Patent Publication Number: US-2023155537-A1

Title: Solar roofing system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 17/499,516, filed on Oct. 12, 2021, entitled “SOLAR ROOFING SYSTEM”, which claims the benefit of U.S. Provisional Patent Application Ser. No. 63/091,017, filed Oct. 13, 2020, entitled “SOLAR ROOFING SYSTEM,” the contents of which are incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to solar roofing systems including roof-integrated photovoltaic modules and roofing shingles. More particularly, the present invention relates to solar roofing systems including roof-integrated photovoltaic modules and roofing shingles having elements with matching widths. 
     BACKGROUND 
     Solar modules can be placed on building roofs (e.g., residential roofs) to generate electricity. One obstacle to mass-market adoption of solar roofing is poor aesthetics. Standard rack-mounted photovoltaic (“PV”) systems have a very different appearance than traditional roofing materials (e.g., asphalt shingles, wooden shingles, slate shingles, etc.), which can draw unwanted attention. Even low-profile PV systems still receive poor aesthetic feedback from consumers. 
     Specifically, typical PV module materials and circuit formations include PV elements having a constant width and a grid-like appearance, while typical roofing shingles include elements having irregular viewed widths, causing the PV modules not to visually match the look of standard roofing shingles. 
     SUMMARY 
     In some embodiments, a system, comprising a photovoltaic module comprising a plurality of photovoltaic cells, wherein each of the plurality of photovoltaic cells has a photovoltaic cell width; and a roofing shingle having a top surface and a bottom surface, the roofing shingle having an exposure zone at a lower end of the top surface and a headlap zone at an upper end of the top surface, wherein a plurality of slots extends from the lower end toward the headlap zone, wherein the plurality of slots defines a plurality of tooth portions therebetween, wherein a first one of the plurality of tooth portions has a first side that is defined by a first one of the plurality of slots and a second side that is defined by a second one of the plurality of slots that is adjacent to the first one of the plurality of slots, wherein the first one of the plurality of tooth portions has a first width that is measured from the first one of the plurality of slots to the second one of the plurality of slots, wherein the first width is the photovoltaic cell width multiplied by a first positive integer, wherein a second one of the plurality of tooth portions has a first side that is defined by a third one of the plurality of slots and a second side that is defined by a fourth one of the plurality of slots that is adjacent to the third one of the plurality of slots, wherein the second one of the plurality of tooth portions has a second width that is measured from the third one of the plurality of slots to the fourth one of the plurality of slots, and wherein the second width is the photovoltaic cell width multiplied by a second positive integer that is different than the first positive integer. 
     In some embodiments, a third one of the plurality of tooth portions has a first side that is defined by a fifth one of the plurality of slots and a second side that is defined by a sixth one of the plurality of slots that is adjacent to the fifth one of the plurality of slots, and wherein the third one of the plurality of tooth portions has a third width that is measured from the fifth one of the plurality of slots to the sixth one of the plurality of slots, wherein the third width is the photovoltaic cell width multiplied by 0.5 and by a third positive integer that is different than the first positive integer and different than the second positive integer. In some embodiments, each of the first and second positive integers is selected from the group consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. In some embodiments, the roofing shingle comprises thermoplastic olefin, polyvinyl chloride, or asphalt. In some embodiments, the top surface of the roofing shingle comprises embedded granules. 
     In some embodiments, a third one of the plurality of tooth portions has a first side that is defined by a fifth one of the plurality of slots and a second side that is defined by one of either (a) the first side, or (b) the second side, and wherein the third one of the plurality of tooth portions has a third width that is measured from the fifth one of the plurality of slots to the one of either the first side or the second side, wherein the third width is the photovoltaic cell width multiplied by 0.5 and by a third positive integer that is different than the first positive integer and different than the second positive integer. 
     In some embodiments, the system further includes a second roofing shingle having a top surface and a bottom surface, the second roofing shingle having an exposure zone at a lower end of the top surface of the second roofing shingle and a headlap zone at an upper end of the top surface of the second roofing shingle, wherein a plurality of slots extends from the lower end of the second roofing shingle toward the headlap zone of the second roofing shingle, wherein the plurality of slots of the second roofing shingle defines a plurality of tooth portions therebetween, wherein a first one of the plurality of tooth portions of the second roofing shingle has a first side that is defined by a first one of the plurality of slots of the second roofing shingle and a second side that is defined by a second one of the plurality of slots of the second roofing shingle that is adjacent to the first one of the plurality of slots of the second roofing shingle, wherein the first one of the plurality of tooth portions of the second roofing shingle has a third width that is measured from the first one of the plurality of slots of the second roofing shingle to the second one of the plurality of slots of the second roofing shingle, wherein the third width is the photovoltaic cell width multiplied by a third positive integer, wherein a second one of the plurality of tooth portions of the second roofing shingle has a first side that is defined by a third one of the plurality of slots of the second roofing shingle and a second side that is defined by a fourth one of the plurality of slots of the second roofing shingle that is adjacent to the third one of the plurality of slots of the second roofing shingle, wherein the second one of the plurality of tooth portions of the second roofing shingle has a fourth width that is measured from the third one of the plurality of slots of the second roofing shingle to the fourth one of the plurality of slots of the second roofing shingle, and wherein the fourth width is the photovoltaic cell width multiplied by a fourth positive integer that is different than the third positive integer. 
     In some embodiments, an arrangement of the tooth portions of the second roofing shingle is not identical to an arrangement of the tooth portions of the roofing shingle. In some embodiments, an arrangement of the tooth portions of the second roofing shingle is identical to an arrangement of the tooth portions of the roofing shingle. In some embodiments, the third one of the plurality of slots is a same one of the plurality of slots as the second one of the plurality of slots, and wherein the first one of the plurality of tooth portions is adjacent to the second one of the plurality of tooth portions. 
