Solar ray mapping via divergent beam modeling
Systems, methods, and computer-readable media are described herein to model divergent beam ray paths between locations on a roof (e.g., of a structure) and modeled locations of the sun at different times of the day and different days during a week, month, year, or another time period. Obstructed and unobstructed divergent beam ray paths are identified. Unobstructed divergent beam ray paths contribute to the calculation of a solar irradiance value for each location on the roof. Divergent beam ray paths, such as cones or pyramid ray paths, allow for sparse or lower-resolution spatial and/or temporal sampling without sacrificing obstacle detection.
1. A method, comprising:
modeling a ray path between each of a plurality of locations on a surface of a structure and modeled locations of a sun relative to the surface of the structure at each of a plurality of different times during a time period;
identifying a first set of the modeled ray paths that, for their respective locations on the surface and times during the time period, are unobstructed between the surface and the respective modeled locations of the sun;
identifying a second set of the modeled ray paths that, for their respective locations on the surface and times during the time period, are obstructed by an obstacle between the surface and the respective modeled locations of the sun; and
calculating a solar irradiance value for each location on the surface between a first time and a second time based, at least in part, on the identified unobstructed ray paths associated with each respective location on the surface between the first time and the second time.
2. The method of claim 1 , further comprising:
calculating an angle of each modeled ray path relative to a normal of each respective location on the surface of the structure at each of the plurality of different times during the time period,
wherein calculating the solar irradiance value for each location on the surface is further based on the calculated angle of each unobstructed ray path.
3. The method of claim 1 , wherein the surface of the structure is divided into a plurality of polygons, and wherein each location on the surface of the structure corresponds to one of the polygons.
4. The method of claim 3 , wherein the plurality of polygons comprises a plurality of triangles, rectangles, rhombi, or hexagons.
5. The method of claim 3 , wherein each polygon has an edge length between 0.1 and 0.5 meters.
6. The method of claim 1 , wherein each location on the surface of the structure corresponds to a surface area of between 0.01 meters squared and 1.0 meters squared.
7. The method of claim 1 , wherein the time period comprises one of: a month, multiple months, a year, and multiple years.
8. The method of claim 1 , wherein the plurality of different times during the time period for which ray paths are modeled is defined in terms of a number of days and a number of times each day to model the ray paths.
9. The method of claim 8 , wherein the plurality of different times during the time period for which ray paths are modeled is defined such that a ray path is modeled for each location on the surface of the structure between 4 and 48 times each day for between 12 and 365 days for a one-year time period.
10. The method of claim 1 , wherein each ray path is modeled as a line segment between a location on the surface of the structure and the modeled location of the sun.
11. A system for divergent beam ray-path modeling, comprising:
a divergent beam ray-path modeling subsystem to model a divergent beam ray path from each of a plurality of locations on a roof of a structure to a modeled location of a sun at multiple, discrete times during a time period;
a beam path analysis subsystem to:
identify obstructed divergent beam ray paths that are obstructed by an obstacle, and
identify unobstructed divergent beam ray paths; and
an irradiance calculation subsystem to calculate a solar irradiance value for each location on the roof of the structure during the time period based on the identified unobstructed divergent beam ray paths associated with each respective location during the time period.
12. The system of claim 11 , further comprising:
a modeling subsystem to identify the plurality of locations on the roof of the structure as a number of locations corresponding to a spatial sampling resolution; and
an analemma resolution subsystem to identify the multiple, discrete times during the time period as a number of times each day and a number of days during the time period for which a divergent beam ray path is modeled from each location on the roof of the structure.
13. The system of claim 12 , wherein the modeling subsystem is configured to model the roof of the structure as a plurality of polygons, wherein each location on the roof of the structure corresponds to one of the polygons.
14. The system of claim 13 , wherein the polygons comprise one or more of: triangles, rectangles, rhombi, and hexagons.
15. The system of claim 11 , wherein the number of locations on the roof of the structure and the number of discrete times are selected based on a function of available computing resources and target completion time.
16. The system of claim 11 , wherein each divergent beam ray path is modeled as a cone with an apex and an altitude, with the apex at the location on the roof of the structure and the altitude extending from the location on the roof of the structure to one of the modeled locations of the sun.
17. The system of claim 11 , wherein each divergent beam ray path is modeled as a pyramid with an apex, an altitude, and an n-sided base, with the apex at the location on the roof of the structure and the altitude extending from the location on the roof of the structure to one of the modeled locations of the sun, wherein n is an integer.
18. The system of claim 11 , wherein the beam path analysis subsystem is configured to identify divergent beam ray paths obstructed by an obstacle as those divergent beam ray paths that are one of:
fully obstructed by the obstacle,
partially obstructed by the obstacle, or
obstructed by the obstacle by more than a threshold amount.
19. A non-transitory computer-readable medium with instructions stored thereon that, when executed by a processor of a computing device, cause the computing device to:
model a divergent beam ray path between each of a plurality of locations on a roof and modeled locations of a sun relative to the roof at each of a plurality of discrete times during a time period;
identify divergent beam ray paths that are obstructed by an obstacle positioned between the roof and the respective modeled locations of the sun;
identify unobstructed divergent beam ray paths; and
calculate a solar irradiance value for each location on the roof during the time period based, at least in part, on the identified unobstructed divergent beam ray paths associated with each respective location on the roof during the time period.
20. The non-transitory computer-readable medium of claim 19 , wherein the divergent beam ray paths are modeled as one of cones and pyramids diverging as they extend from the locations on the roof to the respective modeled locations of the sun.