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Master of Science Thesis
KTH School of Industrial Engineering and Management
Energy Technology EGI-2016-001MSC
Division of Energy Technology
SE-100 44 STOCKHOLM
Generation of wind speed and solar
irradiance time series for power
plants with storage
Léo Mauger
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Master of Science Thesis EGI-2016-001MSC
Generation of wind speed and solar
irradiance time series for power plants with
storage
Léo Mauger
Approved
2016-01-11
Examiner
Pr. Björn Palm
Supervisor
Pr. Björn Palm
Commissioner
AKUO Energy
Contact person
Mr. Julien Cabrera
Abstract
Sizing renewable energy power plants with storage devices needs new resource assessment. Global
amount of energy available has to be replaced by time series to depict the resource as a function of time.
This paper introduces methodology to generate time series for wind speed and solar irradiance with a
granularity between 10minutes and 1seconde. Ground measurements and macro-date from satellite
imagery are analyzed and processed to obtain long-term site-specific time series. Because renewable energy
forecasting is a growing concern, a second part of the work presents how to modify previously generated
profiles in order to obtain forecasts with an expected error.
Keywords: renewable energy power plants, storage, forecast, time series, wind speed, irradiance, irradiation
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Table of Contents
Abstract ........................................................................................................................................................................... 3
Table of figures .............................................................................................................................................................. 7
Table of graphs .............................................................................................................................................................. 8
Table of tables ................................................................................................................................................................ 9
1 Introduction ........................................................................................................................................................10
1.1 Need of time series for renewable energy power plants sizing..........................................................10
1.2 Akuo Energy Presentation .......................................................................................................................11
1.3 Akuo’s tool: Akomis .................................................................................................................................11
2 Wind energy: state of the art.............................................................................................................................13
2.1 Introduction ...............................................................................................................................................13
2.2 Data available .............................................................................................................................................13
2.2.1 Measurements ...................................................................................................................................13
2.2.2 Other data .........................................................................................................................................14
2.3 Data analysis...............................................................................................................................................14
2.3.1 Direct use of data .............................................................................................................................15
2.3.2 Bins methods and histogram of occurrences ..............................................................................15
2.3.3 Statistical analysis .............................................................................................................................16
2.3.4 Wind direction and correction using long-term data set ...........................................................19
2.3.5 Velocity, power and turbine power duration curve ....................................................................21
3 Wind profiles generation ...................................................................................................................................23
3.1 Granularity issues ......................................................................................................................................23
3.2 Work with meteorologist centers data set .............................................................................................24
3.2.1 Site characterization .........................................................................................................................25
3.2.2 Comparison between measurements and meteorological centers data sets ...........................27
3.3 Filling hourly values ..................................................................................................................................28
3.3.1 From hourly values to 10minutes granularity values ..................................................................28
3.3.2 From 10minutes values to 1 second values .................................................................................29
3.4 Conclusion .................................................................................................................................................31
4 Solar energy: state of the art .............................................................................................................................32
4.1 Basis .............................................................................................................................................................32
4.2 Data available .............................................................................................................................................34
4.2.1 Measurement ....................................................................................................................................34
4.2.2 Clear sky model ................................................................................................................................34
4.2.3 Data from satellite outputs .............................................................................................................34
4.2.4 Data from meteorological ground stations ..................................................................................36
4.3 Photovoltaic power plant sizing .............................................................................................................36
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5 Irradiance profile generation ............................................................................................................................38
5.1 Data used ....................................................................................................................................................38
5.2 From yearly average to daily averages - Methodology ........................................................................38
5.2.1 From annual irradiation to monthly irradiation ..........................................................................38
5.2.2 Create several months .....................................................................................................................39
5.2.3 Create days from monthly irradiation ...........................................................................................40
5.3 Sub-daily profiles .......................................................................................................................................42
5.3.1 Methodology .....................................................................................................................................44
5.4 Solar generation parameters set up ........................................................................................................51
5.5 Generation and computing code ............................................................................................................52
5.5.1 Create a 1minute mean value from sixty 1second values ..........................................................52
5.5.2 Create a 10min average value with ten 1minute average ...........................................................53
5.5.3 Create a day with one hundred forty four 10minutes average values ......................................53
5.6 Results and final set up .............................................................................................................................53
5.7 Conclusion .................................................................................................................................................62
6 Forecasting ..........................................................................................................................................................63
6.1 Introduction ...............................................................................................................................................63