     In some embodiments, the system further includes a wireway configured to be positioned between the photovoltaic module and a further photovoltaic module that is adjacent to the photovoltaic module, wherein the wireway is configured to enclose at least one electrical cable, wherein a width of the wireway as measured in a horizontal direction between the photovoltaic module and the further photovoltaic module is the photovoltaic cell width multiplied by two, wherein the wireway includes a dark colored portion and a light colored portion, and wherein the light colored portion extends across the wireway in a vertical direction that is perpendicular to the horizontal direction. In some embodiments, the light-colored portion is positioned at an edge of the wireway that is adjacent to the photovoltaic module. In some embodiments, the light-colored portion is positioned halfway intermediate (1) an edge of the wireway that is adjacent to the photovoltaic module and (2) an edge of the wireway that is adjacent to the further photovoltaic module. In some embodiments, the wireway further comprises a further light colored portion extending across a bottom edge of the wireway in the horizontal direction. 
     In some embodiments, a roofing shingle includes a top surface and a bottom surface, the roofing shingle having an exposure zone at a lower end of the top surface and a headlap zone at an upper end of the top surface, wherein the roofing shingle is configured to be installed on a roof adjacent to a photovoltaic module including a plurality of photovoltaic cells, wherein each of the plurality of photovoltaic cells has a photovoltaic cell width, wherein a plurality of slots extends from the lower end toward the headlap zone, wherein the plurality of slots defines a plurality of tooth portions therebetween, wherein a first one of the plurality of tooth portions has a first side that is defined by a first one of the plurality of slots and a second side that is defined by a second one of the plurality of slots that is adjacent to the first one of the plurality of slots, wherein the first one of the plurality of tooth portions has a first width that is measured from the first one of the plurality of slots to the second one of the plurality of slots, wherein the first width is the photovoltaic cell width multiplied by a first positive integer, wherein a second one of the plurality of tooth portions has a first side that is defined by a third one of the plurality of slots and a second side that is defined by a fourth one of the plurality of slots that is adjacent to the third one of the plurality of slots, wherein the second one of the plurality of tooth portions has a second width that is measured from the third one of the plurality of slots to the fourth one of the plurality of slots, and wherein the second width is the photovoltaic cell width multiplied by a second positive integer that is different than the first positive integer. 
     In some embodiments, a third one of the plurality of tooth portions has a first side that is defined by a fifth one of the plurality of slots and a second side that is defined by a sixth one of the plurality of slots that is adjacent to the fifth one of the plurality of slots, wherein the third one of the plurality of tooth portions has a third width that is measured from the fifth one of the plurality of slots to the sixth one of the plurality of slots, and wherein the third width is the photovoltaic cell width multiplied by a third positive integer that is different than the first positive integer and different than the second positive integer. In some embodiments, each of the first and second positive integers is selected from the group consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. In some embodiments, the roofing shingle comprises thermoplastic olefin, polyvinyl chloride, or asphalt. In some embodiments, the top surface of the roofing shingle comprises embedded granules. In some embodiments, a third one of the plurality of tooth portions has a first side that is defined by a fifth one of the plurality of slots and a second side that is defined by one of either (a) the first side, or (b) the second side, and wherein the third one of the plurality of tooth portions has a third width that is measured from the fifth one of the plurality of slots to the one of either the first side or the second side, wherein the third width is the photovoltaic cell width multiplied by a third positive integer that is different than the first positive integer and different than the second positive integer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    shows a perspective view of an exemplary PV module. 
         FIG.  2 A  shows a schematic view of elements of a layered structure of an exemplary PV module before lamination. 
         FIG.  2 B  shows a schematic view of a layered structure of an exemplary PV module formed by lamination of the elements shown in  FIG.  2 A . 
         FIG.  3    shows an exemplary roofing shingle. 
         FIG.  4 A  shows a first variant of an exemplary roofing shingle. 
         FIG.  4 B  shows a second variant of an exemplary roofing shingle. 
         FIG.  4 C  shows a third variant of an exemplary roofing shingle. 
         FIG.  4 D  shows a fourth variant of an exemplary roofing shingle. 
         FIG.  5    shows exemplary embodiments of a PV module. 
         FIG.  6 A  shows an exemplary embodiment of a wireway. 
         FIG.  6 B  shows an exemplary embodiment of a wireway. 
         FIG.  6 C  shows an exemplary embodiment of a wireway. 
         FIGS.  6 D through  6 F  show another exemplary embodiment of a wireway. 
         FIG.  7    shows an exemplary embodiment of a masking element. 
         FIG.  8 A  shows an exemplary embodiment of a roofing system. 
         FIG.  8 B  shows a magnified view of a first portion of the roofing system of  FIG.  8 A . 
         FIG.  8 C  shows a magnified view of a second portion of the roofing system of  FIG.  8 A . 
         FIG.  8 D  shows a magnified view of a third portion of the roofing system of  FIG.  8 A . 
         FIG.  8 E  shows a magnified view of a fourth portion of the roofing system of  FIG.  8 A . 
     
    
    
     DETAILED DESCRIPTION 
     The present invention will be further explained with reference to the attached drawings, wherein like structures are referred to by like numerals throughout the several views. The drawings shown are not necessarily to scale, with emphasis instead generally being placed upon illustrating the principles of the present invention. Further, some features may be exaggerated to show details of particular components. 
     The figures constitute a part of this specification and include illustrative embodiments of the present invention and illustrate various objects and features thereof. Further, the figures are not necessarily to scale, some features may be exaggerated to show details of particular components. In addition, any measurements, specifications and the like shown in the figures are intended to be illustrative, and not restrictive. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention. 
     Among those benefits and improvements that have been disclosed, other objects and advantages of this invention will become apparent from the following description taken in conjunction with the accompanying figures. Detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely illustrative of the invention that may be embodied in various forms. In addition, each of the examples given in connection with the various embodiments of the invention which are intended to be illustrative, and not restrictive. 
