System and method for estimating photovoltaic energy generation through linearly interpolated irradiance observations with the aid of a digital computer
The accuracy of photovoltaic simulation modeling is predicated upon the selection of a type of solar resource data appropriate to the form of simulation desired. Photovoltaic power simulation requires irradiance data. Photovoltaic energy simulation requires normalized irradiation data. Normalized irradiation is not always available, such as in photovoltaic plant installations where only point measurements of irradiance are sporadically collected or even entirely absent. Normalized irradiation can be estimated through several methodologies, including assuming that normalized irradiation simply equals irradiance, directly estimating normalized irradiation, applying linear interpolation to irradiance, applying linear interpolation to clearness index values, and empirically deriving irradiance weights. The normalized irradiation can then be used to forecast photovoltaic fleet energy production.
1. A system for estimating photovoltaic energy generation through linearly interpolated irradiance observations with the aid of a digital computer, comprising:
a computer coupled to a memory and comprising a processor configured to execute code stored in the memory, the computer configured to:
obtain with a set of irradiance observations that have been recorded for a location at which a photovoltaic plant can be operated with each irradiance observation in the set being separated by regular intervals of time;
obtain a set of clear sky irradiance with each clear sky irradiance in the set corresponding to one of the irradiance observations;
select a fractional offset that comprises an amount of time no bigger than the duration of the regular time intervals and creating a weighting factor array in the computer as a function of the fractional offset taken before, at, and after the ending of one of the regular time intervals;
estimate a set of normalized irradiation with each normalized irradiation in the set corresponding to one of the irradiance observations, the normalized irradiation comprising the product of the weighting factor array and an irradiance array formed by the irradiance observation occurring before the one irradiance observation, the one irradiance observation, and the irradiance observation occurring after the one irradiance observation;
form a time series of clearness indexes with each clearness index in the time series corresponding to one of the irradiance observations, each clearness index comprising a ratio of the irradiance observation's corresponding normalized irradiation estimate and the irradiance observation's corresponding clear sky irradiance; and
forecasting photovoltaic energy production for the photovoltaic plant in the computer as a function of the time series of the clearness indexes and photovoltaic plant's power rating.
2. A system according to claim 1 , the computer further configured to:
set the fractional offset to equal the duration of the regular time intervals.
3. A system according to claim 1 , wherein each normalized irradiation estimate I t −f to t 1−f at time t over a regular time interval defined by the fractional offset f is determined in accordance with:
I
t
-
f
to
t
1
-
f
_
=
[
ω
t
-
1
ω
t
0
ω
t
1
]
[
I
t
-
1
I
t
0
I
t
1
]
where
[
I
t
-
1
I
t
0
I
t
1
]
represents the weighting factor array and the irradiance array
[
ω
t
-
1
ω
t
0
ω
t
1
]
=
[
f
2
2
1
2
+
f
-
f
2
(
1
-
f
)
2
2
]
for
0
≤
f
≤
1.
4. A system according to claim 1 , the computer further configured to:
obtain sets of irradiance observations that have been recorded for a plurality of locations at which a photovoltaic fleet comprising a plurality of photovoltaic plants can be operated;
estimate sets of normalized irradiation for each of the locations and forming time series of clearness indexes in the computer with the sets of normalized irradiation; and
forecast photovoltaic energy production for the photovoltaic fleet as a function of the time series of the clearness indexes and photovoltaic plants' power ratings.
5. A system according to claim 1 , the computer further configured to:
receive raw irradiance observations collected from a plurality of ground- based weather stations; and
assemble the irradiance observations as point statistics, each comprising an average of all values of the raw irradiance observations.
6. A system according to claim 1 , the computer further configured to:
obtain a time series of power statistics collected from a plurality of existing photovoltaic stations;
select a performance model for each of the existing photovoltaic stations and infer apparent irradiance as area statistics based on the performance model selected and the time series of power statistics; and
determine the irradiance observations as average point statistics, each comprising an average of all values of the apparent irradiance.
7. A system according to claim 1 , the computer further configured to:
collect area solar irradiance statistics, each comprising a set of pixels from satellite imagery for a physical area within the geographic region;
convert the area solar irradiance statistics to irradiance statistics for an average point within the set of pixels; and
determine the irradiance observations as average point statistics, each comprising an average of all values of the set of pixels.
8. A system according to claim 1 , the computer further configured to:
represent the irradiance observations on a graph that uses time as one of the axis;
form an irradiance curve comprising interpolating on the graph the plotted irradiance observations; and
find an area under a portion of the curve defined using the fractional offset; and
use the area to determine at least a portion of the set of the normalized irradiance.