6.2 Forecasting methods.................................................................................................................................63
6.2.1 Physical Models: NWP models and MOS Correction ...............................................................64
6.2.2 Satellite imagery ................................................................................................................................64
6.2.3 Devices on-site .................................................................................................................................64
6.2.4 Statistical Models ..............................................................................................................................65
6.3 Metrics used for solar irradiance forecasting error ..............................................................................66
7 Wind speed forecasting .....................................................................................................................................67
7.1 Basis .............................................................................................................................................................67
7.2 Temporal errors .........................................................................................................................................67
7.3 Quantitative errors ....................................................................................................................................68
7.4 Results and comparison ...........................................................................................................................69
7.5 Conclusion .................................................................................................................................................71
8 Irradiance forecasting ........................................................................................................................................72
8.1 Pre analysis .................................................................................................................................................72
8.2 Generation..................................................................................................................................................73
8.3 Conclusion .................................................................................................................................................77
9 Conclusion ...........................................................................................................................................................78
Annex 1: Results Irradiance forecasting benchmark .............................................................................................79
Phase 1: Forecast qualification form ...................................................................................................................79
Phase 2: Trial period ..............................................................................................................................................79
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Specifications and preparation .........................................................................................................................79
Process .................................................................................................................................................................80
Metrics ..................................................................................................................................................................80
Other tests ...........................................................................................................................................................81
Comparison with Meteo France forecast .......................................................................................................82
Comparison with an average day .....................................................................................................................82
Results ......................................................................................................................................................................82
RMSE for Day RMSE for Day Ahead and Intra-Day 3:30 forecasts on a day basis ..............................82
Battery sizing based on Day Ahead forecasts ................................................................................................84
Comparison between Day – Ahead and Intra – Day forecasts ..................................................................85
October ................................................................................................................................................................86
Detection of bad days ........................................................................................................................................88
October ................................................................................................................................................................89
Results – conclusion ..........................................................................................................................................90
Conclusion ...............................................................................................................................................................90
Annex 2: Calibration of satellite data with ground measurements ......................................................................91
First considerations ................................................................................................................................................91
Remove implausible ground measurements.......................................................................................................91
Comparison and calibration for daily values ......................................................................................................91
Calibration of sub daily profile .............................................................................................................................94
First analysis ........................................................................................................................................................94
Raising the profile ..............................................................................................................................................95
Lowering the profile ..........................................................................................................................................96
Conclusion ...............................................................................................................................................................97
Bibliography .................................................................................................................................................................98
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Table of figures
Figure 1: Mast on-site .................................................................................................................................................14
Figure 2: Rayleigh Distributions................................................................................................................................18
Figure 3: Weibull Distributions .................................................................................................................................18
Figure 4: Solar losses through the atmosphere .......................................................................................................32
Figure 5: Solar panel tracking systems .....................................................................................................................34
Figure 6: Coverage of several satellites ....................................................................................................................35
Figure 7 : Sun path ......................................................................................................................................................37
Figure 8 : Satellites placements ..................................................................................................................................64
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Table of graphs
Graph 1: Wind Speed Histogram of occurrences ..................................................................................................17
Graph 2: Histogram of occurrences with Weibull distribution ...........................................................................19
Graph 3: Wind rose diagram with Wind speed distribution for measurements ...............................................20
Graph 4: Wind rose diagram with Wind speed distribution for satellite data ...................................................20
Graph 5: Wind rose diagram with Wind speed distribution for corrected data ................................................20
Graph 6: Velocity duration curve .............................................................................................................................21