     Throughout the specification and claims, the following terms take the meanings explicitly associated herein, unless the context clearly dictates otherwise. The phrases “in one embodiment” and “in some embodiments” as used herein do not necessarily refer to the same embodiment(s), though they may. Furthermore, the phrases “in another embodiment” and “in some other embodiments” as used herein do not necessarily refer to a different embodiment, although they may. Thus, as described below, various embodiments of the invention may be readily combined, without departing from the scope or spirit of the invention. 
     The term “based on” is not exclusive and allows for being based on additional factors not described, unless the context clearly dictates otherwise. In addition, throughout the specification, the meaning of “a,” “an,” and “the” include plural references. The meaning of “in” includes “in” and “on.” 
     The exemplary embodiments relate to a roofing system having elements (e.g., roofing shingles, PV modules, wireways, and masking elements) having visual elements the width of which is harmonized around a constant base width. In some embodiments, the constant base width is a cell pitch. In some embodiments, the cell pitch is defined as the width of a PV element plus the width of a space that exists between two adjacent PV elements. In some embodiments, such harmonization provides a consistent and blended aesthetic appearance across such a roofing system, as will be discussed in further detail hereinafter. 
     In some embodiments, a solar roofing system includes at least one PV module and at least one roofing shingle. In some embodiments, each of the at least one PV modules includes a plurality of PV cells. In some embodiments, each of the PV cells has a PV cell width that is the same for all of the PV cells. In some embodiments, the cell width is a “half-cut” width, e.g., the width of a premanufactured PV cell that has been cut in half. 
       FIG.  1    shows an exemplary PV module  100 . The exemplary PV module  100  includes a headlap region  110  and a PV region  120 . In some embodiments, the headlap region  110  comprises thermoplastic olefin (“TPO”), polyvinyl chloride (“PVC”), or asphalt. In some embodiments, the headlap region  110  includes embedded granules. In some embodiments, the headlap region  110  defines a nailing line  112  extending across the headlap region  110 . In some embodiments, the nailing line  112  extends across the headlap region  110  approximately midway between the end of the headlap region  110  that borders the PV region and the opposite end of the headlap region  110 . In some embodiments, the nailing line  112  defines an area of the headlap region  110  through which mechanical fasteners (e.g., nails, screws, etc.) can be driven to secure the PV module  100  to a roof deck in the standard manner. 
     In some embodiments, the PV region  120  includes a plurality of PV portions  122 . In some embodiments, each of the PV portions  122  includes a layered structure that is typical of a laminate PV module, as discussed below with reference to  FIGS.  2 A and  2 B . In some embodiments, the PV region  120  includes grooves  124  separating adjacent ones of the PV portions. In some embodiments, each of the PV portions  122  is separately formed from others of the PV portions  122 , and the grooves  124  are formed by spaces between adjacent ones of the PV portions  122 . In some embodiments, the PV portions  122  forming the PV region  120  are integrally formed with one another (e.g., form a single layered structure) and the grooves  124  are formed in a superstrate layer thereof. In some embodiments, the grooves  124  between adjacent ones of the PV portions  122  provide the appearance of discrete portions similar to those of conventional shingles. In some embodiments, the PV region  120  is formed atop material of the headlap region  110  (e.g., the substrate of the PV region  120  is deposited on the material of the headlap region  110 ). In some embodiments, the PV region  120  and the headlap region  110  join one another end-to-end. 
     In some embodiments, the PV module  100  includes a junction box  130 . In some embodiments, the junction box  130  is positioned at an end of the headlap region  110  that is opposite the PV region  120 . In some embodiments, the junction box  130  is positioned at a center of an end of the headlap region  110  that is opposite the PV region  120 . In some embodiments, the junction box  130  is electrically connected to the PV region  120  by electrical connectors (e.g., wires) that traverse (e.g., pass under or through) the headlap region  110 . 
     In some embodiments, such as the PV module  100  discussed above with reference to  FIG.  1   , an exemplary PV module includes a layered structure.  FIGS.  2 A and  2 B  show an exemplary embodiment of a layered structure  200  that, in some embodiments, forms part of an exemplary PV module. 
       FIG.  2 A  shows an exploded view of the layers of the layered structure  200  prior to lamination to form the layered structure  200 .  FIG.  2 B  shows the layered structure following lamination. It will be apparent to those of skill in the art that  FIGS.  2 A and  2 B  present schematic views of the layered structure  200  and are not intended to provide a to-scale representation. 
     Referring now to  FIG.  2 A , in some embodiments, the layered structure  200  includes a superstrate layer  210  that forms an upper surface of the layered structure  200  and of the PV module  100  (i.e., the surface that, when the PV module  100  is installed on a roof, faces away from the roof and toward the sun). In some embodiments, the superstrate layer  210  has an upper surface  212  (i.e., the side of the superstrate layer  210  that faces toward the sun when installed as described above) and a lower surface  214  opposite the upper surface  212 . In some embodiments, the superstrate layer  210  is optically transparent (e.g., it has a solar weighted transmittance of 80% or greater). In some embodiments, the superstrate provides electrical insulation and moisture resistance. In some embodiments, the superstrate layer  210  comprises a glass material, such as low-iron solar glass. In some embodiments, the superstrate layer  210  comprises a polymeric material such as ethylene tetrafluoroethylene (“ETFE”), polyethylene terephthalate (“PET”), or an acrylic such as polymethyl methacrylate (“PMMIA”). In some embodiments, the superstrate layer  210  has a thickness of from 50 microns to 250 microns. In some embodiments, the superstrate layer  210  has a thickness of from 50 microns to 200 microns. In some embodiments, the superstrate layer  210  has a thickness of from 50 microns to 150 microns. In some embodiments, the superstrate layer  210  has a thickness of from 50 microns to 100 microns. In some embodiments, the superstrate layer  210  has a thickness of from 100 microns to 250 microns. In some embodiments, the superstrate layer  210  has a thickness of from 100 microns to 200 microns. In some embodiments, the superstrate layer  210  has a thickness of from 100 microns to 150 microns. In some embodiments, the superstrate layer  210  has a thickness of from 150 microns to 250 microns. In some embodiments, the superstrate layer  210  has a thickness of from 150 microns to 200 microns. In some embodiments, the superstrate layer  210  has a thickness of from 200 microns to 250 microns. 