9. A system according to claim 8 , further comprising the steps of:
interpolate a slope between two consecutive ones of the irradiance observations represented on the graph; and
use the slope to determine at least a portion of the set of the normalized irradiance.
10. A system according to claim 1 , wherein a sum of weighting factors in the weighting factor array equals 1.
11. A method for estimating photovoltaic energy generation through linearly interpolated irradiance observations with the aid of a digital computer, comprising the steps of:
providing a computer with a set of irradiance observations that have been recorded for a location at which a photovoltaic plant can be operated with each irradiance observation in the set being separated by regular intervals of time;
providing the computer with a set of clear sky irradiance with each clear sky irradiance in the set corresponding to one of the irradiance observations;
selecting a fractional offset in the computer that comprises an amount of time no bigger than the duration of the regular time intervals and creating a weighting factor array in the computer as a function of the fractional offset taken before, at, and after the ending of one of the regular time intervals;
estimating a set of normalized irradiation in the computer with each normalized irradiation in the set corresponding to one of the irradiance observations, the normalized irradiation comprising the product of the weighting factor array and an irradiance array formed by the irradiance observation occurring before the one irradiance observation, the one irradiance observation, and the irradiance observation occurring after the one irradiance observation;
forming a time series of clearness indexes in the computer with each clearness index in the time series corresponding to one of the irradiance observations, each clearness index comprising a ratio of the irradiance observation's corresponding normalized irradiation estimate and the irradiance observation's corresponding clear sky irradiance; and
forecasting photovoltaic energy production for the photovoltaic plant in the computer as a function of the time series of the clearness indexes and photovoltaic plant's power rating.
12. A method according to claim 11 , further comprising the step of:
setting the fractional offset to equal the duration of the regular time intervals.
13. A method according to claim 1 , wherein each normalized irradiation estimate I t −f to t 1−f at time t over a regular time interval defined by the fractional offset f is determined in accordance with:
I
t
-
f
to
t
1
-
f
_
=
[
ω
t
-
1
ω
t
0
ω
t
1
]
[
I
t
-
1
I
t
0
I
t
1
]
where
[
I
t
-
1
I
t
0
I
t
1
]
represents the weighting factor array and the irradiance array
[
ω
t
-
1
ω
t
0
ω
t
1
]
=
[
f
2
2
1
2
+
f
-
f
2
(
1
-
f
)
2
2
]
for
0
≤
f
≤
1.
14. A method according to claim 11 , further comprising the steps of:
providing the computer with sets of irradiance observations that have been recorded for a plurality of locations at which a photovoltaic fleet comprising a plurality of photovoltaic plants can be operated;
estimating sets of normalized irradiation in the computer for each of the locations and forming time series of clearness indexes in the computer with the sets of normalized irradiation; and
forecasting photovoltaic energy production for the photovoltaic fleet in the computer as a function of the time series of the clearness indexes and photovoltaic plants' power ratings.
15. A method according to claim 11 , further comprising the steps of:
collecting raw irradiance observations from a plurality of ground-based weather stations; and
assembling the irradiance observations as point statistics, each comprising an average of all values of the raw irradiance observations.
16. A method according to claim 11 , further comprising the steps of:
collecting a time series of power statistics from a plurality of existing photovoltaic stations;
selecting a performance model for each of the existing photovoltaic stations and inferring apparent irradiance as area statistics based on the performance model selected and the time series of power statistics; and
determining the irradiance observations as average point statistics, each comprising an average of all values of the apparent irradiance.
17. A method according to claim 11 , further comprising the steps of:
collecting area solar irradiance statistics, each comprising a set of pixels from satellite imagery for a physical area within the geographic region;
converting the area solar irradiance statistics to irradiance statistics for an average point within the set of pixels; and
determining the irradiance observations as average point statistics, each comprising an average of all values of the set of pixels.
18. A method according to claim 11 , further comprising the steps of:
representing the irradiance observations on a graph that uses time as one of the axis;
forming an irradiance curve comprising interpolating on the graph the plotted irradiance observations; and
finding an area under a portion of the curve defined using the fractional offset; and
using the area to determine at least a portion of the set of the normalized irradiance.
19. A method according to claim 18 , further comprising the steps of:
interpolating a slope between two consecutive ones of the irradiance observations represented on the graph; and
using the slope to determine at least a portion of the set of the normalized irradiance.
20. A method according to claim 11 , wherein a sum of weighting factors in the weighting factor array equals 1.