Graph 7: Vestas V80 Power curve ...........................................................................................................................22
Graph 8: Power duration curves ...............................................................................................................................22
Graph 9: Wind Speed Power Spectrum ...................................................................................................................23
Graph 10: Standard deviation of 10min values around their hourly means ......................................................25
Graph 11: Standard deviation as a function of the wind speed - 1s granularity ..............................................26
Graph 12: Intensity of turbulence as a function of the wind speed ....................................................................26
Graph 13: Sample of MERRA and measured data ................................................................................................27
Graph 14: Evolution of hourly average wind speed ..............................................................................................28
Graph 15: Linear regression and 10min granularity values ..................................................................................29
Graph 16: Filling the 10min value with a random number of points .................................................................30
Graph 17: Filling with 1sec granularity points ........................................................................................................30
Graph 18: Typical Distribution of Wind Speed for a very short period ............................................................31
Graph 19: Clear sky irradiance daily profiles ..........................................................................................................33
Graph 20 : Clear sky irradiance daily profile on a 30° tilted plane in La Réunion, France, 1st January .........33
Graph 21: Monthly clear sky irradiation in Sevilla - Spain ....................................................................................38
Graph 22 : Monthly averages from datasets ...........................................................................................................39
Graph 23 : Days distribution over the year .............................................................................................................41
Graph 24 : Day distribution over each month .......................................................................................................41
Graph 25: One day irradiance with a 10min timescale ..........................................................................................43
Graph 26: One day irradiance with a 1min timescale ............................................................................................43
Graph 27: One day irradiance with a 1second timescale ......................................................................................44
Graph 28 : Shape curve and comparison of irradiations ......................................................................................45
Graph 29 : Uniform and dual shapes of day ...........................................................................................................47
Graph 30: Three-part profiles ...................................................................................................................................49
Graph 31: Examples of 1sec granularity profiles ...................................................................................................52
Graph 32 : Typical days generated ............................................................................................................................62
Graph 33 : Typical days measured ............................................................................................................................62
Graph 34: Daily temporal deviation .........................................................................................................................67
Graph 35 : Daily and hourly temporal deviations ..................................................................................................68
Graph 36 : Wind speed forecast ...............................................................................................................................69
Graph 37 : Power curve .............................................................................................................................................70
Graph 38 : Wind speed RMSE versus Power RMSE ............................................................................................71
Graph 39: Deviations as a function of the Clear sky percentage ........................................................................72
Graph 40 : A day of clear Sky index .........................................................................................................................74
Graph 41 : Examples of forecast shapes .................................................................................................................74
Graph 42 : Temporal error ........................................................................................................................................75
Graph 43 : Power error ..............................................................................................................................................75
Graph 44 : Solar irradiance forecast profile ............................................................................................................76
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Table of tables
Table 1: Measuring parameters..................................................................................................................................14
Table 2: Time to switch from a value to another 1% larger .................................................................................24
Table 3: Time to switch from a value to another 5% larger .................................................................................24
Table 4: MERRA and Measurements annual parameters .....................................................................................28
Table 5: MERRA and Measurements monthly parameters ..................................................................................28
Table 6: Deviation of the 10min granularity values generation ...........................................................................29
Table 7 : Main datasets for satellite imagery -1 .......................................................................................................35
Table 8 : Main datasets for satellite imagery -2 .......................................................................................................36
Table 9 : Monthly parameters ....................................................................................................................................40
Table 10 : Bins separations ........................................................................................................................................41
Table 11 : Final monthly deviations .........................................................................................................................42
Table 12 : Appreciations for solar generated profiles ............................................................................................51
Table 13 : Parameters for the solar irradiance profile generation ........................................................................51
Table 14 : RMSE for wind speed for different set of errors ................................................................................69
Table 15 : RMSE for wind power with different set of errors .............................................................................70
Table 16 : Deviations as a function of the Clear sky percentage .........................................................................73
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1 Introduction
Switching our power generation system from conventional and polluting generation to a new system
based on renewable energies is a challenge to take up. Therefore, integrating large amount of variable and
uncertain solar photovoltaic or wind power to the grid is a growing concern. Developments of
decentralized energy production and hybrid power plants with a storage medium are the most promising
solutions.
1.1 Need of time series for renewable energy power plants
sizing
Hybrid power plants are more complex and they need special tools for sizing. The first step of the sizing
involves a resource assessment. Several tools are already available. They give an overview of the amount of
wind power or solar power for a given location during a representative time period. So far, the resource
assessment does not provide information about the resource’s changes over the time. If the assessment
gives a value of 12MWh available for a given location for one year, there is no need to know if there is
1MWh every month or no wind during winter and 2MWh during summer. When this resource is available,
i.e. the wind blows or the sky is clear, it is transformed into electricity and straight sold to the grid.
