D2.1 Assumptions on accuracy of photovoltaic power to

Transcription

Project no: 239456
Project acronym
OPTIMATE
Project title:
An Open Platform to Test Integration in new MArkeT designs of massive
intermittent Energy sources dispersed in several regional power markets
Instrument: Collaborative project
Start date of project: 1st October 2009
Duration: 36 months
D2.1
Assumptions on accuracy of photovoltaic power to be considered
at short term horizons
Revision: Final version
Due date of delivery: 2010-09-30
Actual submission date: 2010-10-01
Organisation name of contractor(s) for this deliverable:
Red Eléctrica de España
Dissemination Level
PU
PP
RE
CO
Public
Restricted to other programme participants (including the Commission Services)
Restricted to a group specified by the consortium (including the Commission Services)
Confidential, only for members of the consortium (including the Commission Services)
X
Document information
Identification
Deliverable number:
Document name:
Revision version, date
Authors
D2.1
Assumptions on accuracy of photovoltaic power to be considered at short term horizons
Final version, 30 September 2010
Carlos Rodríguez / Mayte García Casado, Red Eléctrica de España
General purpose
This document is the deliverable D2.1 of the OPTIMATE project. The document describes briefly the state-of-the-art
in forecasting PV power and describes some characteristics of sun power and the use of forecasting errors generation
in the Optimate-model. Due to the nature of the energy source, the sun, we propose a model based on the statistics
of the atmosphere that simulates the amount of solar energy reaching the earth surface. As solar energy has a
stationary component that fluctuates throughout the year in a predictable cycle in each cluster, the proposed model
eliminates this seasonality centering on what is truly stochastic: the clarity of the atmosphere. Thus, the main source
of error in forecasting PV power generation is the error in predicting radiation. Due to the recent development of PV
forecasting models, the data of accuracy statistics are not available yet or are still preliminary. Not so with the
accuracy forecast data of irradiation that is now available for all Optimate clusters. The proposed model can work
with both sources of statistical error, but initially we will focus on atmospheric variables. Given this framework, a
methodology for generating PV scenarios and forecast errors scenarios from a root forecasted scenario is described
in this document.
Deliverable number:
Deliverable title:
Work package:
Lead contractor:
D2.1
Assumptions on accuracy of photovoltaic power to be considered at short term horizons
WP2
Red Eléctrica de España
Quality Assurance
Status
Verified by Coordinator
Verified by Technical director
Submitted by Coordinator
30/09/2010
By
Athanase Vafeas, Technofi
Jean-Marie Coulondre, RTE
Athanase Vafeas, Technofi
OPTIMATE_D21_Assumptions on accuracy of PV data
Date
2010-08-09
2010-09-17
2010-10-01
Page: 2
Table of Content
Acronyms and definitions ................................................................................................................. 7
1.
Introduction .............................................................................................................................. 8
1.1. The Optimate project ......................................................................................................... 8
1.2. This report as part of Optimate ......................................................................................... 9
1.3. Introduction to the PV technology .................................................................................. 11
2.
1.3.1.
Atmospheric effects, including absorption and scattering ........................................................ 11
1.3.2.
Cloud cover and pollution ........................................................................................................ 11
1.3.3.
Latitude, season and time of the day ........................................................................................ 12
1.3.4.
Other effects ............................................................................................................................. 14
State-of-the-art in PV forecasting ........................................................................................ 16
2.1. Forecasting irradiance ..................................................................................................... 16
2.2. PV forecasting models .................................................................................................... 21
3.
The use of prediction errors in Optimate ............................................................................ 25
3.1. How prediction error enter into the modelling framework of Optimate ......................... 25
3.1.1.
The DA process ........................................................................................................................ 25
3.1.2.
The ID process.......................................................................................................................... 26
3.2. Intermittent generation data needed in Optimate ............................................................ 27
4.
3.2.1.
Output of the proposed methodology used as input for Optimate simulator ............................ 27
3.2.2.
Input data for the proposed methodology ................................................................................. 28
Methodology to handle prediction errors to be used in Optimate .................................... 29
4.1. Atmosphere simulation ................................................................................................... 33
4.1.1.
The Clearness index ................................................................................................................. 34
4.1.2.
The Markov Chain .................................................................................................................... 40
4.1.3.
The Markov Chain Monte Carlo (MCMC) simulation ............................................................. 42
4.1.4.
The scenario selection based on errors forecasting irradiance ............................................... 46
4.2. Calculation of irradiation in tilted surfaces ..................................................................... 47
4.3. Transference function ...................................................................................................... 47
4.4. Distribution of errors forecasting the clearness index ..................................................... 55
5.
Conclusions ............................................................................................................................. 61
6.
References ............................................................................................................................... 62
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List of figures
Figure: 1 Position of the methodology proposed in this document............................................. 10
Figure: 2 Solar energy potential .................................................................................................... 12
Figure: 3 Air Mass........................................................................................................................... 12
Figure: 4 Sun path at Toledo .......................................................................................................... 13
Figure: 5 Sun path at Bobigny ....................................................................................................... 14
Figure: 6 Clear-sky irradiance two axes tracking ........................................................................ 14
Figure: 7 Average temperature in month ..................................................................................... 15
Figure: 8. Relative real measures at PV plant I in minutes. Sunny day .................................... 16
Figure: 9 Relative real measures at PV tracking plant in minutes. Partially
cloudy day ............................................................................................................................... 17
Figure: 10 Clearness index ............................................................................................................. 17
Figure: 11. Errors in Spanish stations ........................................................................................... 19
Figure: 12: Relative errors in forecasted irradiation ................................................................... 20
Figure: 13 Relative errors in forecasted irradiation .................................................................... 21
Figure: 14. REE Forecasting model description .......................................................................... 22
Figure: 15. Forecasting model description .................................................................................... 23
Figure: 16 (a) Correlation coefficient of forecast errors of two stations over
his spatial distance. (b) Error reduction factor RMSEensemble/ RMSEsingle ....................... 24
Figure: 17. Error scenarios from a forecasted (dot line) DA scenario. The
error scenario must be within bands (black lines) .............................................................. 29
Figure: 18. Block diagram 1 ........................................................................................................... 31
Figure: 19. Block diagam 2 ............................................................................................................. 32
Figure: 20. Block diagram 3 ........................................................................................................... 34
Figure: 21. Examples of irradiance in winter and summer time ................................................ 35
Figure: 22. Irradiance for the full year ......................................................................................... 36
Figure: 23. Clearness Index ............................................................................................................ 37
Figure: 24. Clearness index for consecutive solar hours ............................................................. 37
Figure: 25. Histogram distribution of the clearness index. ......................................................... 38
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Figure: 26. Distribution of RKc=(1.05-Kc) ................................................................................... 38
Figure: 27. Clearness index time-series process ........................................................................... 39
Figure: 28. Irradiation overlay of several weather stations. ....................................................... 39
Figure: 29. Correlation coefficient at several weather stations .................................................. 40
Figure: 30. Correlation matrices.................................................................................................... 41
Figure: 31 MCMC Simulation ....................................................................................................... 42
Figure: 32. Simulated energy production at PV plant in winter. ............................................... 43
Figure: 33.Simulated energy production at PV plant in summer. .............................................. 44
Figure: 34. Power duration curves for an average of six years simulated. ................................ 44
Figure: 35. In this flow chart two clusters correlated with a third series of
temperature is shown as an example. ................................................................................... 45
Figure: 36. Bollinger bands in stock markets. .............................................................................. 46
Figure: 37. Irradiation in tilted surfaces ....................................................................................... 47
Figure: 38 Transference function .................................................................................................. 48
Figure: 39. Irradiation in W/m2 .................................................................................................... 49
Figure: 40.Temperature in 10*ºC .................................................................................................. 50
Figure: 41. Wind speed in m2/s ...................................................................................................... 51
Figure: 42. Transference function in 3D ....................................................................................... 52
Figure: 43. Distribution of residuals after interpolation ............................................................. 52
Figure: 44. Transference function in 3D. Real data. .................................................................... 53
Figure: 45. Power loses due to temperature. Real data. .............................................................. 53
Figure: 46. Calculated losses in transfer function due to the increase of Ta
temperature. ........................................................................................................................... 54
Figure: 47. Wind influence in the transference function. ............................................................ 55
Figure: 48 Distribution Errors ....................................................................................................... 56
Figure: 49. Error forecasting irradiation in several weather stations. ...................................... 58
Figure: 50. RMSE forecasting irradiation for the AEMET NWP launched at
0 h for the current day. .......................................................................................................... 58
Figure: 51. Mean error ................................................................................................................... 59
Figure: 52. Relative to de forecasted irradiation mean error. .................................................... 59
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List of tables
Table 1. Weather stations distances used for correlation. ........................................................... 40
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Acronyms and definitions
AM: Air Mass is the path length which light takes through the atmosphere normalized to the
shortness possible path length, that is, mid day.
AR: Autoregressive model.
CECRE: Centro de Control para Régimen Especial (Renewable Energy Sources Control
Center).
DA: Day Ahead.
ID: Intra Day.
kWp (Peak Power Production): The nominal peak power is the power rating given by the
manufacturer of the module or system. It is the power output of the module(s) measured at
1000W/m2 solar irradiance (and a module temperature of 25°C and a solar spectrum
corresponding to an air mass of 1.5 AM1.5). This means that if your modules were 100%
efficient, you would need 1 m2 to get a system with a peak power of 1kW. These conditions are
known as Standard Test Conditions (STC).
MC: Markov Chain. They are processes describing trajectories where successive quantities are
described probabilistically according to the value of their immediate predecessors.
MCMC: Markov Chain and Monte Carlo, techniques that enable simulation from a MC
distribution.
NWP: Numerical Weather Prediction (Models).
PV: Photovoltaic.
REE: Red Eléctrica de España.
RES: Renewable Energy Sources.
RMSE: Root mean squared error.
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Introduction
1.
1.1.
The Optimate project
Optimate is a numerical simulation platform to recommend new electricity market designs
integrating massive flexible generation in Europe.
The project aims at developing a numerical test platform to analyse and to validate new
market designs which may allow integrating massive flexible generation dispersed in
several regional power markets. OPTIMATE will therefore contribute to the construction
of a pan-European electricity market.
Optimate is a collaborative research and demonstration project co-funded by the European
Commission under the 7th Framework Programme (DG Energy).
The Consortium is made of twelve partners:



5 TSOs:
o ELIA (Belgium),
o EnBW TSO (Germany),
o REE (Spain),
o RTE (France),
o 50 Hertz Transmission (Germany)
6 Research providers specialised in market design and modelling:
o ARMINES,
o K.U.Leuven,
o RISOE,
o University of Madrid-Comillas,
o University of Manchester,
o SEAES (University of Paris)
1 company dedicated to innovation management and related dissemination
activities in the power sector: TECHNOFI.
Today’s electricity markets rely mostly on conventional generation, and, to a much smaller
extent, on interruptible loads since such loads are less flexible than generation. Thus,
European market rules have so far been developed to deal with the most widely used
generation units (nuclear, hydro and thermal power plants). For instance, some block bids
used in power exchanges can be understood as reflecting the dynamic constraints of the
generating units.
Intermittent generation, based on wind and/or solar power, have specific features which do
not fit easily in these current electricity market frameworks. On the one hand, their dayahead forecasts are significantly less accurate than load forecasts. On the other hand, they
are not dispatchable like most of the conventional generation units. Their increasing share
in generation portfolios bidding into spot markets sets new challenges for improved market
designs, e.g. balancing and congestion management rules: in some instances, congestion
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and balancing costs might indeed jeopardize the expected benefits of such new generation
capacities.
1.2.
This report as part of Optimate
This paper describes a methodology approach to generate DA error PV scenarios in each
intra-day and “real-time” simulations from a given DA forecasted PV production from
clusters.
The OPTIMATE Simulator will go successively through the 365 days of the simulated
year. The key point to be analyzed is then the functional process proposed to simulate each
day and to link those successive daily simulations, the whole being called Meta-Model.
The differences of market design, whose costs and benefits will be quantified by the
Simulator, shall indeed be either in input data (such as Portfolio definitions), or in
parametric variants allowed within the Meta-model (such as imbalance settlements rules).
The 8760 hours OPTIMATE scenario standing for ”real time RT” (root scenario) values of
load, PV and wind generation, are fixed data. The relationship between those fixed data,
task 2.1 (PV power forecast), task 3.1 (Wind power forecast), task 1.2 (Data management)
and the simulator itself is shown on the figure below.
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Figure: 1 Position of the methodology proposed in this document
Fixed data
Dispatchable
generation fixed data
(capacity & location)
Scenario of Load, Wind &
PV (per country)
Grid data
Data management
Task 1.2
Task 2.1
Task 3.1
Clustering
RT scenario of Load,
Wind and PV, per cluster
Draw
DA forecast error for
Load, Wind & PV
(per cluster, per country)
ID forecast error for
Load, Wind & PV
(per cluster, per country)
DA reference scenario:
unit commitment, market
prices, cross-border
exchanges
OPTIMATE
Simulator
Data
Management
Task 1.2
Day Ahead process
Intra-Day process
Scheduler
Time aggregation process
Day Ahead and Intra-Day scenario for load, wind power and PV power is derived from this
real time scenario and from the clustering (OPTIMATE data management). There will be a
scenario generator with a Monte Carlo draw to select the current scenario. Correlation
matrices will take care of consistency:


inside each the trajectory during 36 hours;
between trajectories of neighbouring clusters, therefore between cluster-wide
trajectories and area-wide trajectories.
Then initial thermal & hydro programmes consistent both with load, PV and Wind power
DA scenario and with other fixed characteristics are assessed over the 8760 hours of the
year within OPTIMATE data management task.
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ID forecast are mostly for wind speed, solar irradiation and load (strongly related to
temperature in some countries). RT values of those items are considered as input data. The
trajectory of each forecast (from 36 hours-before-RT to ½ hour-before-RT, per cluster and
per area, and over the 17520 half-hours of the year) will be allowed to move away both
from DA forecast and from those RT values according to distribution functions related to
the 36 hours timeframe and to their geographical location.
1.3.
Introduction to the PV technology
While the solar radiation incident outside the Earth’s atmosphere is relatively constant, the
radiation at the Earth’s surface varies widely due to:





Atmospheric effects, including absorption and scattering
Local variations in the atmosphere, clouds, pollution, and water vapour
Latitude of the location
The season of the year
The time of day.
Atmospheric effects, including absorption and scattering
1.3.1.
Light is absorbed as it passes through the atmosphere and at the same time is subject to
scattering. Red light has a wavelength larger than most particles and is unaffected. Blue
light has a wavelength similar to the size of particles in the atmosphere and so is scattered.
The irradiation is the energy power in W.h/m2 incident in a solar cell and can be
decomposed in:



Direct Beam
Diffuse (scattering). For a clear day a 10% of global. (The blue of the sky)
Albedo or reflected; light from ground or clouds.
1.3.2.
Cloud cover and pollution
Information in relation to cloud cover levels is used to provide estimates of the solar
irradiation at a specific location. Such cloud cover data represents an important resource to
determine the radiation at a broader level.
In the following picture from European Commission PVgis [2] we see the solar energy
potential for Spain in optimal tilted planes Figure: 2. It depends on the frequency of clouds
and pollution averages over years.
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Figure: 2 Solar energy potential
1.3.3.
Latitude, season and time of the day
Due to the daily rotation of the earth, changing power every hour is the result of a variation
of the air mass (AM) of flowing through the sunlight.
Figure: 3 Air Mass
θ
AM1
(1)
if θ= 30º the AM1.1547
if θ= 0º the AM1
if θ= 90º the AM2.37
if θ= 48º the AM1.5G (standard for cells 1 kW/m2)
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AM0 means outside the Earth’s atmosphere.
The rotation of the Earth around the sun and the tilt on its axis by 23.45º changes the
declination angel, denoted δ. This change the sunlight path thought the atmosphere and, for
instance, the AM. The seasonal declination has the following formula:
(2)
Where d is the day of the year with Jan 1 as d = 1.
The elevation α and the azimuth z angles depends on the latitude.
(3)
(4)
So PV plants change their maximum power every hour and every day of the year and thus
depend on time and location. Figure: 4 and Figure: 5 show two examples at two different
locations. The landscape of each location determines finally the sun rise and sun set.
Figure: 4 Sun path at Toledo
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Figure: 5 Sun path at Bobigny
The final figure shows the tracked clear-sky irradiance in Nanterre, France on June. Figure:
6 Clear-sky irradiance
Figure: 6 Clear-sky irradiance two axes tracking
1.3.4.
Other effects
Finally the power incident on a PV module depends not only on the power contained in the
sunlight, but also on the angle between the module and the sun, this is the power density of
the sunlight. To simplify we call this the geometry of solar cells and it depends on the cells
tracking mode and surface.
The increase of PV module temperature reduces its voltage and the power output about 5%
for each 10ºC increase in temperature. These loss mechanisms depend on the thermal
resistance of the module materials, the emissive properties of the PV module, and the
ambient conditions (particularly wind speed) in which the module is mounted.
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The ambient temperature also affects inverters. The facilities were inverters are installed
physically can be outhor or in houses with air conditioning. Its electrical power output can
be less than the peak power installed solar panels. This depends on economic factors.
Figure: 7 Average temperature in month
For a typical commercial PV module operating at its maximum power point, only 10 to
15% of the incident sunlight is converted into electricity, with much of the remainder being
converted into heat.
The Figure: 7 shows the average temperature variation in Toledo (Spain) in January.
The conversion efficiency depends on the spectrum of the solar radiation. Where nearly all
PV technologies have good performance for visible light, there are large differences in the
efficiency for near-infrared radiation. If the spectrum of the light were always the same this
effect would be assumed to be part of the nominal efficiency of the modules. But the
spectrum changes with the time of day and year, and with the amount of diffuse light (light
not coming directly from the sun but from the sky, clouds, etc.).
Some of the light is reflected from the surface of the modules and never reaches the actual
PV material. The level of this reflection depends on the angle at which the light strikes the
module. The more the light comes from the side (narrow angle with the module plane), the
higher the percentage of reflected light. This effect varies (not strongly) between module
types.
Almost all module types show decreasing efficiency with low light intensity. The strength
of this effect varies between module types.
The light from albedo (reflected light) depends on the angle of the modules and the
reflexion from the surrounding ground. It should be noted that there is no reflection from
the ground if the orientation of the plate is horizontal. In this case the albedo light would
come only from the reflection of clouds mainly.
Finally, some module types have long-term variations in the performance. Especially
modules made from amorphous silicon are subject to seasonal variations in performance,
driven by long-term exposure to light and to high temperatures.
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State-of-the-art in PV forecasting
2.
2.1.
Forecasting irradiance
Forecast solar radiation is the key factor to predict the PV energy production. The clouds
are therefore by far the very first driver on solar forecast. There are “stable” clouds with
coherent patterns and motion that it will be predictable in the future. But convective events
(“unstable” clouds) will always be a challenge to predict.
Also there are excellent satellite-base cloud resources available to guide short term solar
forecast. In the prediction of the wind cannot use this methodology. See [8].
Aerosols and haze also have significant impact on energy production (but less so on
ramps).
The PV energy is characterized by very short term ramp rates and variability forecasting in
minutes in a particular PV plant for small clouds. This is a serious problem of voltage dips
in small systems. Taking care to separate solar plants more than 10 km in the system
reduces the risk of simultaneity.
Forecast PV energy power is equivalent to forecast irradiation at the solar cells. See
Figure: 8. Relative real measures at PV plant I in minutes. Sunny day and Figure: 9
Relative real measures at PV tracking plant in minutes. Partially cloudy day
Figure: 8. Relative real measures at PV plant I in minutes. Sunny day
1.20
1.00
0.80
0.60
Irra W/m2
kW
ºC
Wind m/s
0.40
0.20
1
31
61
91
121
151
181
211
241
271
301
331
361
391
421
451
481
511
541
571
601
631
661
691
721
751
781
811
841
871
901
931
961
991
1021
1051
1081
1111
1141
1171
1201
1231
1261
1291
1321
1351
1381
1411
0.00
-0.20
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Figure: 9 Relative real measures at PV tracking plant in minutes. Partially cloudy day
1.20
1.00
0.80
0.60
Irr W/m2
kW
ºC
wind m/s
0.40
0.20
1
31
61
91
121
151
181
211
241
271
301
331
361
391
421
451
481
511
541
571
601
631
661
691
721
751
781
811
841
871
901
931
961
991
1021
1051
1081
1111
1141
1171
1201
1231
1261
1291
1321
1351
1381
1411
0.00
-0.20
Clear-sky models for direct beam and diffuse irradiance on horizontal and tilted planes at
the Earth’s surface are described in detail in [4]. The models give us an upper and lower
bounds of the irradiation in clear-sky conditions. This is an important tool as starting point
for prediction.
Figure: 10 Clearness index
Dynamic Range
irradiance
of
Upper bound consider
geometry/time/location
Clear-sky model
% clearness
Lower bound consider
geometry/time/location
Clear-sky model
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Numerical weather prediction programs (NWP) are the best actual tools for forecast
irradiance. In the last years various research organizations and companies have developed
different methods to forecast irradiance as a basis for respective power forecasts. For the
end-users of these forecasts it is important that standardized methodology is used when
presenting results on the accuracy of a prediction model in order to get a clear idea on the
advantages of a specific approach. The paper “Benchmarking of different approaches to
forecast solar irradiance” [9] is an evaluation in this way. The result shows a strong
dependence of the forecast accuracy on the climatic conditions. For Central European
stations the relative RMSE ranges are from 40 % to 60 %, for Spanish stations relative
RMSE values are in the range of 20 % to 35 % (They have been tested in Andalucia where
the atmosphere is more stable) that it is consistent with our owns results (see chapter 4.4).
The paper also shows a benchmarking of several methods including the use of mesoscale
numerical weather prediction models, the application of statistical post-processing tools to
forecasts of a numerical weather prediction (NWP) model, and also a synoptic approach
combining different forecasting models. For checking the behaviour of the irradiance
models, they agree that a trivial model as persistence of the cloud situation is a suitable
reference model for irradiance forecasts.
The NWP tested was:



European Centre for Meium-Range Weather Forecasts (ECMWF)
Global Forecast System (GFS)
Model of the National Center for Environmental Prediction (NCEP).
These global models have a coarse temporal and spatial resolution and do not allow for a
detailed mapping of small-scale features. Different methods to derive optimized hourly and
site specific irradiance forecasts are proposed. These include the use of mesoscale NWP
models, statistical post-processing tools or a combination of both and also a synoptic
combining different forecasting models.
The final conclusions where: at the current stage of research, irradiance forecasts based on
global numerical weather prediction models in combination with post-processing show
best results. All proposed methods perform significantly better than persistence.
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Figure: 11. Errors in Spanish stations
Another important conclusion is during winter with low solar elevations and low clear sky
irradiances absolute errors are small and relative errors are large. The improvement in
comparison to persistence is low during December, for all other months the NWP based
forecasts perform significantly better than persistence.
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Figure: 12: Relative errors in forecasted irradiation
The following Figure: 13 Relative errors in forecasted irradiation, give an idea of relative
RMSE errors of some forecasted methods of irradiation under development:





Sky persistence (clearness)
Cloud motion (satellite)
Cloud motion with smooth
NWP
Heliosat [1]
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Figure: 13 Relative errors in forecasted irradiation
The Heliosat method converts images acquired by meteorological geostationary satellites,
such as Meteosat (Europe), GOES (USA) or GMS (Japan), into data and maps of solar
radiation received at ground level.
2.2.
PV forecasting models
A simple forecasting model is running at REE CECRE based on the irradiation forecast see
Figure: 14. REE Forecasting model description
The global forecasted irradiation data acquired from Aemet [3] and the data of the main
PV locations installed in each region is used to forecast the energy production. The
irradiation forecast comes from a NWP running one’s a day at 0 h for the rolling horizon of
the next 72 hours.
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Figure: 14. REE Forecasting model description
NWP (run at 0h (1h resolution)
global irradiation J/m2 forecast for
72h
INSTALATIONS
Total
installed kWp for regions
Forecast Model 0
Energy forecasted
production kW.h
This model is now working but his accuracy has only been tested for a short time interval.
The data of all meters of PV power output energy are available with several month of
delay.
REE is developing several more advance d forecasting models in collaboration with
Spanish universities. There are also private companies that offer these services and are
working to improve their models. Just as with the predictions of wind generation, the final
model for REE will be a combination of the outputs of the models for different horizons, as
none of them proved to be the best for the entire range of estimates.
A special effort to bring is being done to model the solar thermal plants. They use direct
bean irradiance instead global and has some storage capacity and management.
In Germany some Energy and Weather companies provides forecasted production series to
Utilities. His methodology is described in the scheme of Figure: 15. Forecasting model
description.
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Figure: 15. Forecasting model description
NWP - ECMWF
global irradiation J/m2
forecast (3h) for 72h
Irradiation
algorithms
Correction
Corrected Hz irradiation
J/m2 forecast
PV modules
locations and
orientation
Calculation of irradiation in PV
modules (Algorithm)
Clear-Sky
planes
model
for
tilted
Irradiation at PV tilted
modules J/m2.
Model of PV (Transference
Function)
Medium-term energy
production forecast up to
48 h (1h resolution)
Sample of actual
data from “selected”
PV modules
Short-term corrections up to 4h
Final (aggregated)
energy production
forecast
Those companies have access to the historical and quasi-real time data from the owners of
smalls PV plants. The forecast is an aggregated for all PV plants.
The prediction of the PV power production is based on irradiance forecasts up to three
days ahead provided by the global model of the ECMWF. The temporal resolution is 3h
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and spatial of 0.25º. For the management of the power network is necessary derivate
specific site and hourly forecasts, so spatial and time interpolation is done.
One main point is the estimation of forecast accuracy for ensembles (aggregations) of
distributed PV plants depending on the size of the region.
The evaluation of PV power prediction in a case study presented in IEEE for this
methodology (see [10]) has shown that the accuracy of the global horizontal irradiance
forecast is the determining factor for the accuracy of the power forecast. For single PV
systems, the RMSE of the hourly power prediction is in the range of 0.10 to 0.12 Wh/Wp.
For the ensemble power prediction for a small region of 200 km x 120 km an RMSE in the
range of 0.06 to 0.09 Wh/Wp was found. So the aggregation reduces the error of the model
versus a single PV plant.
Figure: 16 (a) Correlation coefficient of forecast errors of two stations over his spatial
distance. (b) Error reduction factor RMSEensemble/ RMSEsingle
Either way, the accuracy of the models has not been tested yet against energy meters in an
exhaustive manner.
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3.
The use of prediction errors in Optimate
3.1.
How prediction error enter into the modelling framework of
Optimate
A central assumption of Optimate is that all stakeholders have access to the same forecast:
either they use the same tools, or the forecast of the most accurate tool is published and
used by everybody.
For each current day, Optimate links together iteratively two processes, the DA process
and the ID process.
The DA process
3.1.1.
In the DA process, the whole 24 hours of the current day are dealt considering a unique
DA forecasts of load and intermittent generation:
Time-to-go
10:00 11:00 12:00 13:00 14:00 15:00 16:00
1:00 2:00
Scheduling hours
12:00
24:00
Current hours
Day Ahead (scheduling day)
Current day
The forecast is assumed to be the one made at DA 12:00, on the scheduling day, for the 24
hours of the current day. In other words, the time-to-goes range from 13 to 36 hours. This
DA 12:00 forecast is used in each module of the DA process, whatever scheduling hour
corresponds to the module in the real world (the modules’ real scheduling hour range
between DA 10:00 to DA 16:00).
But the decision simulated at DA takes into account not only the DA forecast average
values, but also the standard deviation of their errors. Each stakeholder has indeed a certain
degree of risk aversion, which means for instance that she wants to make the decision that
hedges her against x% of possible case due to forecast errors.
In terms of congestion management, a TSO stakeholder is looking at the distortion between
nodal effect and zonal effect. To assume the risk of deviating from the DA forecast, each
TSO assesses a mixed standard deviation of each cluster1 combining those of wind power
forecast error, photovoltaic forecast error, load forecast error and generation sudden outage
1
In Optimate, cluster of nodes are used to mimic the nodal effects
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Page: 25
risk error. This combination can be done straightforwardly assuming that wind, P, load and
generation outage errors are not correlated.
In terms of balancing requirements, a TSO stakeholder is looking at its Control block 2. To
assume the risk of deviating from the DA forecast, each TSO assesses a mixed standard
deviation of her Control block combining those of wind power forecast error, photovoltaic
forecast error, load forecast error and generation sudden outage risk error. This
combination can be done straightforwardly assuming that wind, P, load and generation
outage errors are not correlated.
This information is key for Control block Reserve requirements. Assuming that this
information is either published, or known through experience, it is also key for Marketers:
it provides an indication of volume of the physical IntraDay upward / downward3 market
they should partly4 anticipate when making their DA unit commitment.
But each of those DA standard deviations (for wind, PV, load and generation) per Control
Block cannot be straightforwardly assessed from standard deviations per cluster, as they
are related by geographical cross-correlations. Therefore DA forecast error standard
deviations must be assessed both per cluster and per Control Block to feed in Optimate
Simulator.
DA forecast error standard deviations plays also a role when aggregated by Balance
Responsible Party: depending on its Balance Responsible Perimeter (BRP) a Marketer
tends to prefer to be slightly imbalanced in proportion of the imbalance prices asymmetry.
In theory this effect would need to assess DA forecast error standard deviations also per
BRP, which once again could not be straightforwardly assessed from standard deviations
per cluster, as they are related by geographical cross-correlations. In practice, the BRP
definition itself is already a proxy in Optimate5, then some proxy will be used to assess DA
forecast error standard deviations per BRP out of the other simulation input data. Some
guidelines for building this proxy are given in this document.
3.1.2.
The ID process
In the ID process, the next 8 hours from any scheduling hour are dealt considering
successive hourly forecasts of load and intermittent generation.
2
A Control block currently correspond approximately to a country. Some evolutions are under discussion but
Optimate first version will stick to the current situation
3
Optimate simulates only the upward anticipation of marketers, the downward one being basically fulfilled
due to other assumptions made
4
Assuming a non strategic behaviour, they will anticipate the part of it which corresponds to the quantity
they can expect to supply.
5
The BRP definition is commercial data out of reach of the Project. Moreover, it is not a persistent data over
time and its anticipation at year 2015 would anyhow be questionable.
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Time-to-go
16:30 17:00 17:30 18:00 18:30 19:00 19:30 20:00 20:30
Scheduling 1/2 hour
00:30
Current 1/2 hours
DAY AHEAD
CURRENT DAY
The first scheduling hour dealt by the Intra-Day process is 16:30 at DA, as some starting
up /shutting down decisions can be made then for 00:30 on the current day.
Then the ID process iterates on the scheduling hour per ½ hourly steps. The time-to-go
period analysed at a scheduling hour of 6 am would be for instance:
Time-to-go
6:00 6:30 7:00 7:30 8:00 8:30 9:00 9:30 10:00
Scheduling 1/2 hour
14:00
Current 1/2 hours
CURRENT DAY
Each current half hour benefits from its own Forecast, which is becoming more and more
accurate when the time-to-go decreases (in other words, its error standard deviation
decreases). The time consistency of those successive forecasts is to be ensured in between
them, with the DA forecast previously used, and with the RT output used at the very end of
the ID process.
Standard deviation of errors being used to build consistent sets of successive forecasts,
their consideration is enough in Optimate simulation to capture the anticipative behaviour
of stakeholder: at each scheduling hour, Optimate simulates that each stakeholder
considers the successive forecast of each next eight hours to make her decisions.
The errors coming from load, wind, PV forecast and unit outages are joined
straightforward assuming that the tree sources of error are independent. It should be
pointed out that in reality this is a proxy because load demand is correlated with the PV
power generation trough the temperature variable and recent researches from Jaen
University [11] show that wind and PV generation are correlated and complementary in
some cases.
3.2.
Intermittent generation data needed in Optimate
3.2.1.
Output of the proposed methodology used as input for Optimate simulator
The following input data are needed per cluster and per (half) hours over the whole year:
 DA forecast of Photovoltaic power generated
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


DA standard deviation of Photovoltaic power forecast error
ID forecasts of Photovoltaic generation for time-to-go ranging from ½ hour to 8
hours
RT outputs of Photovoltaic generation
The following input data are needed per Control Block and per (half) hours over the
whole year:
 DA standard deviation of Photovoltaic power forecast error
The following input data may also be needed per Balance Responsible Party and per
(half) hours over the whole year:
 DA standard deviation of Photovoltaic power forecast error
In order to keep the methodology feasible, those last inputs could be assumed to be
assessed from the previous ones considering parameters such as installed capacities of each
BRP per clusters, in each Control area. This calculation is part of the data pre-processing.
Input data for the proposed methodology
3.2.2.
Three types of data are needed in Optimate for the modeling the intermittent PV
generation:

Hourly realistic “Real Time PV scenario” data expected for the year to simulate
will used as a starting point, see figure 1.
Nevertheless this input data needed for the methodology could alternatively be
output of it. In case there are too few data for PV in previous studies (e.g. EWIS)
from which fixed data are going to be imported, a methodology to generate realistic
“real time” PV scenarios will be also proposed within this deliverable.

The kWp installed power, technology and earth coordinates of solar plants or
ensembles within each cluster is needed.

