Multi-phase backtracking of photovoltaic modules
A method may include calculating a solar position of the Sun and a projected solar zenith (PSZ) relative to a position of a photovoltaic (PV) module. The method may include determining whether an orientation of the PV module is configurable to prevent shading of an upper substring of the PV module while shading a lower substring of the PV module. Responsive to determining that such an orientation is not configurable, the method may include determining whether the orientation of the PV module is configurable to prevent shading of both the upper substring and the lower substring. Responsive to determining that such an orientation is not configurable, the method may include determining whether the PSZ is within a maximum tracker angle range. A target tracker angle may be identified based on the PSZ and the maximum tracker angle range and used as a tracker angle control setpoint.
1. A method, comprising:
calculating a solar position of the Sun;
calculating a projected solar zenith (PSZ) based on the solar position of the Sun and a position of first photovoltaic (PV) modules on a first tracker row and second PV modules on a second tracker row, wherein each of the first and second PV modules include an upper substring of solar cells and a lower substring of solar cells;
evaluating the following expressions to determine whether it is possible to position the PV modules in an orientation that limits shading of the upper substring of the PV modules by not more than a first threshold amount while shading the lower substring of the PV modules by at least a second threshold amount:
PSZ
min
,
50
=
Row
Spacing
-
0.5
·
Table
Width
·
cos
(
R
min
+
CS
)
0.5
·
Table
Width
·
sin
(
R
min
+
CS
)
-
CS
PSZ
max
,
50
=
Row
Spacing
-
0.5
·
Table
Width
·
cos
(
R
max
+
CS
)
0.5
·
Table
Width
·
sin
(
R
max
+
CS
)
-
CS
where Row Spacing is a horizontal spacing between the first and second tracker rows, Table Width is the width of the first and second tracker rows, Rmin is a maximum tracker angle towards a direction that PSZ is negative, Rmax is a maximum tracker angle towards a direction that PSZ is positive, and CS is a slope angle between the first and second tracker rows;
responsive to determining that it is possible to position the PV modules in an orientation that prevents shading of the upper substring of the PV modules by at least the first threshold amount while shading the lower substring of the PV modules by at least the second threshold amount, calculating a target tracker angle that prevents shading of the upper substring of the PV modules by at least the first threshold amount while shading the lower substring of the PV modules by at least the second threshold amount; and
positioning the PV modules at the target tracker angle.
2. The method of claim 1 , wherein calculating the PSZ includes:
projecting the solar position of the Sun to a plane orthogonal to the first and second tracker rows;
measuring an angle from a vertical axis to the projection of the solar position of the Sun; and
determining a positive notation or a negative notation of the PSZ based on whether a time associated with the calculation of the PSZ is before or after solar noon.
3. The method of claim 1 , wherein the first threshold is 10%.
4. The method of claim 1 , wherein the second threshold is 90%.
5. The method of claim 1 , wherein calculating the target tracker angle includes evaluating the following expression:
Δ
R
=
cos
-
1
(
Row
Spacing
0.5
·
Table
Width
·
(
cos
PSZ
-
tan
CS
·
sin
PSZ
)
)
.
6. A method, comprising:
calculating a solar position of the Sun;
calculating a projected solar zenith (PSZ) based on the solar position of the Sun and a position of first photovoltaic (PV) modules on a first tracker row and second PV modules on a second tracker row, wherein each of the first and second PV modules include an upper substring of solar cells and a lower substring of solar cells;
determining whether it is possible to position the PV modules in an orientation that limits shading of the upper substring of the PV modules by not more than a first threshold amount while shading the lower substring of the PV modules by at least a second threshold amount;
responsive to determining that it is not possible to position the PV modules in an orientation that prevents shading of the upper substring of the PV modules by at least the first threshold amount while shading the lower substring of the PV modules by at least the second threshold amount, evaluating the following expressions to determine whether it is possible to position the PV modules in an orientation that prevents shading of the upper and lower substrings of the PV modules by at least a third threshold amount while an amount of beam irradiance incident on the upper and lower substrings of the PV modules exceeds a fourth threshold:
PSZ
min
,
100
=
Row
Spacing
-
Table
Width
·
cos
(
R
min
+
CS
)
Table
Width
·
sin
(
R
min
+
CS
)
-
CS
PSZ
max
,
100
=
Row
Spacing
-
Table
Width
·
cos
(
R
max
+
CS
)
Table
Width
·
sin
(
R
max
+
CS
)
-
C
S
where Row Spacing is a horizontal spacing between the first and second tracker rows, Table Width is the width of the first and second tracker rows, Rmin is a maximum tracker angle towards a direction that PSZ is negative, Rmax is a maximum tracker angle towards a direction that PSZ is positive, and CS is a slope angle between the first and second tracker rows;
responsive to determining that it is possible to position the PV modules in an orientation that prevents shading of the upper and lower substrings of the PV modules by at least the third threshold amount, calculating a target tracker angle that prevents shading of the upper and lower substrings of the PV modules by at least the third threshold amount; and
positioning the PV modules at the target tracker angle.
7. The method of claim 6 , wherein calculating the PSZ includes:
projecting the solar position of the Sun to a plane orthogonal to the first and second tracker rows;
measuring an angle from a vertical axis to the projection of the solar position of the Sun; and
determining a positive notation or a negative notation of the PSZ based on whether a time associated with the calculation of the PSZ is before or after solar noon.
8. The method of claim 6 , wherein the first threshold is 10%.
9. The method of claim 6 , wherein the second threshold is 90%.
10. The method of claim 6 , wherein the third threshold is 90%.
11. The method of claim 6 , wherein the fourth threshold is 90%.
12. The method of claim 6 , wherein determining whether it is possible to position the PV modules in an orientation that limits shading of the upper substring of the PV modules by not more than a first threshold amount while shading the lower substring of the PV modules by at least a second threshold amount includes evaluating the following expressions:
PSZ
min
,
50
=
Row
Spacing
-
0.5
·
Table
Width
·
cos
(
R
min
+
CS
)
0.5
·
Table
Width
·
sin
(
R
min
+
CS
)
-
CS
PSZ
max
,
50
=
Row
Spacing
-
0.5
·
Table
Width
·
cos
(
R
max
+
CS
)
0.5
·
Table
Width
·
sin
(
R
max
+
CS
)
-
CS
.
13. The method of claim 6 , wherein calculating the target tracker angle includes evaluating the following expression:
Δ
R
=
cos
-
1
(
Row
Spacing
0.5
·
Table
Width
·
(
cos
PSZ
-
tan
CS
·
sin
PSZ
)
)
.