     In some embodiments, the superstrate layer  210  has a thickness of from 200 microns to 500 microns. In some embodiments, the superstrate layer  210  has a thickness of from 200 microns to 450 microns. In some embodiments, the superstrate layer  210  has a thickness of from 200 microns to 400 microns. In some embodiments, the superstrate layer  210  has a thickness of from 200 microns to 350 microns. In some embodiments, the superstrate layer  210  has a thickness of from 200 microns to 300 microns. In some embodiments, the superstrate layer  210  has a thickness of from 250 microns to 500 microns. In some embodiments, the superstrate layer  210  has a thickness of from 250 microns to 450 microns. In some embodiments, the superstrate layer  210  has a thickness of from 250 microns to 400 microns. In some embodiments, the superstrate layer  210  has a thickness of from 250 microns to 350 microns. In some embodiments, the superstrate layer  210  has a thickness of from 250 microns to 300 microns. In some embodiments, the superstrate layer  210  has a thickness of from 300 microns to 500 microns. In some embodiments, the superstrate layer  210  has a thickness of from 300 microns to 500 microns. In some embodiments, the superstrate layer  210  has a thickness of from 300 microns to 450 microns. In some embodiments, the superstrate layer  210  has a thickness of from 300 microns to 400 microns. In some embodiments, the superstrate layer  210  has a thickness of from 300 microns to 350 microns. In some embodiments, the superstrate layer  210  has a thickness of from 350 microns to 500 microns. In some embodiments, the superstrate layer  210  has a thickness of from 350 microns to 450 microns. In some embodiments, the superstrate layer  210  has a thickness of from 350 microns to 400 microns. In some embodiments, the superstrate layer  210  has a thickness of from 400 microns to 500 microns. In some embodiments, the superstrate layer  210  has a thickness of from 400 microns to 450 microns. In some embodiments, the superstrate layer  210  has a thickness of from 450 microns to 500 microns. In some embodiments, the superstrate layer  210  has a thickness of from 325 microns to 375 microns. In some embodiments, the superstrate layer  210  has a thickness of about 300 microns. In some embodiments, the superstrate layer  210  has a thickness of 300 microns. 
     In some embodiments, the superstrate layer  210  has a thickness of from 1.6 millimeters to 4 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 1.6 millimeters to 3.2 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 1.6 millimeters to 2.4 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 2.4 millimeters to 4 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 2.4 millimeters to 3.2 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 3.2 millimeters to 4 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 2.8 millimeters to 3.6 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 3 millimeters to 3.4 millimeters. In some embodiments, the superstrate layer  210  has a thickness of from 3.1 millimeters to 3.3 millimeters. In some embodiments, the superstrate layer  210  has a thickness about 3.2 millimeters. In some embodiments, the superstrate layer  210  has a thickness of 3.2 millimeters. 
     Continuing to refer to  FIG.  2 A , in some embodiments, the layered structure  200  includes an upper encapsulant layer  220 . In some embodiments, the upper encapsulant layer  220  has an upper surface  222  and a lower surface  224  opposite the upper surface  222 . In some embodiments, the upper surface  222  of the upper encapsulant layer  220  contacts the lower surface  214  of the superstrate layer  210 . In some embodiments, the upper encapsulant layer  220  is optically transparent (e.g., it has a solar weighted transmittance of 80% or greater). In some embodiments, the upper encapsulant layer provides electrical insulation. In some embodiments, the upper encapsulant layer  220  comprises an encapsulating material such as ethylene-co-vinyl acetate (“EVA”), polydimethyl siloxane (“PDMS”), a polyolefin elastomer (“POE”), polyvinyl butyral (“PVB”), polyurethane epoxy, silicone, or an ionomer such as the series of ionomer-based encapsulants commercialized by DuPont de Nemours, Inc. under the trade name PV5400. In some embodiments, the thickness of the upper encapsulant layer  220  varies across the layered structure  200 , as will be discussed in greater detail hereinafter. 
     Continuing to refer to  FIG.  2 A , in some embodiments, the layered structure  200  includes a PV layer  230  having an upper surface  232  and a lower surface  234  opposite the upper surface  232 . In some embodiments, the upper surface  232  of the PV layer  230  contacts the lower surface  224  of the upper encapsulant layer  220 . In some embodiments, the PV layer  230  includes at least one PV element  236  (e.g., at least one PV cell having a constant PV cell width  237  as described above). In some embodiments, the PV layer  230  includes an array of PV elements  236 . In some embodiments in which the PV layer  230  includes a plurality of the PV element  236 , the PV elements  236  are electrically interconnected with one another. In some embodiments, the PV layer  230  includes an array of interconnected PV elements  236 . In some embodiments, gaps are formed between adjacent ones of the PV elements  236 . In some embodiments, the gaps are significantly smaller than the PV elements  236 ; for example, in some embodiments, a width of each of the PV elements  236  is 160 millimeters and the gaps are from 2 millimeters to 5 millimeters in size. In some embodiments, the PV layer  230  also includes other active and/or passive electronic components. 