However, electricity is generated to meet a demand. Without substantive storage medium connected to
the grid, a real time monitoring has to be done between demand and supply. In the case of a micro grid
sizing, the developer of the power plant must consider that the demand has to be met continuously. In
large electricity grids, renewable energy producers are part of the energy market and they need to control
their production.
Considering a large integration of renewable energies, yearly potential of a location is not sufficient
anymore because the electricity generation has to take into account the electricity demand. It is important
to know when renewable resources are available and if they can meet the electricity demand. This paper
presents a way of generating renewable resources time series.
Renewable energy forecasting is a growing industry that helps to cope with renewable energies variability.
Grid operators can deal with power fluctuation more easily if they know it in advance. With forecasting,
they can start conventional generator early enough. Even the energy producer is interested in power
forecasting. In large grids with electricity markets, it can sell or buy the difference between its expected
production and its real production. With a storage medium, it can choose to sell to the grid latter. As
forecasting is getting better, it becomes more and more important and reliable.
This work adds forecast time series to renewable resources time series.
In short, the first priority of the renewable energy sector was to produce as cheap as possible to compete
with conventional generation. Renewable energies are already competitive in several part of the world.
Today, the renewable energy sector faces a new challenge: mastering its production over time. This
document introduces the work on generating time series of renewable resources and time series of
forecasts.
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1.2 Akuo Energy Presentation
Akuo Energy is a French company founded in 2007. It develops, finances, builds and operates renewable
energy power plants (Akuo Energy). Main activities are solar photovoltaic and wind power but Akuo also
operates two biomass power plants and develop several hydraulic projects.
Akuo’s power plants are mainly in France and developing projects are all over the world.
Innovation is very important within the company. Akuo Energy is the leader of photovoltaic power plants
with battery storage. Several solar photovoltaic plants are associated with other activities such as fish
farming and crops under glass. Last but not least, Akuo leads the development of the Ocean Thermal
Energy Conversion with DCNS. The two companies develop together the project NEMO. It is expected
to produce 16MW by the end of 2018 for the French oversea island, Martinique.
Akuo is using its special expertise related to power plants with storage to the development of micro grids.
Nowadays, numerous regions around the world remain with no access to electricity or only thanks to
small diesel generators and micro grids. However, locally diesel-generated electricity presents two issues:
first it is expensive due to oil import costs. Villages are dependent from oil’s volatile market price and high
costs to guarantee secure supply. Second, electricity generation from diesel generators is very polluting.
Thus, because of the volatility of the oil price and the cost of imports, renewable energies are already
competitive to bring electricity to villages. To meet continuously the demand, storage devices must be
added to the renewable energy generation part. Akuo’s special expertise for renewable energy power plants
with storage is employed to develop a new tool for stand-alone hybrid power plants.
1.3 Akuo’s tool: Akomis
For one year, the R&D department of Akuo Energy has developed software named Akomis to design
hybrid power plants for micro grid applications. Indeed, for a given electricity demand, it simulates the
behavior of each component of the hybrid system (PV panels, storage system, PCS, diesel generator…)
allowing the user to select the best combination according to its own criteria.
Akomis has four input categories. First it uses time series of electricity demand and time series of
renewable resources. These are based on site survey. Then, users choose a set up for generators and
storage mediums. Last, economic parameters can be added such as oil price, inflation. Akomis calculates
the energy mix that minimizes the operational expenses while meeting the demand. For hybrid power
plants with conventional and renewable energy generation it means minimizing the diesel consumption.
Demand profile, resource profile and generation mix with their parameters are mandatory. With economic
inputs, the tool is able to calculate the Levelized Cost Of Energy, and payback times.
One of the drawbacks of this tool is its lack of data profiles to run simulations. Having a good overview
of the entire life of a micro grid system involves simulations over numerous years. It is possible to install
anemometers and pyranometers during the project’s development stage and obtain a one year dataset.
