Estimating photovoltaic energy through averaged 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 method for estimating photovoltaic energy through averaged 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 connected to a power grid can be operated with each irradiance observation in the set being separated by regular intervals of time, the power grid comprising a plurality of power generators other than the photovoltaic plant, a transmission infrastructure, and a power distribution infrastructure for distributing power from the photovoltaic plant and the power generators to consumers;
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;
estimating a set of normalized irradiation in the computer comprising the steps of:
for each normalized irradiation estimate, selecting in the computer any three irradiance observations and a fractional offset about the middle irradiance observation;
interpolating a pair of linear slopes in the computer between the clear sky irradiance corresponding to the middle irradiance observation selected and the clear sky irradiances corresponding to each of the other two irradiance observations selected;
for each of the linear slopes, finding a weighting in the computer relative to the part of the fractional offset that falls under that linear slope; and
determining the normalized irradiation estimate in the computer as a product of the averages of the clear sky irradiances corresponding to each of the linear slopes and the averages of the areas under each of the linear slopes in proportion to their respective weightings;
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; and
controlling the photovoltaic energy production for the photovoltaic plant with an output controller to produce the photovoltaic energy based upon the photovoltaic plant's forecasted photovoltaic energy production,
wherein an amount of the power requested from one or more of the power generators and distributed from the one or more power generators using the transmission infrastructure and the distribution infrastructure to one or more of the customers is based on the forecasted photovoltaic energy production.
2. A method according to claim 1 , wherein each normalized irradiation estimate Irradiation t 0 to t 0 +Δt from time t 0 over a regular time interval Δt comprises the area under an irradiance curve determined in accordance with:
Irradiation
t
0
to
t
0
+
Δ
t
_
=
E
[
∫
t
0
t
0
+
Δ
t
I
t
d
t
]
where I t is an irradiance observation in the set of irradiance observations at time t.
3. A method according to claim 1 , wherein each normalized irradiation estimate Irradiation t 0 to t 0 +Δt from time t 0 over a regular time interval Δt is determined in accordance with:
Irradiation
t
0
to
t
0
+
Δ
t
_
≈
(
1
N
)
∑
i
=
0
N
-
1
I
t
0
+
i
*
Δ
t
N
where N is the number of irradiance observations between time t 0 over a regular time interval Δt and I t represents the irradiance observation in the set of irradiance observations at time
t
0
+
i
*
Δ
t
N
.
4. A method according to claim 1 , further comprising the step 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.
5. A method according to claim 1 , 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.
6. A method according to claim 1 , 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.
7. A method according to claim 1 , 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.