     Continuing to refer to  FIG.  2 A , in some embodiments, the layered structure  200  includes a lower encapsulant layer  240  having an upper surface  242  and a lower surface  244  opposite the upper surface  242 . In some embodiments, the upper surface  242  of the lower encapsulant layer  240  contacts the lower surface  234  of the PV layer  230 . In some embodiments, the lower encapsulant layer  240  provides electrical insulation. In some embodiments, the lower encapsulant layer  240  is optically transparent. In some embodiments, the lower encapsulant layer  240  is not optically transparent. In some embodiments, the thickness of the lower encapsulant layer  240  is in the range of 100 to 1000 microns. In some embodiments, the thickness of the lower encapsulant layer  240  is sufficiently large (e.g., greater than 100 microns) so as to prevent delamination between the PV layer  230  and the substrate  250 . In some embodiments, the thickness of the lower encapsulant layer  240  is consistent across the entirety of the layered structure  200 . In some embodiments, the lower encapsulant layer  240  comprises an encapsulating material such as ethylene-co-vinyl acetate (“EVA”), polydimethyl siloxane (“PDMS”), a polyolefin elastomer (“POE”), polyvinyl butyral (“PVB”), polyurethane epoxy, silicone, or an ionomer such as the series of ionomer-based encapsulants commercialized by DuPont de Nemours, Inc. under the trade name PV5400. In some embodiments, the lower encapsulant layer  240  comprises the same encapsulating material as the upper encapsulant layer  220 . 
     Continuing to refer to  FIG.  2 A , in some embodiments, the layered structure  200  includes a substrate  250  having an upper surface  252  and a lower surface  254  opposite the lower surface  252 . In some embodiments, the upper surface  252  of the substrate  250  contacts the lower surface  244  of the lower encapsulant layer  240 . In some embodiments, the lower surface  254  of the substrate  250  forms the lower surface  204  of the layered structure  200 . In some embodiments, the substrate  250  provides electrical insulation and moisture resistance. In some embodiments, the substrate  250  is optically transparent. In some embodiments, the substrate  250  is not optically transparent. In some embodiments, the substrate  250  comprises a glass material. In some embodiments, the substrate  250  comprises a polymeric material such as ETFE, PET, an acrylic such as PMMA, polypropylene, polyvinyl chloride (“PVC”), or a glass-reinforced or fiber-reinforced composite such as a material meeting the National Electrical Manufacturers Association (“NEMA”) grades FR-4 or G-10. In some embodiments, the substrate  250  has a thickness in the range of 200 microns to ¼ inch. In some embodiments, the substrate  250  is sufficiently rigid to provide mechanical stiffening to the PV module  100 . 
     Referring now to  FIG.  2 B , the layered structure  200  is shown following lamination. In some embodiments, during the lamination process, the encapsulating material of the upper encapsulant layer  220  and the encapsulating material of the lower encapsulant layer  240  are melted and flow within the gaps between adjacent ones of the PV elements  236  shown in  FIG.  2 A , thereby encapsulating (e.g., surrounding on all sides) each of the PV elements  236  with encapsulating material. In some embodiments, as a result of this process, the PV layer  230  includes encapsulant portions  238  located between adjacent ones of the PV elements  236 , and providing continuity between the encapsulating material of the upper encapsulant layer  220  and the encapsulating material of the lower encapsulant layer  240 . In some embodiments, the resulting region of the layered structure  200  (e.g., the upper encapsulant layer  220 , the PV layer  230 , and the lower encapsulant layer  240 ) resembles a single block of encapsulant material with the PV elements positioned therein. 
       FIG.  3    shows an exemplary roofing shingle  300 . In some embodiments, the roofing shingle  300  comprises thermoplastic olefin (“TPO”), polyvinyl chloride (“PVC”), or asphalt. In some embodiments, roofing shingle  300  includes embedded granules. In some embodiments, the roofing shingle  300  includes a top end  302 , a bottom end  304 , a first side  306 , and a second side. In some embodiments, the roofing shingle  300  includes a headlap region  310  adjacent the top end  302  and a tooth region  320  adjacent the bottom end  304 . In some embodiments, the headlap region  310  defines a nailing line  312  extending across the headlap region  310 . In some embodiments, the nailing line  312  extends across the headlap region  310  approximately midway between the end of the headlap region  310  that borders the tooth region  320  and the opposite end of the headlap region  110 . In some embodiments, the nailing line  312  defines an area of the headlap region  310  through which mechanical fasteners (e.g., nails, screws, etc.) can be driven to secure the roofing shingle  300  to a roof deck in the standard manner. 
     In some embodiments, the tooth region  320  includes a plurality of slots  322  that are spaced apart along the width of the tooth region  320  from the first side  306  to the second side, and extend from the bottom end  304  toward the top end  302 . In some embodiments, each of the slots  322  has a width that is the same as, or is similar to, the gaps between adjacent ones of the PV elements  236  in the PV module  100 . In some embodiments, the width of each of the slots  322  is ½ inch. In some embodiments, the width of each of the slots  322  is 6 millimeters. In some embodiments, the first side  306 , the slots  322 , and the second side define a plurality of tooth portions  324 ,  326 ,  328 ,  330 ,  332 ,  334  therebetween. The exemplary roofing shingle  300  shown in  FIG.  3    includes six (6) of the tooth portions  324 ,  326 ,  328 ,  330 ,  332 ,  334 , but it will be apparent to those of skill in the art that various embodiments of the roofing shingle  300  may have any other number of tooth portions. In some embodiments, the width of the tooth portions  324 ,  326 ,  328 ,  330 ,  332 ,  334  is variable, e.g., for a given instance of the roofing shingle  300 , a first one of the tooth portions (e.g., tooth portion  324 ) has a first width, and a second one of the tooth portions (e.g., tooth portion  326 ) has a second width that is different than the first width. In some embodiments, each of the tooth portions  324 ,  326 ,  328 ,  330 ,  332 ,  334  has a width that is an integer multiple of the PV cell width  237  (e.g., is equal to the PV cell width  237 , or is two times, or three times, or four times, or five times, or six times, or seven times, or eight times, or nine times, or ten times, or eleven times, or twelve times, or thirteen times, or fourteen times, or fifteen times, or sixteen times, or seventeen times, or eighteen times, or nineteen times, or twenty times the PV cell width  237 ). 
