is found that the first tracker is occluding the second tracker, backtracking is performed on either the first or second tracker, or both. This process is performed similarly for all tracker pairs in the solar array where occlusion occurs.

[0128] After all desired shading-generating trackers and / or shading trackers have been backtracked to a predetermined amount, the process can return to 805 if necessary, in which case the solar array is modeled as a backtracked solar array with the backtracked orientation rather than the initial orientation. This loop is repeated until all shading is removed, until one or more (e.g., all) trackers reach zero degrees (horizontal orientation), or until other stopping criteria are met. Other stopping criteria include, if a predetermined amount of backtracking is achieved by one or more trackers before the solar array reaches zero shading, the process stops the loop and sets the desired orientation at that point on the backtracking schedule as the initial orientation of the solar array before backtracking occurred. Alternatively, the desired orientation can be set as one or more predetermined default orientations.

[0129] In either case, the desired orientation of the tracker at a given point in time is determined, and this process can be repeated for the next time step in the backtracking schedule. The time steps in the backtracking schedule can be any interval, such as 5-minute intervals, 3 minutes or less, or 1 minute or less. Once the backtracking schedule is obtained, it can be used in combination with other inputs described above, such as POA, to ultimately model the power generated by the solar array. For example, the backtracking schedule can be input into a program to obtain the POA for one or more bays, such as a solar array for an entire site. This polygon interior point method may be computationally less expensive than the raycasting method.

[0130] The processes and methods described herein may be implemented by hardware computer systems. A computer system may include at least one of a processor, memory, non-volatile storage device, and interface. A typical computer system may include at least one of a processor, memory, a general-purpose central processing unit (CPU) such as a microprocessor, or a dedicated processor such as a microcontroller.

[0131] Memory can include, but is not limited to, random access memory (RAM), such as dynamic RAM (DRAM) and static RAM (SRAM). Memory can be local, remote, or distributed. The bus can also connect the processor to non-volatile storage devices. Non-volatile storage devices often include magnetic floppy disks, hard disks, magneto-optical disks, optical disks, read-only memory (ROM) such as CD-ROMs, EPROMs, and EEEPROMs, magnetic and optical cards, or other forms of storage for storing large amounts of data. Some of this data is often written to memory by direct memory access (DNA) processes when software is executed on the computer system. Non-volatile storage devices can be local, remote, or distributed. Non-volatile storage devices are optional because they allow for the construction of systems that hold all applicable data in memory.

[0132] Software may be stored in non-volatile memory. In fact, for large programs, it may be impossible to store the entire program in memory. However, it should be understood that in order to run software, it is moved to a computer-readable location suitable for processing as needed, and for explanatory purposes, this location will be referred to as memory. Even when software is moved to memory for execution, the processor may use hardware registers to store values ​​related to the software, and ideally, a local cache to improve execution speed. When a software program is said to be "implemented in a computer-readable storage medium," it can be assumed that the program is stored in a known or appropriate location (from non-volatile memory to hardware registers). When a processor is said to be "configured to run a program," it means that at least one value related to the program is stored in a processor-readable register.

[0133] This computer system may be compatible with, as part of, or implemented through a cloud-based computing system. In this specification, a cloud-based computing system means a system that provides virtualized computing resources, software, and / or information to client devices. Computing resources, software, and / or information may be virtualized by maintaining centralized services and resources accessible to edge devices via communication interfaces such as networks. “Cloud” is a marketing term and, for the purposes of this specification, may include any network described herein. Cloud-based computing systems may involve service subscriptions or may use a pay-as-you-go model. Users may access the protocols of the cloud-based computing system through a web browser or other container application deployed on a client device.

[0134] A computer system can be implemented as an engine, as part of an engine, or through multiple engines. As used herein, "engine" includes at least two components: 1) a dedicated or shared processor, and 2) hardware, firmware, and / or software modules executed by the processor. Depending on implementation-specific considerations and other circumstances, an engine may be centralized or its functions distributed. An engine may include dedicated hardware, firmware, or software implemented on a computer-readable medium for execution by the processor. The processor may transform data into new data using implemented data structures and methods, such as those described with reference to the drawings herein.

[0135] The engines described herein, or engines that enable the implementation of the systems and devices described herein, may be cloud-based engines. A cloud-based engine may refer to an engine that can run applications and / or functionalities using a cloud-based computing system. All or part of the applications and / or functionalities may be distributed across multiple computing devices and are not limited to a single computing device. In some embodiments, a cloud-based engine can run functionalities and / or modules that end users access via a web browser or container application without installing those functionalities and / or modules locally on the end user's computing device.