These are useful information but it is not enough to ensure the best sizing of a system with a 20 years life.
Moreover, wind analysis shows very different wind speeds over the years. Good estimation is done with
values for more than 10 years (Riso National Laboratory, 1991).
The goal of the work explained in this document is to generate solar and wind time series for as many
years as needed. Profiles are generated randomly under constrains using samples of measurements. These
profiles have a practical application as inputs for the Akuo’s tool. Moreover, they are the basis of a
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completely new approach concerning the design of renewable energy power plants because it involves the
variability of the resource.
This document summarizes what are the current tools for renewable energy resources assessment and it
presents means to generate profiles with timescales ranging from 1 sec to 10 min. The second part of this
document introduces a way of generating forecasts on the profiles previously generated.
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2 Wind energy: state of the art
2.1 Introduction
The first step of a wind farm development is the choice of a location. Good locations include high wind
resources and nearby infrastructures (roads, telecommunications...). Some area are forbidden such as
military zones or natural parks. Site selection methodology is outside of this study. It is considered that the
localization is chosen.
Site potential assessment starts with on-site measurements that give the site’s patterns. These are the very
basis of the assessment, they are used in any case. External data might be used to take a longer-term view.
Measured data processing is the second step of the site potential assessment. The data set with
measurements is not as large as the expected power plant’s lifetime. Data processing methods reveal the
patterns of the measurements data set. Then these patterns are extrapolated to determine an expected
production during the entire lifetime.
Methods vary relating to the way the power plant is used: does it take part in the network balancing
process between demand and supply? In most cases, the answer is no because renewable energy
generation is a very small part of the entire energy mix. This part explains methods used to determine the
potential in this case. If the answer is yes, i.e. if demand has to be taken into account, a new assessment
method is used. It is depicted in the next part.
Guidance for wind potential analysis presented in this document is from MEASNET documentation
(Meastnet, 2009). MEASTNET is a network of measurement institutes. Its publications aim to harmonize
wind energy-related measurement procedures. Following this guidance is important to assess the potential
of the site for external investors.
2.2 Data available
As soon as the power plant’s location is chosen, a measurement campaign is implemented on-site.
Other data sets are collected from measuring tools and satellite views. Combinations of these data are
used to determine the site potential.
2.2.1 Measurements
A mast is placed on-site with sensors to measure the following parameters at different heights:
• Wind speed,
• Wind direction,
• Wind speed standard deviation,
• Temperature,
• Pressure,
• Air moisture,
• Flow inclination.
The first three parameters has to be measured on-site. The other ones might be derived from available
non-site specific data or estimations.
The highest measurement level of wind speed is at least 2/3 of the planned hub height. The best height is
the planned height hub. Additional anemometers are used at lower heights to assess the wind shear and
determine the wind profile at the site. It has to be considered that the most important heights are those
which lie within the rotor-swept area.
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The sampling rate of the wind speed measurement is 1Hz or
faster. However, 10-min average is recorded and saved with
additional values such as minimum, maximum and standard
deviation.
Wind direction measurements have the same requirement.
One year of data is the minimum measurement duration. It shows
seasonal patterns. In case of measurement failure, the campaign
has to be extended.
Figure 1 shows a mast on-site with 5 measuring heights (Table 1).
The measurement period started 2012-06-24 and ended 2015-01-
07. The considered hub heights for this project are 60m, 67m and
78m.
Measuring heights [m] Parameter measured
50.1 Wind speed
49.9 Wind speed
40.0 Wind speed and direction
25.0 Wind speed
24.7 Wind direction
Table 1: Measuring parameters
2.2.2 Other data
Other data are available to assess wind power potential. First meteorological stations close to the
considered location provide accurate data.
Second, data from satellite observations are used to study long term patterns. They are analyzed using
global atmospheric models. These data are often updated using new models and larger computational
resources. It means that even results from old measurement have the best accuracy available. There are
two mains derived data from satellite observations:
• MERRA: from NASA (US)
• ERA: from ECMWF (EU) These data are post processed by private companies that sell their output. It is possible to obtain 20years of wind speed values with a granularity of one hour.