     In some embodiments, different ones of the exemplary roofing shingle  300  have differently sized and differently arranged tooth portions. For example, in some embodiments, a manufacturer of the roofing shingle  300  may manufacture different versions of the roofing shingle  300  so as to provide a roofing system including a plurality of the roofing shingle  300  that differ from one another so as to provide a non-uniform appearance to the roofing system.  FIGS.  4 A- 4 D  show different variants  410 ,  420 ,  430 , and  440  of the exemplary roofing shingle  300 . In some embodiments, each of the variants  410 ,  420 ,  430 , and  440  has a plurality of tooth portions that vary in width among the different tooth portions of any given one of the variants  410 ,  420 ,  430 , and  440 , and the widths of all tooth portions are integer multiples of the PV cell width  237 . In some embodiments, each of the variants  410 ,  420 ,  430 , and  440  has tooth portions that differ in arrangement as compared to those of the others of the variants  410 ,  420 ,  430 , and  440 . In some embodiments, a manufacturer of the roofing shingle  300  may manufacture a suitable number of different variants so as to impart a random appearance to a roofing system incorporating such variants. For example, in some embodiments, a roofing system includes four of the variants  410 ,  420 ,  430 , and  440 , as shown in  FIGS.  4 A- 4 D , but it will be apparent to those of skill in the art that this is only exemplary, and that any other number of variants may be produced. 
     In some embodiments, the roofing shingle  300  is composed of a single layer. In some embodiments, the roofing shingle  300  is composed of multiple layers. In some embodiments, the roofing shingle  300  is laminated. 
     As discussed above, in some embodiments, the assembled PV module  100  includes a plurality of PV elements  236  that are spaced apart by a quantity of encapsulant portions  238  that are positioned between the PV elements  236  as part of the lamination process. In some embodiments, the space between the PV elements  236  that is formed in this manner is referred to as a “cell gap”. In some embodiments, due to uniform sizing and spacing of the PV elements  236 , the PV elements  236  and the cell gaps therebetween provide a uniform, grid-like appearance. In some embodiments, to provide a non-uniform appearance, the cell gap is selectively revealed or hidden. 
       FIG.  5    shows PV elements  500  forming PV modules  510 ,  520 ,  530 . For clarity, the PV elements  500  are substantially the only elements of the PV modules  510 ,  520 ,  530  shown in  FIG.  5   , but it will be apparent to those of skill in the art that the PV modules  510 ,  520 ,  530  will include other elements as described above. Also for clarity, only one of the PV elements  500  forming each of the PV modules  510 ,  520 ,  530  is specifically called out in  FIG.  5   , but it will be apparent to those of skill in the art that discussion of the PV elements  500  may refer to any of the PV elements  500  forming the PV modules  510 ,  520 ,  530 , whether or not specifically identified in  FIG.  5   . 
     In some embodiments, as shown in  FIG.  5   , each of the PV modules  510 ,  520 ,  530  includes sixteen (16) of the PV elements  500  that are “half-cut” cells having a width of about 90 mm and a cell gap of about 4 mm between adjacent ones of the PV elements, thereby to produce the PV modules  510 ,  520 ,  530  that are 60 inches wide, but it will be apparent to those of skill in the art that these dimensions are only exemplary. In some embodiments, the PV modules  510 ,  520 ,  530  include portions  512 ,  522 ,  532 , respectively, of a color-contrasting material positioned behind the PV elements  500  (e.g., positioned in or on the PV modules  510 ,  520 ,  530  so as to be positioned between the PV elements and a roof deck to which the PV modules  510 ,  520 ,  530  are installed). In some embodiments, the color-contrasting material comprises a patterned backsheet. In some embodiments, the color-contrasting material comprises a cloaking tape. As shown in  FIG.  5   , the inclusion of the portions  512 ,  522 ,  532  at different locations within the PV modules  510 ,  520 ,  530  provides a non-uniform appearance to the PV modules  510 ,  520 ,  530 , despite each of the PV modules  510 ,  520 ,  530  having the same arrangement of the PV elements. Though  FIG.  5    shows three of the PV modules  510 ,  520 ,  530  having different arrangements of the portions  512 ,  522 ,  532 , it will be apparent to those of skill in the art that any number of different arrangements are possible without departing from the general concept embodied by the PV modules  510 ,  520 ,  530 . Throughout this disclosure, the PV module  510  is indicated when it is desired to reference a PV module having color-contrasting material applied to the boundaries between some of the PV elements  500  so as to provide a non-uniform appearance as described above, but such reference to the PV module  510  is intended to refer to any of the PV modules  510 ,  520 ,  530 , or any other PV module having such features. 
     In some embodiments, an exemplary solar roofing system includes wireways that are positioned between PV modules and are configured to enclose electrical cables that connect to the PV modules. In some embodiments, to facilitate providing an aesthetic appearance that is consistent both for the PV modules and the roofing shingles that form a solar roofing system, an exemplary solar roofing system includes wireways having a width that is matched to a width of the PV elements within the PV modules.  FIGS.  6 A,  6 B, and  6 C  show embodiments of an exemplary wireway  600  having an upper end  602 , a lower end  604 , a first side  606 , and a second side  608 . In some embodiments, the exemplary wireway  600  is configured to be installed on a roof deck such that the lower end  604  is at a lower elevation than is the upper end  602 . In some embodiments, the exemplary wireway  600  has a width as measured in a horizontal direction from the first side  606  to the second side  608  that is equal to an integer multiple of the PV cell width  237  for PV elements  236  that are used in the same solar roofing system as the exemplary wireway  600 . In some embodiments, the width of the wireway  600  is two times the PV cell width  237 . In some embodiments, the wireway  600  is rounded (e.g., so as to be concave on the side that faces the roof deck) to provide space to accommodate electrical cables and to soften the appearance of the wireway  600 . In some embodiments, the top surface of the wireway  600  (e.g., the side that faces away from the roof deck) includes at least one dark-colored portion and at least one light-colored portion. 