[0136] A datastore can include a repository with any applicable data organization method, including tables, comma-separated value (CSV) files, conventional databases (e.g., SQL), and other applicable known or convenient organizational formats. A datastore can be implemented, for example, as software, firmware, hardware, a combination thereof, embodied on a physical computer-readable medium on a purpose-specific machine, or as an applicable known or convenient device or system. Datastore-related components, such as database interfaces, can be considered "parts" of the datastore, parts of other system components, or a combination thereof, but the physical location or other characteristics of datastore-related components are not important for understanding the techniques described herein.

[0137] A data store can contain data structures. A data structure may be associated with a method of storing and organizing data within a computer for efficient use within a specific context. A data structure may be based on a computer's ability to retrieve and store data at any location in memory (specified by an address). This address is a bit sequence stored in memory and manipulable by a program. Therefore, some data structures rely on arithmetic calculation of data item addresses, while others rely on storing data item addresses within a structure. Many data structures utilize both principles, sometimes combined in complex ways. An implementation of a data structure may include a description of a set of procedures for creating and manipulating instances of that structure. A data store can optionally be a cloud-based data store. A cloud-based data store may refer to a data store compatible with cloud-based computing systems and engines.

[0138] Figure 13 is a block diagram of a machine in an exemplary form of computer system 320, within which instructions for causing the machine to perform one or more of the methodologies discussed herein are stored and / or executed. The machine can operate as a standalone device or be connected to other machines (e.g., a network). In a networked deployment, the machine may operate as a server or client machine in a server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The device may be a personal computer (PC), tablet PC, set-top box (STB), personal digital assistant (PDA), mobile phone, web appliance, network router, switch, bridge, or any device capable of executing instructions (sequential or otherwise) that define the actions the device should perform. Furthermore, although only a single machine is illustrated, the term “machine” shall be interpreted to include a collection of machines that individually or collectively execute a set (or more sets) of instructions to perform one or more of the methodologies discussed herein.

[0139] The illustrated computer system 320 includes a processor 326 (e.g., a central processing unit (CPU), a graphics processing unit (GPU), or both), main memory 329, and static memory 332, which communicate with each other via a bus 323. The computer system 320 may further include a video display device 340 (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)). The computer system 320 also includes an alphanumeric input device 346 (e.g., a keyboard), a user interface (UI) navigation (or cursor control) device 343 (e.g., a mouse), a disk drive device 349, a signal generator 352 (e.g., a speaker), and a network interface device 335 connected to a network 338.

[0140] The disk drive unit 349 (e.g., a hard disk) may include a computer-readable medium containing a set of one or more data structures and instructions (e.g., software and / or algorithms) that embody or utilize one or more of the methodologies or functions described herein. The instructions may reside entirely or at least partially in the main memory 329 and / or processor 326 during execution by the computer system 320. The main memory 329 and processor 326 may also constitute a machine-readable medium. The instructions may reside entirely or at least partially in static memory 332.

[0141] The term “machine-readable medium” may include a single or multiple mediums (e.g., a centralized or distributed database, and / or associated caches and servers) that store one or more instructions or data structures. The term “machine-readable medium” is interpreted to include any tangible medium capable of storing, encoding, or holding instructions for execution by a machine and causing the machine to execute one or more methodologies of this embodiment, or data structures used or associated with such instructions. Accordingly, the term “machine-readable medium” is interpreted to include, but not be limited to, solid-state memory, as well as optical and magnetic media. Specific examples of machine-readable media include non-volatile memory (semiconductor memory devices (e.g., erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), flash memory devices, etc.)), magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and compact disk read-only memory (CD-ROM) and digital versatile disk (or digital video disk) read-only memory (DVD-ROM) disks. Machine-readable media may also include random access memory (RAM) (such as dynamic RAM (DRAM) and static RAM (SRAM)).

[0142] Instructions may also be transmitted or received via a communication network 338 using a transmission medium. Instructions may be transmitted using a network interface device 335 and one of many known transport protocols (e.g., HTP). Examples of communication networks include LANs, WANs, the Internet, cellular networks, POTS networks, and wireless data networks (e.g., WiFi and WiMAX networks). The term “transmission medium” is interpreted to include any intangible medium on which instructions for machine execution can be stored, encoded, or transmitted, including digital or analog communication signals and other intangible media that facilitate communication of such software. The network interface device 335 may include one or more modems, network interface cards, wireless network interfaces, or other interface devices such as those used for connecting to Ethernet, Token Ring, or other types of networks.

