System and method for estimating photovoltaic energy through linearly interpolated clearness indexes 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 through linearly interpolated clearness indexes 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 processor configured to:
obtain 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 create 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;
determine an average of the irradiance observations;
determine a set of sky clearness indexes as a ratio of each of the irradiance observations and clear sky global horizontal irradiance;
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 average of the irradiance observations and the product of the weighting factor array and an sky clearness index array formed by the sky clearness index corresponding to the irradiance observation occurring before the one irradiance observation, the sky clearness index corresponding to the one irradiance observation, and the sky clearness index corresponding to 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
forecast photovoltaic energy production for the photovoltaic plant 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 processor 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 sky clearness index 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 processor 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 by 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 4 , wherein the photovoltaic fleet is integrated into a power grid and wherein the power grid is operated based on the forecast photovoltaic energy production for the photovoltaic fleet.
6. A system according to claim 1 , the processor further configured to:
provide the forecast photovoltaic energy production to at least one of a planner and an operator of the power grid.
7. A system according to claim 1 , the processor further configured to:
collect raw irradiance observations 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.
8. A system according to claim 1 , the processor further configured to:
collect a time series of power statistics from a plurality of existing photovoltaic stations;
select 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
determine the irradiance observations as average point statistics, each comprising an average of all values of the apparent irradiance.
9. A system according to claim 1 , the processor 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.
10. A system according to claim 1 , wherein and a sum of weighing factors within the weighing factor array is 1.
11. A method for estimating photovoltaic energy through linearly interpolated clearness indexes with the aid of a digital computer, comprising the steps of:
obtaining by a computer 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;
obtaining by the computer a set of clear sky irradiance, with each clear sky irradiance in the set corresponding to one of the irradiance observations;
selecting by the computer 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;
determining by the computer an average of the irradiance observations;
determining by the computer a set of sky clearness indexes as a ratio of each of the irradiance observations and clear sky global horizontal irradiance;
estimating by the computer 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 average of the irradiance observations and the product of the weighting factor array and an sky clearness index array formed by the sky clearness index corresponding to the irradiance observation occurring before the one irradiance observation, the sky clearness index corresponding to the one irradiance observation, and the sky clearness index corresponding to the irradiance observation occurring after the one irradiance observation;
forming by the computer 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 by the computer photovoltaic energy production for the photovoltaic plant 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 steps of:
setting the fractional offset to equal the duration of the regular time intervals.
13. A method according to claim 11 , 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 sky clearness index 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 step of:
obtaining by the computer 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 by the computer sets of normalized irradiation for each of the locations and forming time series of clearness indexes by the computer with the sets of normalized irradiation; and
forecasting photovoltaic energy production for the photovoltaic fleet by the computer as a function of the time series of the clearness indexes and photovoltaic plants' power ratings.
15. A method according to claim 14 , wherein the photovoltaic fleet is integrated into a power grid and wherein the power grid is operated based on the forecast photovoltaic energy production for the photovoltaic fleet.
16. A method according to claim 15 , further comprising:
providing the forecast photovoltaic energy production to at least one of a planner and an operator of the power grid.
17. 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.
18. 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.
19. 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.
20. A method according to claim 11 , wherein and a sum of weighing factors within the weighing factor array is 1.