And for solar simulation three types of time series data are necessary for the
implementation of the proposed methodology:



30/09/2010
Historical values of solar irradiation weather stations are available for all
clusters, at least commercially.
Historical estimates (forecasts) of this energy is available in the same way at the
European Centre for Medium-Range Weather Forecasts or meteorological
institutes of participant countries. These are the forecast solution of NWP
models.
Data from actual PV energy power production in a representative limited set of
solar installations or farms where is also available both actual solar radiation
and temperature measures.
Page: 28
Methodology to handle prediction errors to be used
4.
in Optimate
From an initial forecasted PV energy production for the DA, called “the root forecast from
now”, we want to generate alternative scenarios in each ID with deviations from the initial
one compatible with the precision obtained by the forecasting program tools that made the
original root forecast.
The Figure: 17. Error scenarios from a forecasted (dot line) DA scenario. The error
scenario must be within bands (black lines), show a possible result.
Figure: 17. Error scenarios from a forecasted (dot line) DA scenario. The error scenario must
be within bands (black lines)
1.2000
Error scenarios from a forecasted root scenario
1.0000
0.8000
scen 1
scen 2
scen 3
scen 4
0.6000
scen 5
scen 6
scen root
max
0.4000
min
0.2000
0.0000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Knowing the error of PV generation forecasts and its distribution law, it would be possible
to generate scenarios that simulate actual production, which we call error scenarios (or RT
scenarios), which deviate from the initial planned within the error range of the initial
estimate root forecast.
As forecasting PV power generation models are being developed, we have no statistical
data of the errors available yet, and it is difficult to extrapolate the degree of accuracy in
the future that these models can achieve and even more difficult calculate the error
distribution law.
Moreover, individual hourly data of actual PV production power of PV modules are not
widely available in the majority of cases or actual data are only available in aggregated
form and longer time intervals.
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On the other hand, predict photovoltaic power energy production is closely linked to the
prediction of radiation incident on solar cells in a particular location of the land surface.
The theoretical radiation reaching a point on the earth each day and time of year it is
mathematically calculated by the clear-sky irradiation models. These models have an
acceptable error, and holding constant the parameters serve as a good starting point of
reference. Thus, simplifying the model, the only uncertainty left is the irradiance absorbed
by the atmosphere.
The final value of radiation incident on the solar cells is subject to fluctuations in the
atmosphere due to clouds, water vapor or dust.
The ending conversion of the sun's energy into power is determined ultimately by the tilted
of panels, technology of the cells, temperature and performance of ancillary equipment.
Finally, we see that the variables of the atmosphere: radiation, temperature and wind are
the only random input variables in the process of PV power generation. We do not consider
maintenance of solar cells, unavailability of equipment, solar cells dirt coming from snow
or dust, and loses of performance of power modules in long-term.
Given these factors, we propose a simplified model that uses common data available in
the all the TSO, but at the same time, keeping the statistical seasonal variations of the
atmosphere for each cluster. The errors are cluster dependent.
Optimate is subdivided into a number of clusters for network considerations and each
cluster needs forecasts error scenarios (RT scenarios) for wind, PV and load power
production alongside the forecasted for the DA (root scenario).
Within the clusters as defined by Optimate the prediction error will depend on a number of
different issues:



The installed capacities, characteristics of PV power within the cluster (kWp) and
its location.
The area size km2
Atmosphere conditions in the cluster
The irradiation data shows a wide spatial correlation and time correlation (persistence) is
very strong but not too much far away in time. The model should consider these two facts.
Due to the high correlation of the atmosphere over large regions, an averaged model of
atmospheric parameters is manageable. If two adjacent clusters are strongly correlated is
better to make them a single PV cluster for the model. We will see this issue in more detail
later on.
The main idea is simulating the atmosphere through the Markov chain and then enters its
variables into the transfer function which converts meteorological variables into power and
then make a selection of scenarios.
The process works as follows.
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The starting point is a particular level of clearness index at time t. This clearness index is
calculated from the inverse of the transfer function.
With this initial level the MCMC simulation process starts, and now for each n, where n is
the time ahead distance from t period, it generates a new t + n scenario for that particular
instant.
If the distribution law of PV power production time-series for forecast at t + n hours from t
instant of prediction was known the methodology follows the next graph.
Figure: 18. Block diagram 1
clearness
index at t
Atmosphere
simulation MCMC
Clearness
index t+n
Clear-sky model
for tilted surfaces
PV plants data
Geometry,
Tracking and
location
Irradiation
calculation
Irradiation
for tilted
surfaces
Forecasted
Temperature
Transference
function
Root scenario
index
Is the scenario within
limits at t+n?
Power Error Scenario
No
Yes
PV Power
Error
scenario
t+n
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The resulting trajectory is then compared with the root scenario. If the distance to the root
scenario is within the limits of k times the standard deviation, the path to t + n is accepted,
if the solution is not feasible, then the limits should be relaxed to increase k. The process
will continue for the next interval t+n+1 to cover the forecast horizon.
Since the previous distribution law of errors in power production from a forecast is
unknown for almost all clusters an alternate method is proposed base on the errors in
forecasting irradiance.
Thus the schema is modified as follows.
Figure: 19. Block diagam 2
clearness
index at t
Atmosphere
simulation MCMC
Clearness
index t+n
Weather Error
Scenario
root scenario
clearness
index
Is the scenario
within limits at
t+n?
No
Yes
Clear-sky model
for tilted surfaces
Irradiation
calculation
PV plants data
Geometry,
Tracking and
location
Irradiation
for tilted
surfaces
Forecasted
Temperature
Transference
function
PV Power
Error
scenario
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In this new situation, the errors in forecasting the irradiance drives the process instead the power
energy production of PV.
4.1.
Atmosphere simulation
The methodology simulates the irradiation of the atmosphere along seasons in a cluster. In
this way the different behavior between errors in winter and in summer are taken in
account.
For a cluster, the available data from irradiation of the different weather stations inside are
first normalized. Then data are averaged together and form a single set of clearness-index
time series for a whole cluster.
A Markov chain of matrices is performed with real data clearness index of horizontal
surfaces. This chain models the atmosphere.
Finally the random walk Markov Chain and Monte Carlo MCMC procedure simulates
possible scenarios for the atmosphere.
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Figure: 20. Block diagram 3
Weather
station_1 &
location
Global
irradiation
J/m2
Weather
station_n &
location
Global
irradiation
J/m2
Clear-sky model
Clear-sky 1
for Hz
planes
Clearness index 1
Clear-sky n
for Hz
planes
Clearness index n
Cluster
aggregation
Aggregated
Clearness
index timeseries
Transition
matrices
MC
Starting
level
MCMC
simulation
Roulete
draw
Weather
scenario
(Irradiation)
4.1.1.
The Clearness index
The actual irradiance data are land vary according to location and weather conditions.
To reduce the effect of the location, is seeking to standardize the value of the actual and
forecasted radiation with the theoretical clear-sky radiation and work with the concept of
clearness index (cloud index), and thereby obtain a more stationary time series and
standardized these.
This eliminates the time and location component, calculated using a mathematical model,
and let the time series of atmospheric clouds index alone.
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These series are likely to be standardized and averaged coupled, which would otherwise be
impossible.
The clearness index is defined as the ratio of actual irradiance and irradiance that
theoretically reaches the pyranometer on the physical location in clear-sky of the weather
station for each time interval of the year.
(5)
Where kc (t) is the clearness index from the upper bound Hcsky(t) in clear-sky conditions in
horizontal surfaces versus the real irradiation Hreal(t) metered in a weather station.
kc(t) take in account the AM transmissivity follow the sun light. This is a way to normalize
the solar power to make it more stationary. Thus the effect of changes over the day is much
lower for the normalized power than the real solar power. In other words the AM turbidity
is more or less constant for next hours.
The only data needed for this process is the real irradiation time-series at several weather
stations along the cluster and a mathematical model for the clear-sky calculation in each
weather station. The parameters of the clear-sky model can be constant since it is just a
reference. The clear-sky irradiance calculation is done by any of this well known models
[4] and [6].
Next plots are an example of the irradiation at Albacete’s weather station.
Figure: 21. Examples of irradiance in winter and summer time
800
Irradiation in Albacete in winter time (spain)
700
600
Wh/m2
500
400
300
200
Real Wh/m2
100
Clear-Sky Wh/m2
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
64
67
70
73
76
79
82
85
88
91
94
97
100
103
106
109
112
115
118
121
124
127
130
133
136
139
142
0
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1000
Irradiation in Albacete in summer time(Spain)
900
800
700
Wh/m2
600
500
400
300
Real Wh/m2
Clear-Sky Wh/m2
200
100
118
115
112
109
106
97
103
94
100
91
88
85
82
79
76
73
70
67
64
61
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
7
4
13
10
1
0
Figure: 22. Irradiance for the full year
It may be unexpected to see clearness indexes that are greater than the maximum value for
a clear sky day. However, this is quite common, and results from the reflection of sunlight
off the sides of clouds.
And the clearness index calculated as above is illustrated below:
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Page: 36
Figure: 23. Clearness Index
1.2
Clearness Index in Albacete
1
0.8
0.6
0.4
0.2
1
14
27
40
53
66
79
92
105
118
131
144
157
170
183
196
209
222
235
248
261
274
287
300
313
326
0
And if we take off the night hours the time-series results are more suitable for later
statistical analysis.
Figure: 24. Clearness index for consecutive solar hours
1.2
Clearness Index in Albacete for consecutive solar hours
1
0.8
0.6
0.4
0.2
1
23
45
67
89
111
133
155
177
199
221
243
265
287
309
331
353
375
397
419
441
463
485
507
529
551
573
595
617
639
661
683
705
727
749
771
793
815
837
859
881
903
925
947
969
991
1013
1035
1057
1079
1101
1123
1145
1167
0
Histograms of this time-series are showed in Figure: 25. Histogram distribution of the
clearness index. And Figure: 26. Distribution of RKc=(1.05-Kc).
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Page: 37
Figure: 25. Histogram distribution of the clearness index.
0.16
0.14
Frecuencia relativa
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.2
0.4
0.6
0.8
1
kc
Figure: 26. Distribution of RKc=(1.05-Kc)
4.5
Rkc
gamma(1.0124,0.25837)
Estadístico de contraste para gamma:
z = -0.776, valor p = 0.43767
4
3.5
Densidad
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
0.8
1
1.2
Rkc
For the whole sky in the cluster taking in account the strong correlation in wide areas we
make an aggregated clear sky-index making an average of all weather stations. This is a
reasonable assumption and will make a better approximation for the cluster that look at
particular locations.
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Page: 38
Figure: 27. Clearness index time-series process
Weaher stations
historical measures
time-series
J/m2
Time-serie
of
irradiation
J/m2
Time &
Location
Clear-sky model
Agregated
Clearness index
calculation
Clearness
Index time
serie for
cluster
Time-series
of
clear-sky
To proof the correlation of the atmosphere an example of between several weather stations
is shown in the next figures.
Figure: 28. Irradiation overlay of several weather stations.
In the following table a representation of weather stations at different location and its
correlations coefficients is presented. The time frame is a year.
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Page: 39
Figure: 29. Correlation coefficient at several weather stations
Correlation Coefficient
0.94
0.92
0.9
0.88
0.86
0.84
0.82
0.8
0.78
0
200
400
600
800
1000
km
Weather stations used in the graph are listed in the table below.
Table 1. Weather stations distances used for correlation.
Station
Station
Huelva
Cadiz
Huelva
Albacete
Cadiz
Reus
Albacete
Córdoba
Reus
Córdoba
Córdoba
Cadiz
Huelva
Albacete
Albacete
Coruña
Coruña
Coruña
4.1.2.
Km
(Apox.)
200
200
100
480
470
356
731
680
809
The Markov Chain
With the aggregated clearness index for a time-series as long as possible it will have a
good sample of atmosphere conditions for all the seasons in the cluster.
The behavior of a time-based system is represented using a state–transition matrix, which
consists of a set of discrete states that the system can be in, and defines the speed at which
transitions between those estates take place. Markov models consist representations of
possible chains of events in our case, states in the atmosphere, which could be happen.
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Page: 40
With the set of transitions matrices starting for a particular clearness level (state) at period t
we are able to build a simulated clearness time-series scenario kcscen(t) using the state
transition matrices, and the Monte Carlo simulation.
Where,
•
•
•
•
i and j are levels of Kc
Pij = P( Kc(t+1)=j | Kc(t)=i ) is the probability of reach the level j starting at level i
i is the level at t
j is the level at t+1
Figure: 30. Correlation matrices
Transition Matrix from 9 to 10 h , season
1.43E-01
1.91E-01
2.86E-01
0.00E+00
3.23E-02
3.23E-02
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
3
2.86E-01
3.23E-02
0.00E+00
0.00E+00
0.00E+00
0.00E+00
9.52E-02
7.10E-01
1.25E-01
0.00E+00
0.00E+00
0.00E+00
0.00E+00
1.94E-01
8.75E-01
0.00E+00
0.00E+00
0.00E+00
Transition Matrix from 10 to 11 h , season 3
5.56E-01
1.11E-01
1.11E-01
2.22E-01
0.00E+00
3.33E-01
3.33E-01
0.00E+00
0.00E+00
0.00E+00
0.00E+00
2.22E-01
0.00E+00
1.67E-01
1.11E-01
0.00E+00
1.67E-01
6.67E-01
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0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
3.70E-02
1.43E-01
0.00E+00
0.00E+00
0.00E+00
3.70E-02
0.00E+00
2.86E-01
7.41E-02
7.41E-02
5.71E-01
8.89E-01
8.89E-01
Transition Matrix from 11 to 12 h , season 3
5.56E-01
4.44E-01
0.00E+00
0.00E+00
5.00E-01
5.00E-01
0.00E+00
0.00E+00
2.50E-01
0.00E+00
5.00E-01
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
3.39E-02
0.00E+00
0.00E+00
0.00E+00
6.67E-01
6.25E-01
3.39E-02
0.00E+00
0.00E+00
2.50E-01
3.33E-01
3.75E-01
9.32E-01
In the above example some MC matrixes are showed. They are transition matrices from
t,t+1 in a “season” in this case, the season is a whole month of March.
A row with all zeros means that state level never happens.
In the example, a poor sample of the sky of only one year long is taken. Even so, the
results obtained for a single PV plant are acceptable.
For the PV problem, the Markov chains of clearness index are generated with the
irradiation data series. This data should extend at least 10 year (some research says 20
years). At REE we have data series of 5 years long for Spanish peninsula and a reduced set
of locations of weather stations.
4.1.3.
The Markov Chain Monte Carlo (MCMC) simulation
For simulation a Monte Carlo draw is used and one transition matrix in each step.
Figure: 31 MCMC Simulation
This method is the simplest way to generate scenarios for the future. The scenarios only
depend on the clearness of AM conditions, nor the installed capacity, location, technology
of plants or variation of the sunlight during the day.
Markov chains have been tested successfully for generate wind power hourly annual
production series scenarios for the stochastic long-term unit commitment (UC) problem.
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We are using the proposed methodology also to generate error scenarios derivating from a
root forecasted wind power production scenario. Those scenarios are a data input for the
stochastic medium-term (1 week) UC. The root scenario was generated from the wind
power energy forecasted tool. The error scenarios are generated taking in consideration the
errors of the wind-power forecasting tool using the Markov chain.
Also, the proposed methodology has been tested to generate annual hourly scenarios of just
one PV plant. The results are showed in the following plots in winter and summer. The
model simulates an adequate power output in each month, which reproduces the behaviour
of the evaluated year.
Figure: 32. Simulated energy production at PV plant in winter.
Simulated scenarios vs real production of a PV plant with tracking in January
1.2
1
0.8
0.6
0.4
0.2
0
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109 112 115 118
Real MWh
30/09/2010
Scaled CSky Hz
Markov Sim MWh
Page: 43
Figure: 33.Simulated energy production at PV plant in summer.
Simulated scenarios vs real production of a PV plant with tracking in July
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109 112 115 118
Real MWh
Scaled CSky Hz
Markov Sim MWh
Figure: 34. Power duration curves for an average of six years simulated.
9.00E-01
Power Duration Curves. PV Tracking.
8.00E-01
7.00E-01
6.00E-01
5.00E-01
Jan Real
Jan Sim Markov
MW
4.00E-01
Abr Real
Apr Sim Markov
3.00E-01
Jul Real
Jul Sim Markov
2.00E-01
1.00E-01
0.00E+00
1
16
31
46
61
76
91
10
6
12
1
13
6
15
1
16
6
18
1
19
6
21
1
22
6
24
1
25
6
27
1
28
6
30
1
31
6
33
1
34
6
36
1
37
6
39
1
40
6
42
1
43
6
45
1
46
6
48
1
49
6
51
1
52
6
54
1
55
6
57
1
58
6
60
1
61
6
63
1
64
6
66
1
67
6
69
1
70
6
72
1
73
6
This example is made using the matrices shown above. We have simulated a full six years
hourly-time series. In the example the MC behaves well.
A Markov Chain will build for the future things that happened before. The method catches
an “empirical distribution”. What did not happen in the past, not likely to happen in the
future. A way to solve this is to adjust rows (in two dimensional matrixes) to a well known
distribution instead use the empirical distribution. This is a sophistication improvement in
the methodology. A point to investigate is the adjustment of the distribution function of
the index of clarity to a known distribution, and in this way solve the possible problem of
not have data enough. This ultimate process makes also a data cleanup.
When two clusters are strongly correlated in PV a split of them into two separated Markov
chain (MC) is not a good idea. Instead, it must generate a multidimensional Markov chain.
30/09/2010
Page: 44
Assume for simplicity that we have two clusters strongly correlated. For each cluster we
construct our time series index of clarity. These two series are independent but are related
by their time of occurrence. Now for each pair of clearness-index level of each cluster we
will have a probability of occurrence by season and time of day to go to another couple of
levels in the next hour. So we will have a mesh of pairs of points whose sum of
probabilities of occurrence is one. This can be extended to three or more clusters. For
three, the sum of probabilities of the resulting cube is one. To simulate a transition from
one hour to the next hour is used by just a single Monte Carlo roulette spin for all clusters.
Each cheese wheel has a size proportional to the probability of each node in the resulting
hypercube. This ensures that with one spin of roulette obtain a clearness-index correlated
for each cluster which follows the empirical distribution of time series.
Figure: 35. In this flow chart two clusters correlated with a third series of temperature is
shown as an example.
Cluster 1
aggregation
Cluster 2
aggregation
Aggregated
Clearness
index timeseries 1
Aggregated
Clearness
index timeseries 2
Averaged
Temperature
time-series
cluster 1 & 2
Multidimensional
Transition
matrices
MC
Starting
level for the
tree
variables
MCMC
simulation
Roulette
draw
Weather scenario
(Irradiation custers
1 &2, temperature)
The output of this stage is a set of three weather variables, two indices of clarity and a
single temperature for both clusters.
30/09/2010
Page: 45
The temperature can be used in the load demand forecasting model to correlate this in turn.
The scenario selection based on errors forecasting irradiance
4.1.4.
Given an estimate of photovoltaic power generation from a root-forecast scenario we can
calculate the index of clarity that corresponds using the inverse of the transformation
function of irradiance into power energy.
From the root forecasted scenario we will get a root forecasted clearness index.
Now we define two bands, similar to the Bollinger bands used in stock markets.
Figure: 36. Bollinger bands in stock markets.
Bollinger Bands consist of:



a middle band being an N-period simple moving average (MA)
an upper band at K times an N-period standard deviation above the middle band
(MA + Kσ)
a lower band at K times an N-period standard deviation below the middle
band (MA − Kσ)
Typical values for N and K are 20 and 2, respective.
These bands in PV case will be:

a middle band being the root forecasted scenario RE

an upper band at ku times the standard deviation std (of the clearness error
forecasted) above the middle band
min (Hclear-sky, (RE + ku*std))
30/09/2010
Page: 46

a lower band at kl times the standard deviation below the middle band
if (RE - kl *std) > 0 then (RE – kl*std)
if (RE – kl *std) <= 0 then 0.
Starting at the first hour of clearness root forecasted scenario index, the MCMC hourly
simulation process generates new transitions scenarios restricted to levels within the bands.
Now we have transitions that differ less or equal than the statistical error of forecast at
different horizons derivates from the NWP prediction errors.
Similarly to what happens in the Bollinger bands, our actual production can go outside the
expected, so relax the k could be necessary for feasibility in some situations.
4.2.
Calculation of irradiation in tilted surfaces
Figure: 37. Irradiation in tilted surfaces
Clear-sky
index
Clear-sky model
for tilted surfaces
Irradiation
calculation
PV plants data
Geometry,
Tracking and
location
Irradiation
for tilted
surfaces
Using the index of clarity multiplying by the theoretical radiation on a tilted plane, we can
calculate the radiation will impact on the solar panel. We can also simulate the track.
4.3.
Transference function
The Transference Function is the way to convert radiation and temperature into energy
photovoltaic power for aggregated plants. Aggregation must be done in reasonably close
plants for accurate results. One way to do this is the following:
30/09/2010
Page: 47
Figure: 38 Transference function
If Ppk is the nominal peak power of a PV plant 0, and A is the area of the PV module:
(6)
The actual power depends of the Hreal(t) irradiance and the real module efficiency Ef which
is a function of module temperature Tm and more things not taking in account here.
(7)
(8)
So we don’t need to know the area A or Efnom .
Efr is the relative efficiency.
(9)
(10)
The Efr take in account the system losses which cause the power actually delivered to the
electricity grid to be lower than the power produced by the PV modules. There are several
causes for this loss, such as losses in cables, power inverters, dirt (sometimes snow) on the
modules and so on.
This means that the method can only be used on PV technologies that do not depend
strongly on the solar spectrum, and do not show effects of long term exposure to irradiation
or high temperatures.
30/09/2010
Page: 48
The formula for estimating the relative efficiency looks like
(11)
Where ^Hreal= Hreal/1000
The coefficients ki depends on the technology of PV plants and can be fit with linear
regression.
The module temperature Tm is calculated from the ambient temperature by the following
formula:
(12)
Kt =0.035°- 0.05°C/(W/m2) for free-standing systems, for building-integrated
systems, based on values taken from literature.