     In some embodiments, the at least one light-colored portion includes a horizontal light-colored portion  610  extending across the wireway  600  from the first side  606  to the second side  608  adjacent the lower end  604 . In some embodiments, a height of the horizontal light-colored portion  610  (e.g., as measured in a vertical direction from the lower end  604  toward the upper end  602 ) is equal to a creepage distance. As used herein, the creepage distance is the shortest distance along the surface of the insulating material between two conductive live parts or between conductive live parts and accessible part. For example, in embodiments detailed herein, the creepage distance is the shortest distance along the surface of an insulative portion of the PV module  510  between two conductive or accessible portions of the PV module  510 . In some embodiments, the creepage distance results in the appearance of a light-colored region along the long edges of the PV module  510 . Consequently, in some embodiments, the sizing of the horizontal light-colored portion  610  as equal to the creepage distance provides continuity of visual appearance between the wireway  600  and PV modules  510  that are adjacent thereto. In some embodiments, the height of the horizontal light-colored portion  610  is in a range of from 10 millimeters to 30 millimeters. In some embodiments, the height of the horizontal light-colored portion  610  is in a range of from 12.5 millimeters to 27.5 millimeters. In some embodiments, the height of the horizontal light-colored portion  610  is in a range of from 15 millimeters to 25 millimeters. In some embodiments, the height of the horizontal light-colored portion  610  is in a range of from 17.5 millimeters to 22.5 millimeters. In some embodiments, the height of the horizontal light-colored portion  610  is about 20 millimeters. In some embodiments, the height of the horizontal light-colored portion  610  is 20 millimeters. 
     In some embodiments, the at least one light-colored portion includes a vertical light-colored portion extending along the wireway  600  from the upper end  602  toward the lower end  604 . In some embodiments, as shown in  FIG.  6 A , the vertical light-colored portion  612  extends along the wireway  600  and along the first side  606 . In some embodiments, as shown in  FIG.  6 B , the vertical light-colored portion  614  extends along the wireway  600  and intermediate the first and second sides  606 ,  608 . In some embodiments, as shown in  FIG.  6 C , the vertical light-colored portion  616  extends along the wireway  600  and along the second side  608 . In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is about equal to (e.g., within plus or minus 25%) the width of a cell gap, as described above with reference to  FIG.  5   . In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is equal to the width of a cell gap. In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is 6 mm. In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is about 6 mm. In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is from 5 mm to 7 mm. In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is from 4 mm to 8 mm. In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is from 3 mm to 9 mm. In some embodiments, the width of the vertical light-colored portion  612 ,  614 ,  616  is from 3% of a width of the wireway  600  to 10% of the width of the wireway  600 . In some embodiments, the vertical light-colored portion  612  or  616  either provides a dark-colored region having a width that is twice the PV cell width  237 . In some embodiments, the vertical light-colored portion  614  provides two dark-colored regions, each of which has a width that is equal to the PV cell width  237 . Accordingly, in some embodiments, vertical light-colored portions  612 ,  614 ,  616  cause the wireway to have an appearance that is consistent with those of the roofing shingle  300  and the PV module  510 , thereby improving the consistency, visual flow, and aesthetic appearance of a roofing system including the wireway  600 . 
     In some embodiments, an exemplary wireway  630 , as shown in  FIG.  6 D  positioned between adjacent PV modules, is substantially similar to the wireway  600  described above with reference to  FIGS.  6 A- 6 C , other than as described hereinafter. In some embodiments, the wireway  630  has a flat top surface  632  and angled sides  634 ,  636 . In some embodiments, the flat top surface  632  and angled sides  634 ,  636  of the wireway  630  define a channel  638  within the wireway  630  to provide space to accommodate electrical cables. In some embodiments, the top surface of the wireway  630  (e.g., the side that faces away from the roof deck) includes at least one dark-colored portion and at least one light-colored portion. In some embodiments, the wireway  630  includes a horizontal light-colored portion  640  that is substantially similar to the horizontal light-colored portion  610  of the wireway  600  described above. In some embodiments, the wireway  630  includes a vertical light-colored portion  642 . The vertical light-colored portion  642  shown in  FIG.  6 D  extends across the top surface  632  of the wireway  630  intermediate the sides  634 ,  636 , in a manner similar to the vertical light-colored portion  614  shown in  FIG.  6 B , but it will be apparent to those of skill in the art that, in other embodiments, the vertical light-colored portion  642  of the wireway  630  may extend along either of the sides  634  or  636 , in a manner similar to the vertical light-colored portions  612  and  616  shown in  FIGS.  6 A and  6 C , respectively. 
     In some embodiments, an exemplary wireway  660 , as shown in perspective in  FIG.  6 E  and in a front view in  FIG.  6 F , is substantially similar to the wireway  600  described above with reference to  FIGS.  6 A- 6 C , other than as described hereinafter. In some embodiments, the wireway  660  has a flat top  662  and sides  664 ,  666  that are substantially perpendicular to the flat top  662 . In some embodiments, the flat top  662  and angled sides  664 ,  666  of the wireway  660  define a channel  668  within the wireway  660  to provide space to accommodate electrical cables. In some embodiments, the top surface of the wireway  660  (e.g., the side that faces away from the roof deck) includes at least one dark-colored portion and at least one light-colored portion. In some embodiments, the wireway  660  includes a horizontal light-colored portion  670  that is substantially similar to the horizontal light-colored portion  610  of the wireway  600  described above. In some embodiments, the wireway  660  includes a vertical light-colored portion  672 . The vertical light-colored portion  672  shown in  FIG.  6 E  extends across the top surface  632  of the wireway  630  along the side, in a manner similar to the vertical light-colored portion  612  shown in  FIG.  6 A , but it will be apparent to those of skill in the art that, in other embodiments, the vertical light-colored portion  672  of the wireway  660  may extend along the side  636 , in a manner similar to the vertical light-colored portion  616  shown in  FIG.  6 C , or may extend across the top surface  632  intermediate the sides  634 ,  636 , in a manner similar to the vertical light-colored portion  614  shown in  FIG.  6 B . 