[0143] Embodiments of the computer system may not require all the elements shown in Figure 7, and therefore the elements shown in Figure 7 may be optional. For example, embodiments of the computer system used to implement embodiments of the present invention may not include the signal generator 352 or the cursor control device 343.

[0144] Some of the detailed descriptions in this specification are presented using algorithms and symbolic representations of operations on data bits in computer memory. These algorithmic descriptions and representations are the means used by experts in data processing technology to most effectively communicate the nature of their work to others skilled in the art. Here, and generally, an algorithm is conceptualized as a self-consistent set of steps leading to a desired result. These steps require the physical manipulation of physical quantities. Usually (but not always), these physical quantities take the form of electrical or magnetic signals that can be stored, transferred, combined, compared, and otherwise manipulated. For mainly conventional reasons, it is sometimes convenient to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, etc.

[0145] However, it should be noted that all these and similar terms should be associated with appropriate physical quantities and are merely convenient labels attached to those quantities. Unless otherwise stated, as will be evident from the following descriptions, throughout this specification, any use of terms such as “processing,” “calculation,” “calculation,” or “determination” refers to the actions and processes by which a computer system or similar electronic computing device manipulates and transforms data represented as physical (electronic) quantities in its registers or memory, and converts it into other data represented as similar physical quantities in the computer system’s memory, registers, or other information storage, transmission, and display devices.

[0146] This disclosure also relates to apparatus for performing the operations described herein. Such apparatus may be built specifically for a required purpose, or may consist of a general-purpose computer that is selectively operated or reconfigured by computer programs stored within the computer. Such computer programs may be stored in computer-readable storage media. Storage media include, but are not limited to, any type of disk connected to a computer system bus, including, but not limited to, floppy disks, optical disks, CD-ROMs, magneto-optical disks, read-only memory (ROM), random access memory (RAM), EPROM, EEPROM, magnetic or optical cards, or any type of medium suitable for storing electronic instructions.

[0147] The algorithms described herein are not specific to any particular computer or other device. Various general-purpose systems, messaging servers, or personal computers can be used with programs following the teachings herein, or it may be convenient to construct more specialized devices to perform the necessary method steps. The structures required for these various systems are described above. Various programming languages ​​can be used to implement the teachings of the disclosures described herein.

[0148] Examples of solar power sites

[0149] For model generation, a real-world solar array system installed in the United States was selected. This system is built with terrain-adaptive trackers that include stake-to-stake azimuth and angular variation. For each model, a tracking schedule was generated using the actual physical shape of the site. The Perez transpose model was used for all models. All models use hourly TMY weather datasets (38% diffusivity) based on the NSRDB PSMv3 model. A rigorous study comparing the effects of 5-minute and hourly interval data in terrain-following performance modeling has shown that the impact of shorter time intervals on the overall model results is almost negligible. Figure 20 shows a 3D model of a solar site. The trackers are oriented north-south and arranged in four independent columns. The x, y, and z axis intervals are shown as numerical values ​​in italics.

[0150] a.) Topography: The project modeled in this paper is located on hilly terrain and therefore slopes in all directions, although the majority of the site is predominantly northeast-facing. Table I shows statistics for torque tube axis tilt angle, cross axis tilt angle, and axis tilt angle mismatch. Torque tube axis tilt is reported from south to north, and a positive value indicates that the module is tilted toward the southern horizon. A histogram of torque tube axis tilt per bay at the solar site is shown in Figure 15. Cross axis tilt is reported from west to east, and a positive value indicates that a particular bay has a lower elevation angle than a bay located due east. A histogram of cross axis tilt is shown in Figure 16. The negative peak in the distribution indicates that most trackers in the system have a lower elevation angle than the tracker located due west. The calculation process for cross axis tilt is difficult for trackers where the torque tubes are not continuous, because the torque tube axis angle of a particular bay may differ from the angle of a bay located due east or due west. Furthermore, bays may be offset to the north or south relative to bays directly to the east or west. In all cases, the center point of each bay was used for comparison, and it was assumed that there were no differences in torque tube axis tilt. Differences in torque tube axis angle when comparing a particular bay with another bay on another tracker located in the cross axis direction are classified as axis tilt mismatches. For example, if the north-south torque tube axis tilt of bay 1 on tracker 1 is 1 degree, and the north-south torque tube axis tilt of bay 1 on tracker 2, which is due east, is 2 degrees, the resulting axis tilt mismatch is -1 degree. Only bays that are being compared for cross axis tilt are included in the comparison for axis tilt mismatches. The histogram of axis tilt mismatches is shown in Figure 17. The concentration of peaks around 0 degrees indicates that most trackers have no difference in north-south torque tube axis tilt with adjacent cross axis trackers. Table I Site topographic characteristics (unit: degrees) TIFF2026518010000002.tif39155