Simplifications can be done in the above formula (11), to take out the temperature effect,
and an aggregation of representative plants can be done to fit the coefficients.
The European Commission shows a method of estimating average daytime and daily
temperature profiles within Europe [5] . The temperature should be the same as that used to
calculate the load demand.
The data used for the calculation of the transference function plot as example has the
following characteristics:
The solar irradiation.
Figure: 39. Irradiation in W/m2
Irradiance W/m2
1400
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
5
x 10
30/09/2010
Page: 49
4
Histogram of Irradiance
x 10
8
7
6
5
4
3
2
1
0
0
200
400
600
800
1000
1200
1400
Irradiance W/m2
The temperature.
Figure: 40.Temperature in 10*ºC
Variation of temperature
450
400
350
300
10 x ºC
250
200
150
100
50
0
-50
0
0.2
0.4
0.6
0.8
4
3.5
1
days
1.2
1.4
1.6
1.8
2
5
x 10
Temperature Distribution
x 10
3
2.5
2
1.5
1
0.5
0
-50
0
50
100
150
200
10 x ºC
250
300
350
400
450
And wind speed.
30/09/2010
Page: 50
Figure: 41. Wind speed in m2/s
Wind speed
45
40
35
30
m/s
25
20
15
10
5
0
0
0.2
0.4
0.6
0.8
4
8
1
Days
1.2
1.4
1.6
1.8
2
5
x 10
Wind distribution
x 10
7
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
45
Speed m/s
30/09/2010
Page: 51
And its transference function calculated by linear interpolation of nonlinear functions looks
like
Figure: 42. Transference function in 3D
With a residual distribution of:
Figure: 43. Distribution of residuals after interpolation
4
8
x 10
7
6
5
4
3
2
1
0
-0.6
30/09/2010
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Page: 52
Figure: 44. Transference function in 3D. Real data.
The influence of temperature is shown in the following plot.
Figure: 45. Power loses due to temperature. Real data.
30/09/2010
Page: 53
Figure: 46. Calculated losses in transfer function due to the increase of Ta temperature.
The wind has some effect in the performance of solar plants. Wind increase performance in
sunny days with low Ta temperatures Figure: 47. Wind influence in the transference
function. For simplicity we will not consider this variable into the model.
30/09/2010
Page: 54
Figure: 47. Wind influence in the transference function.
The calculation of transfer functions is another challenge. Each PV plant has its own,
which depends on the cell technology, its cleanliness and efficiency of inverters.
These data are not available for all plants, so a representative aggregated transfer function
should be used as an approximation. This case is normal for Germany and Spain.
The cluster is the relevant geographic area of work within the OPTIMATE project. Then, a
transfer function for the total set of PV plants in the cluster and a forecast of solar
irradiation for the cluster can be used, but in this way his location must be calculated.
Working with several smaller geographical areas allows more accurate results. This is due
not so much the accuracy of the transfer function as the difference due to solar rotation of
the earth. In this way, we can work with a single aggregate transfer function but is
particularized for different locations.
4.4.
Distribution of errors forecasting the clearness index
Presently there are no good forecasting PV production models in operation yet. TSOs only
have at their disposal what could be seen as still rudimentary tools if compared with wind
30/09/2010
Page: 55
production forecast tools. In fact only some TSOs are now in the process of developing
what could be considered the firsts quality tools for PV production forecast.
As it happened with the forecast of wind production, it is expected that the models that are
being developed now will evolve in the future, improving their characteristics,
incorporating knowledge. Nowadays it is difficult to evaluate the degree of accuracy that
the future models will be able to achieve and even more difficult calculate the error
distribution laws of the tools.
Moreover, individual hourly data of the real production of PV modules or plants are not
widely available in the majority of cases.
Because time-series errors in the PV forecasting process are not available at the time being,
and accuracy of PV forecast depends stronger on the accuracy forecasting the irradiation
we propose a methodology based on errors forecasting of the irradiation.
With the forecasted irradiation data form de NWP Hfor and real irradiation data metered for
actuated pyranometers in some locations Hreal the error statistics can be calculated, the
variance and the standard deviation.
Figure: 48 Distribution Errors
At the end we have a distribution error of forecasting kc for 1, 2… up to 36 h.
The error increase with the distance of the prediction time and it will be cluster dependent.
Keep in mind that this distribution function depends on time of day and season of the year.
It also depends on the time of day at which the model is launched, as improvements in the
next three or four hours are waiting from the actual PV generation/meteorological -
30/09/2010
Page: 56
variables data feedback. This is mainly valid for the current day when the sun has risen on
the horizon. There is not feedback at nights (something that in wind not happens).
In the case of wind, the errors are not dependent on time of day when the forecast is
released, and only depend on how far away we are the starting point of the beginning of the
forecast process.
The temperature in the proposed model can be simulated to be taken into account in the
transference function only. It can be derived from that used for demand forecasting
models.
Introducing stochasticity in this variable is possible also and implies to add a new
dimension to the MC process. Earlier in multidimensional MC has been shown how to do
it. Statistics of this variable must then also be taken into account to narrow the scenarios.
In the proposed model the errors are not “random variables” instead of that are a set of
time-series solutions that follow the same distribution function and properties observed for
the time-series “errors” in the forecast of solar irradiation. In particular, the error at hour h
must fall within the maximum error range valid for the particular value of the real solar
irradiance at hour h.
Coming from the AEMET model irradiation forecasting model interesting information is
already available. For example, the Root Mean Square Errors (RMSE) of the solar
irradiance forecasts from 1 to 72 hours ahead in several locations in Spain are represented
in the Figure: 49. Error forecasting irradiation in several weather stations. Of course it is
natural that the errors in the night hours are zero. Similarly, the absolute errors in the first
and lasts hours of sun light are smaller than in the mid day hours.
For simplicity, the errors are assuming that the irradiation model runs just once a day at 0h
in progress.
In the NWP the errors are more or less constant with the distance to the prediction time.
Only increases a few with the time instant from the prediction.
30/09/2010
Page: 57
Figure: 49. Error forecasting irradiation in several weather stations.
30
CORUÑA
RMSE errors of the NWP in several weather stations
BILBAO
CACERES
CADIZ
C.REAL
25
CORDOBA
GIRONA
GRANADA
HUELVA
20
LEON
L.RIOJA
% Error
MADRID
MURCIA
15
ASTURIAS
PALMA
NAVARRA
PONTEVEDRA
10
SALAMANCA
GUIPUZCUA
CANTABRIA
SORIA
5
TERUEL
TOLEDO
VALENCIA
VALLADOLID
0
VICTORIA
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71
ZARAGOZA
Hours from the prediction time 0h
Figure: 50. RMSE forecasting irradiation for the AEMET NWP launched at 0 h for the
current day.
RMSE Forecasting the irradiation
25
% rmse
20
15
10
MEAN
5
0
1 3 5 7 9 11131517192123252729313335373941434547495153555759616365676971
Hours from the prediction time (0 h)
30/09/2010
Page: 58
Figure: 51. Mean error
18
ME
16
14
% Error EM
12
10
8
6
4
2
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71
Hours from the forecasted time (at 0h)
Figure: 52. Relative to de forecasted irradiation mean error.
200
Relative Mean Error to the forecasted irradiation
180
160
140
% RME
120
100
80
60
40
20
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71
Hours from the forecasted time
Lower errors are expected in the following hours from the initial root node scenario tree as
the accuracy of irradiation forecast increase.
30/09/2010
Page: 59
The latter method simulates the error, but does not take into account improvements in the
very short-term that can occur when taking into account the real time data feedback.
Due to the persistence of the kc index, is natural to assume that the generation in a certain
hour may depend on the generation in the hours immediately preceding. This is the case of
an ID market during solar hours.
Following part of the methodology used for error scenarios of wind this behavior can be
introduced in the proposed model using a simple AR model to simulate the first following
hours. This AR model will be used instead the MCMC in the first hours. After that, the MC
chain model will be used, starting at the clearness level of last AR forecast hour.
The simplest case is the AR(1) model
(13)
This AR model is also built on the index of clarity.
30/09/2010
Page: 60
5.
Conclusions
The present report starts by describing the need for error scenarios generation module for
Optimate. This is the result of the large integration of renewable energy in the power
system and its failure to accurately estimate its energy hourly production. The day-ahead
forecast of these RES energy is subject to some uncertainty and it is a risk for bidders in
the spot market of energy because they have to pay penalties when they do not fulfil their
commitments (due to over/under estimation of RES production).
Simulating the forecast error of RES sources would be a very complex task if it should be
done in an operational process. Wind, PV, hydro inflows and load demand stochastic
changes are indeed four sources of error and they are correlated spatially and time.
In the context of OPTIMATE project, we just aim at an approach able to capture the
economic trends induced by the combination of those forecast errors and therefore we can
afford a large simplification of the problem.
This report constitutes the deliverable D2.1 on the assumptions on accuracy of PV power
to be considered at short and long-term horizons. The methodologies to be used for
generate PV power error scenarios are outlined in this report for a further implementation
in the project.
For illustration purposes, REE has developed a program to test their feasibility and
accuracy. In the next phases of the Optimate model, clusters will be defined and the needed
data collected for the defined clusters.
One important thing is that errors in the proposed model are not “random variables”: on the
contrary, they are a set of time-series solutions that follow the same distribution function
and properties observed for the time-series “errors” in the forecast process of solar
irradiation.
Moreover, the methodology allows generating PV scenarios for any cluster, even those
who do not currently have solar production yet. These scenarios follow the solar power
production specific constraints: energy and ramps, from period to period for each day of
the year, taking into account also seasonal variations. The historical irradiation time-series
data, location of the plants, technology and kWp are the only data needed.
In a first version, OPTIMATE simulator will use the yearly scenario of forecasted errors
generated as if they were deterministic. An extension is then to be foreseen where a certain
number of yearly scenarios will be used. In such case, scenario reduction will become an
important task for future development.
30/09/2010
Page: 61
References
6.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
Peder
Bacher;
Henrik
Madsen;
Henrik
Aalborg
Nielsen:
Online short-term solar power forecasting, 2 September 2008;
Further information: Solar Energy 83 (2009), Issue 10,1772–1783, 22 July 2009
Heliosat
Further information: http://www.helioclim.net/index.html
Photovoltaic Geographical Information System - Interactive Maps
Further information: http://re.jrc.ec.europa.eu/pvgis/
Aemet (Agencia Estatal de Meteorología)
http://www.aemet.es/es/portada
Richard E. Bird; Roland L. Hulstrom
A Simplified Clear Sky Model for Direct and Diffuse Insolation on Horizontal
surfaces. 1981
Further information:
Thomas A. Huld; Marcel Suri; Ewan D. Dunlop; Fabio Micale
Estimating average daytime and daily temperature profiles within Europe
Further information: Environmental Modelling & Software 21 (2006) 1650e1661
Jaroslav Hofierka, GeoModel, s.r.o. Bratislava, Slovakia; Marcel Suri, GeoModel,
s.r.o. Bratislava, Slovakia
Clear-sky model r-sun
Further information: http://grass.itc.it/gdp/html_grass5/html/r.sun.html
A. Shamshad, M.A. Bawadi, W.M.A. Wan Hussin, T.A. Majid, S.A.M. Sanusi
First and second order Markov chain models for synthetic generation of wind
speed time series
Richard Perez, Jim Schlemmer
Improving the performance of satellite-to-irradiance models using the satellite’s
infrared sensors (may 2010)
Future information: [email protected],edu
Elke Lorenz1, Jan Remund2, Stefan C. Müller2, Wolfgang Traunmüller3, Gerald
Steinmaurer4, David Pozo5, José Antonio Ruiz-Arias5, Vicente Lara Fanego5,
Lourdes Ramirez6, Martin Gaston Romeo6, Christian Kurz7, Luis Martin Pomares8,
Carlos Geijo Guerrero9
1
University of Oldenburg, Institute of Physics, Energy and Semiconductor
Research Laboratory, Energy Meteorology Unit, Carl von Ossietzky Strasse 9-11,
26129 Oldenburg, Germany, elke.lorenz@uni-oldenburg,de
2
Meteotest, Fabrikstrasse 14, 3012 Bern, Switzerland
3
Blue Sky Wetteranalysen, Steinhüblstr.1, 4800 Attang Puchheim, Austria 4ASiC
– Austria Solar Innovation Center, Roseggerstraße 12,4600 Wels, Austria,
5
University of Jaén, Department of Physics, Campus Lagunillas, 23071, Jaén,
Spain
6
CENER, Ciudad de la Innovación 7, 31621 Sarriguren (Navarre), Spain
7
Meteocontrol GmbH, Spicherer Straße 48, 86157 Augsburg, Germany
8
Ciemat, Energy Department, Av. Complutense 22, 28040, Madrid, Spain
30/09/2010
Page: 62
9
[10]
[11]
AEMet, Leonardo Prieto Castro, 28071, Madrid, Spain
Benchmarking of different approaches to forecast solar irradiance
Elke Lorenz, Johannes Hurka, Detlev Heinemann and Hans Greorg Beyer
Irradicende Forecasting for the Power Prediction of Grid-Connected Photovotaic
Systems
IEEE journal of selected topics in applied earth observations and remote sensing,
vol 2 #1, March 2009
Joaquin Tobar Pescador
Análisis de la complementariedad del recurso eólico y solar en Andalucía y estudio
pormenorizado de diversas zonas.
Further information: http://matras.ujaen.es/es/index.php
30/09/2010
Page: 63

D2.1 Assumptions on accuracy of photovoltaic power to

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