     In some embodiments, an exemplary roofing system includes a masking element applied to the border between adjacent PV modules.  FIG.  7    shows an exemplary masking element  700  applied to the border between adjacent PV modules  710 ,  720  (e.g., the PV modules  510 ,  520 ,  530  as described above with reference to  FIG.  5   ). In some embodiments, the masking element  700  is a dark color. In some embodiments, the masking element  700  is black. In some embodiments, the masking element  700  is made from a polymeric material. In some embodiments, the masking element  700  is made from a polymeric foam. In some embodiments, the masking element  700  is made from expanded polyethylene (“EPE”). In some embodiments, the masking element  700  is used in connection with the PV modules  710 ,  720  that have a high-contrast backsheet  730 . In some embodiments, due to the high contrast of the backsheet  730 , any color difference between the masking element  700  and the PV modules  710 ,  720  is swamped out, thereby hiding the boundary between the masking element  700  and the PV modules  710 ,  720 . In some embodiments, by hiding the boundary between adjacent PV modules, use of the masking element  700  reduces the uniform, grid-like appearance of a roofing system including the PV modules  710 ,  720 . 
     In some embodiments, a solar roofing system including one or more of the roofing shingle  300 , the PV module  510 , the wireway  600 , and/or the masking element  700  provides an appearance that includes similar degrees and types of irregular/randomized appearance across all elements of the roofing system. In some embodiments, such a randomized appearance is harmonized around the cell pitch, i.e., the sum of the width of each PV cell and the cell gap. In some embodiments, such a similarly-randomized appearance causes the various elements of the solar roofing system to visually blend with one another, thereby providing a more aesthetically pleasing appearance to the overall solar roofing system 
       FIG.  8 A  shows an exemplary roofing system  800  that includes a plurality of the roofing shingle  300 , a plurality of the PV module  510 , a plurality of the wireway  600 , and a plurality of the masking element  700 . For clarity, only one of each of the elements noted above is specifically identified by a reference numeral in  FIG.  8 A .  FIG.  8 B  shows a magnified view of a portion of the roofing system  800  including a plurality of the roofing shingle  300 , a plurality of the PV module  510 , and a plurality of the wireway  600  separating adjacent ones of the PV module  510 .  FIG.  8 C  shows a magnified view of a portion of the roofing system  800  including a plurality of the roofing shingle  300 , a plurality of the PV module  510 , and a plurality of the masking element  700  ones of the PV module  510  from adjacent ones of the roofing shingle  300 .  FIG.  8 D  shows a magnified view of a portion of the roofing system  800  including a plurality of the roofing shingle  300 , a plurality of the PV module  510 , and a plurality of the wireway  600  separating ones of the PV module  510  from adjacent ones of the roofing shingle  300 .  FIG.  8 E  shows a magnified view of a portion of the roofing system  800  including a plurality of the roofing shingle  300 , a plurality of the PV module  510 , and a plurality of the masking element  700  separating adjacent ones of the PV module  510 . It may be seen from  FIGS.  8 A- 8 E  that the roofing system  800  including a plurality of the roofing shingle  300 , a plurality of the PV module  510 , a plurality of the wireway  600 , and a plurality of the masking element  700  provides an aesthetic appearance in which the various elements of the roofing system  800  blend with one another aesthetically, rather than one in which the PV module  510  stands out. It will be apparent to those of skill in the art that the roofing system  800  shown in  FIGS.  8 A- 8 E  is only one exemplary manner of arranging a plurality of the roofing shingle  300 , a plurality of the PV module  510 , a plurality of the wireway  600 , and a plurality of the masking element  700 , and that any number of other arrangements of these same elements may be made. It will be further apparent to those of skill in the art that while the roofing system  800  shown in  FIGS.  8 A- 8 E  includes all of the roofing shingle  300 , the PV module  510 , the wireway  600 , and the masking element  700 , the same or similar aesthetic effect may be accomplished with a subset of these elements (including, but not limited to, with the roofing shingle  300  and the PV module  510 ; with the roofing shingle  300 , the PV module  510 , and the wireway  600 ; or with the roofing shingle  300 , the PV module  510 , and the masking element  700 ). 
     In some embodiments, the various elements of the exemplary roofing system  800  mimic the water-shedding ability of a conventional roof shingle. In some embodiments, the various elements of the exemplary roofing system can be affixed to a roof deck using typical roofing methods such as nails or screws. 
     In some embodiments, the roofing system  800  also includes at least one starter bar, a foot module, and a plurality of water shedding layers. In some embodiments, the roofing shingle  300  and/or the PV module includes an upper portion and a lower portion and is configured to be installed such that the upper portion is at a higher elevation than the lower portion. In some embodiments, the at least one starter bar is configured to be installed to a roof deck and includes a foot base. In some embodiments, a first one of the water shedding layers is configured to be installed over the foot base of the at least one starter bar, and at least one other one of the water shedding layers is configured to overlap and be installed over the first one of the plurality of water shedding layers. In some embodiments, the foot module is configured to be attached to the upper portion of the PV module  510  and/or the roofing shingle  300 . In some embodiments, the lower portion of the PV module  510  and/or the roofing shingle  300  is adapted to align with the foot base of the at least one starter bar, and the foot module is configured to be affixed to a last overlapping layer of the at least one of another of the first plurality of water shedding layers to the roof deck. 
     While a number of embodiments of the present invention have been described, it is understood that these embodiments are illustrative only, and not restrictive, and that many modifications may become apparent to those of ordinary skill in the art. Further still, the various steps may be carried out in any desired order (and any desired steps may be added and/or any desired steps may be eliminated).