[0151] b.) Backtracking: In the field, the time step of backtracking accounts for approximately 20% of the total solar radiation tracking time step. This 20% time step has a proportionally small impact on the total transposed solar radiation compared to the true tracking time step. This is because backtracking is limited to sunrise and sunset when the sun is low in the sky. Assuming a flat model, the backtracking time step contributes to approximately 16% of the total array plane radiation. As ground cover increases, the time the system spends on backtracking increases. As the proportion of diffuse radiation increases, the amount of direct radiation that can be captured from the radiation component decreases.

[0152] Table II shows the results of nine transpose modeling techniques used to model the system. For emphasis, three main results are shown in bold. The first, "GCR-based," represents the case when the site is operated on terrain using a standard GCR-based backtracking algorithm. "Average transpose" represents the expected transpose when the site is operated using a terrain-adaptive backtracking algorithm. "Flat model" represents the case when the system is modeled assuming it is built on flat ground. This table is sorted in ascending order of transpose gain, and a reference column is provided to allow each result to be easily compared with the underlying techniques described herein. Global horizontal solar radiation used in the meteorological file is listed at the end of the table for reference. Table II Example solar power site: Backtracking POA TIFF2026518010000003.tif67153

[0153] Table II shows that when using a standard GCR-based backtracking strategy with a GCR of 0.36, approximately 6% of effective transposition was lost due to terrain shading compared to a model assuming a flat site. Effective transposition was calculated by limiting the contribution of a specific bay to the total transposed solar radiation of the plant to the diffuse component only at the time step in which shading occurred. Although this loss is an approximation, its magnitude is consistent with a more rigorous model. Increasing the GCR to 0.42 can recover approximately 2% (absolute value) or 33% (relative value) of the lost transposition. Furthermore, using a terrain-adaptive raycasting method, an additional 2.4% (absolute value) or 73% (relative value) of lost transposition can be recovered. These model results are in very good agreement with field test results mentioned in previous studies. Figures 18a and 18b compare the rotation angles and resulting array solar radiation obtained from backtracking strategies based on various ground cover rates with the rotation angles and array solar radiation based on raycasting. Figure 18a shows the average bias of the tracker rotation angle when comparing a standard backtracking algorithm and limiting ray projection using different GCRs, and Figure 18b shows a comparison of available unshielded POAs and adaptive backtracking using different GCRs. Terrain-adaptive backtracking outperforms all ground cover-based backtracking strategies at the site.

[0154] In the table above, averaging only the axis inclination allows us to simulate a terrain with a northward inclination of only 1.07 degrees and no east-westward gradient. This allows us to estimate that approximately 0.9% of the total transpose loss is due to the northward inclination of the site. This amount of energy cannot be recovered by a terrain-adaptive backtracking plan at this site. On the other hand, assuming the axis inclination is horizontal and averaging only the rotation angle, we assume a terrain with no north-southward inclination but a change in inclination in the east-west direction. This allows us to infer that the cross-axis inclination and the resulting backtracking cause a similar 0.9% decrease. You may notice that the linear sum of both elements, 1.8%, does not match the 2.4% transpose gain difference observed with the average transpose method. The additional loss may be due to the mismatch in axis inclination, but since the amount of mismatch in axis inclination is small at this observation site, it can be inferred that the contribution of this element is small. The difference is inferred to be due to the nonlinearity of the Perez transpose model.

[0155] Another noteworthy finding is that averaging the time-series data of the tracker's rotation angle and the tracker's axial tilt before calculating the transpose yields an energy gain nearly equivalent to calculating the transpose for each bay individually. Calculating the transpose after averaging the rotation angle and tracker axial tilt removes information necessary to calculate subsequent electrical mismatches inherent in most utility-scale sites that lack module-level maximum power point tracking capabilities, but improves calculation speed. In practice, this method is likely to underestimate electrical mismatch losses, leading to an overestimation of system performance.

[0156] A method for inversely transforming the array surface solar radiation generated by a terrain-adaptive backtracking strategy and then calculating the horizontal solar radiation component required to achieve equivalent array surface solar radiation on a single-axis tracker employing a standard ground-coverage-based backtracking strategy is R 2 A correlation coefficient of 0.9998 was observed. Figure 19 shows a scatter plot comparing the array surface solar radiation with the array surface solar radiation re-transposed by PVSyst.