2.3 Data analysis
Data measured are analyzed to characterize the location. This part depicts usual methods. The demand is
not taken into account and thus only the overall energy available is assessed without any temporal
considerations.
Several methods can be used from the direct use of data to the use of probability distributions (McGowan,
2009). For every method, it is considered time series of N wind speed observations Ui. The sampling time, ∆� is constant.
Figure 1: Mast on-site
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2.3.1 Direct use of data
First calculations are the long-term average wind speed �� and the standard deviation �:
�� = 1���� �
� = � 1 − 1(�� −��)��� �
The average power density, ��/�, is the average available wind power per unit area and is given by:
��/� = (1/2)�∆� 1����� �
Then, consider the energy density per unit area for a given extended time period ∆� long:
��� = �12��∆������ � = ����� ∗ ∆�
Finally, the average machine power ��! and the energy from a wind machine ��! are:
��! = 1��!(�� � ��)
��! = 1��!(�� � ��)(∆�)
Where ��!(��)is the power output defined by a machine power curve.
These gross results can be summarized using different methods. The two following paragraphs present the
histogram of occurrences and the duration curve.
2.3.2 Bins methods and histogram of occurrences
The method of Bins is to separate the data into wind speed intervals (or bins) in which they occur. It is
most convenient to use the same size bins. Suppose that the data are separated into NB bins of width wj,
with midpoints mj, and with fj, the number of occurrences in each bin or frequency, such that:
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= "#�$# �
Equations shown in the section before become:
�� = 1"#%#�$# �
� = � 1 − 1&%#�"# −����$# � '
��/� = (1/2)�∆� 1%#�"#�# �
��! = 1��!(�$# � %#)"#
��! = 1��!(�$# � %#)"#(∆�)
Results from this method are shown in a histogram showing the number of occurrences, or as a
percentage, and bin widths.
The graph 1 below shows the percentage of occurrence of the integer wind speeds.
2.3.3 Statistical analysis
For statistical analysis, a probability distribution is a term that describes the likelihood that certain values
of a random variable will occur. In this part, the random variable considered is the wind speed.
Nevertheless, probability distribution and probability density function will be use as well for solar
irradiance in the part 5. The frequency of occurrence of wind speeds may be described by the probability
density function, p(U), of wind speed. The probability of a wind speed occurring between Ua and Ub is:
((�) ≤ � ≤ �+) = , ((�)-�./.0
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Graph 1: Wind Speed Histogram of occurrences
As for any probability density function, the total area under the probability density curve is equal to 1:
, ((�)-�12 = 1
The lower limit is 0 since neither wind speed nor solar irradiance can be less than zero.
The cumulative distribution function represents the probability that the random variable is smaller or
equal to a given value, U:
3(�) = , ((�′)-�′.2
With probability distributions, the average and the standard deviation are calculated with the following
equations:
�� =, �((�)-�12
� = 5, (� − ��)�((�)-�12
0
5
10
15
20
25
0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
[%]
Wind speed [m/s]
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Two probability distributions are commonly used in wind data analysis, the Rayleigh distribution and the
Weibull distribution.
The Rayleigh distribution uses the mean wind speed as the unique parameter. The figure 2 shows
examples with different mean wind speeds. A higher mean implies higher wind speeds as well as more
wind speed variations.
Figure 2: Rayleigh Distributions
The Rayleigh distribution has the following equations:
((�) = 62 � ����� exp(−64 ������) 3(�) = 1 − exp(−64 ������)
The Weibull distribution has two parameters: k, the shape factor and A, the scale factor. The figure 3
shows examples of Weibull parameters. Higher the shape factor less important the wind speed variation.
Figure 3: Weibull Distributions
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The Weibull distribution has the following equations:
((�) = �;�� ����<=� exp(− ����<) 3(�) = 1 − exp(− ����<)
Probability distributions are used to get a continuous distribution from the cumulative histogram
described before.
The graph 2 adds a Weibull distribution to the data shown in the graph 1. It considers every directions.
Graph 2: Histogram of occurrences with Weibull distribution1
2.3.4 Wind direction and correction using long-term data set
Compilation of measured data gives information about wind direction. They are plotted with a wind rose
diagram. The graph 3 shows the wind distribution for the measurement values used in the previous parts.