[0157] c.) True tracking: Table III True tracking TIFF2026518010000004.tif39153 In the case of true tracking, averaging the tilt of the tracker axis resulted in a 1.5% loss. Averaging the relevant tracker angles confirms that the averaged transpose results calculated for each bay can be reproduced. While this appears to be less loss than in the case of backtracking, additional proximity occlusion losses are expected but not modeled here.

[0158] d.) Results: Several possible approaches were tested to demonstrate both ideal and approximate methods that can help bridge the gap between different modeling software in this example solar site. It was demonstrated that using a denser ground cover backtracking algorithm can recover approximately 33% of the losses caused by topographic shading in the modeled site. On the other hand, terrain-adaptive backtracking can recover approximately 70% of the losses caused by topographic shading. In flat terrain, modeling terrain-adaptive backtracking as a standard ground cover-based backtracking system may result in an overestimation of the transpose gain by approximately 2.4%. It was also shown that averaging the rotation angle and torque tube axis tilt variables before calculating the transpose can reasonably approximate a more robust method (at least with respect to transpose) that calculates a custom transpose result for each bay of the system. However, other performance modeling chains are ignored.

[0159] This disclosure is illustrative and not limiting. Those skilled in the art can make further modifications based on this disclosure, which are intended to be within the scope of the appended claims.

Claims

1. A method for modeling the performance of a solar array, Determining the first array plane (POA) of a first bay of a solar array, wherein the first bay contains a first number of one or more solar panels, Determining the second POA of the second bay of the solar array, wherein the first bay contains a second quantity of one or more solar panels, The weighted global POA (GPOA) of the solar array is determined based on the first POA, the second POA, the first quantity, the second quantity, and the third quantity of solar panels in the solar array. Based on the weighted GPOA, predict the power generated by the solar array, A method that includes this.

2. The method according to claim 1, wherein determining the weighted GPOA includes weighting the first POA based on the first quantity and weighting the second POA based on the second quantity.

3. The method according to claim 1, wherein the first bay includes a different number of solar modules than the second bay.

4. The method according to claim 1, wherein the first bay is composed of a single solar module.

5. The method according to claim 1, wherein the first bay includes a plurality of modules.

6. The method according to claim 1, wherein the first bay has a first normal vector, the second bay has a second normal vector, and the first normal vector and the second normal vector are not parallel to each other.

7. moreover, The method according to claim 1, comprising obtaining a backtracking schedule for the solar array before determining the weighted GPOA.

8. The method according to claim 7, wherein obtaining the backtracking schedule includes performing a polygonal point determination to determine the amount of shading in the solar array.

9. The method of claim 8, wherein obtaining the backtracking schedule includes obtaining highly encoded position points of the bays in the solar array and modeling the bays as polygons.

10. Obtaining the aforementioned backtracking schedule means The process involves modeling a solar position vector based on the position of the sun at a predetermined time, and modeling a normal plane that intersects with and is perpendicular to the solar position vector. The method according to claim 9, comprising modeling the x-y plane that intersects the solar position vector.

11. The method according to claim 10, wherein the xy-plane is not parallel to the normal plane.

12. The method according to claim 10, wherein obtaining the backtracking schedule includes projecting the polygon onto a normal plane to obtain a first projection.

13. The method according to claim 12, wherein the step of obtaining the backtracking schedule includes reprojecting the second projection onto the x-y plane.

14. The method according to claim 13, wherein obtaining the backtracking schedule includes backtracking the polygon to obtain a new orientation of the bay in the solar array.

15. The method according to claim 1, wherein the back tracking includes rotating at least one of the polygons by 1 degree or less.

16. To provide a first rotation schedule for a solar panel array of a solar power plant, wherein the first rotation schedule includes a time step and a first rotation angle of the solar panel array at each time step. Determining a second rotation angle in each of the aforementioned time steps, wherein the second rotation angle is based on the first rotation angle in the aforementioned time step, The second rotation schedule is provided, including the aforementioned time steps, and based on the second rotation angle in each time step. Based on the second rotation schedule, the power generated by the solar panel array is determined, A method that includes this.

17. The method according to claim 16, wherein at least some of the first rotation angles in any one of the time steps are different from one another.

18. The method according to claim 16, wherein the second rotation angle is the smallest rotation angle among the first rotation angles in the time step.

19. The method according to claim 16, wherein the second rotation angle is the average rotation angle of the first rotation angles in the time step.

20. The method according to claim 16, wherein providing the second rotation schedule includes associating the second rotation angle in each time step with each solar panel array in the time step.

21. The method according to claim 16, wherein the solar power plant includes bays, each comprising one of the solar panel arrays and a module support on which solar modules are arranged, and at least two of the bays include module supports having different axial tilt angles from each other.

22. The method according to claim 16, wherein determining the amount of power generated includes virtually modeling the solar panel array.

23. The method according to claim 22, wherein the virtual modeling of the solar panel array includes modeling trackers having the same axial tilt angle.

24. The method according to claim 23, wherein the same axial tilt angle is the average axial tilt angle of the solar panel array in the solar power plant.

25. The method according to claim 23, wherein the same axial inclination angle is 0 degrees.

26. The method according to claim 16, wherein the solar power plant is installed on a sloping site.

27. The method according to claim 16, wherein the first rotation angle includes a backtracking angle that prevents inter-row shielding of the solar panel array.

28. The solar panel array includes a first group of solar panel arrays and a second group of solar panel arrays, and further, Determining a third rotation angle in each time step, wherein the third rotation angle is based on the first rotation angle in that time step, To provide a third rotation schedule that includes a time step and is based on the third rotation angle in each time step, Associating the second rotation schedule with the first group, and associating the third rotation schedule with the second group, The method according to claim 16, comprising determining the amount of power generated based on the second and third rotation schedules.

29. The method according to claim 16, wherein providing the first rotation schedule includes obtaining the first rotation schedule using raycasting.

30. Using raycasting, To obtain highly encoded location points corresponding to the aforementioned solar panel array, To provide a preliminary schedule for the preliminary rotation angle of the aforementioned solar panel array, wherein the preliminary schedule includes time steps. To generate a ray toward a first bay of the solar panel array, wherein the first bay is directed toward a first preliminary rotation angle of a first time step, The method involves using the light rays generated for the first bay to determine whether it intersects with the second bay of the solar panel array, wherein the second bay is adjacent to the first bay. Based on the result of the crossover determination, at least one of the first bay and the second bay is backtracked to at least one new rotation angle, Associating at least one new rotation angle with the first time step, The method according to claim 16, including the method described in claim 16.

31. The method according to claim 16, wherein generating the rays includes tracing up to two rays from a first position of the sun in the first time step toward the two upper corners of the first bay.

32. The method according to claim 16, further comprising generating a second ray toward the first bay after backtracking, and using the second ray to perform intersection determination with the second bay.

33. To provide a first global plane (GPOA) for a solar panel array of a solar power plant, To provide a backtracking schedule based on ground coverage ratio (GCR) for the aforementioned solar panel array, The first GPOA is inversely transformed to obtain adjusted total solar radiation (GHI) and adjusted diffuse solar radiation (DHI), A second GPOA is determined based on the adjusted GHI, adjusted DHI, and the backtracking schedule based on the GCR. Based on the second GPOA, determine the energy generated by the solar array over a certain period of time. A method that includes [this].

34. The method according to claim 33, wherein the second GPOA is substantially consistent with the GPOA.

35. The method according to claim 33, wherein the inverse transformation is based on a backtracking schedule based on the GCR.

36. The inverse transform is the method according to claim 33, based on the Perez model.

37. The solar power plant is installed on a sloping site, according to claim 33.

38. The method according to claim 33, wherein the solar power plant includes a tracker, each including one solar panel array.

39. Providing the first GPOA is, The method according to claim 33, comprising providing GHI and DHI of a solar panel array and obtaining a terrain-adaptive backtracking schedule for the solar array.

40. The method according to claim 39, wherein at least one of the GHI and DHI is different from the adjusted GHI and adjusted DHI.

41. The method according to claim 39, wherein providing the terrain-adaptive backtracking schedule includes raycasting.

42. The method according to claim 39, wherein the terrain-adaptive backtracking schedule includes at least one time step in which at least two trackers in a solar array have different rotation angles from each other.

43. The method according to claim 42, further comprising physically rearranging the solar panel array based on the terrain-adaptive backtracking schedule.

44. The method according to claim 33, wherein the GCR-based backtracking schedule includes the same rotation angle with respect to the solar panel array within each time step of the GCR-based backtracking schedule.

45. The method according to claim 33, wherein determining a second GPOA includes transposing the adjusted GHI and adjusted DHI using the Hay model.

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