1 This distribution and the following three are extracted from Akuo Energy project (confidential).
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Graph 3: Wind rose diagram with Wind speed distribution for measurements
The graph 4 shows the same plot for the satellite data used to correct the measurement.
Graph 4: Wind rose diagram with Wind speed distribution for satellite data
Finally, the graph 5 shows the corrected plot for the site studied. The calibration method is not developed
in this document because it varies from a company to an other. Next part introduces this issue.
Graph 5: Wind rose diagram with Wind speed distribution for corrected data
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2.3.5 Velocity, power and turbine power duration curve
Another means to illustrate the potential of a location is to plot a duration curve. The duration curve is a
graph that indicates the number of hours in the year (x axis) for which the variable equals or exceeds each
particular value on the y axis.
First the velocity duration curve is plotted. It gives an approximate idea about the nature of the wind
regime.
Then, this plot can easily be converted to a power duration curve by cubing the ordinates.
Lastly, using the power curve of the studied machine, the turbine power duration curve can be obtained.
The example below is from the same data as before. The graph 6 plots the velocity duration curve. The
graph 7 is the power curve of the Vesta turbine V80. Its rated power is 2MW with a wind speed cut in of
4m/s and a wind speed cut off of 15m/s.
Graph 6: Velocity duration curve
0
2
4
6
8
10
12
14
16
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Win
d s
pee
d (
m/
s)
Duration, hours
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Graph 7: Vestas V80 Power curve
Finally, the graph 8 plots both the wind power duration curve and the turbine power duration curve. The
gap between the two curves for a given duration is due to aerodynamic losses.
Graph 8: Power duration curves
Note that this curve is related to the cumulative distribution function. We have the relation: >?@ABC�D-EFG�CAHBEFI? = 8760 ∗ (1 − 3(�)). To obtain the same representation just reverse the x
and y axis.
0,000
0,500
1,000
1,500
2,000
2,500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0,000
0,500
1,000
1,500
2,000
2,500
0 2000 4000 6000 8000 10000
Po
wer
(k
W)
Duration, hours
Wind power
Turbine power
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3 Wind profiles generation
Wind profiles generation is based on random processes calibrated to describe wind speed as a function of
time. An analysis of the wind power spectrum is achieved first. It gives how wind power fluctuates over
the time: does it change every second, every minute or even less frequently? Of course, wind power
fluctuates continuously but it is important to know when the main switches are.
3.1 Granularity issues
First of all, the wind power spectrum analysis is mainly based on Van der Hoven’s work (Hoven, 1956). It
has shown that the power spectrum of wind as the following shape:
Graph 9: Wind Speed Power Spectrum
Power spectrum is a measure of the contribution of oscillations of wind speed. It describes how the
power of wind speed is distributed over the different frequencies. It clearly shows 3 peaks. The first one is
around 4 days. It is caused by the passage of large scale weather systems - most usually low pressure
depressions. The second one is around half a day and depicts diurnal changes. The last one is larger with a
top around one minute. Profiles generated have to depict these changes.
A second analysis were lead over Akuo’s data. SCADAs (Supervisory Control And Data Acquisition)
installed on new Akuo’s sites measure data every second. The analysis measures the time needed to switch
from one value to a next 1% or 5% larger one (in absolute terms).
Data were processed to delete every bad value that occurs when connection with the SCADA was lost.
Indeed, if the internet connection with the site is lost data can be stored in the SCADA’s internal memory.
This one is small and if the site is not reconnected fast enough, the same value will be recorded during the
entire time without connection. In our analysis, this can bias the result to a higher value than expected.
-24-
One year analysis gives the following results:
Time period
1% difference
Mean [s] Max [s] Min [s] Median [s]
January, February, Mars 13.7 1404 0 10
Mars, April, May 15.3 1777 0 10
Mai, June, July 15.2 1372 0 10
September, October,
November, December 14.9 3751 2 10
Table 2: Time to switch from a value to another 1% larger
Time period
5% difference
Mean [s] Max [s] Min [s] Median [s]
January, February, Mars 92.9 11111 0 25
Mars, April, May 235.5 34439 0 30
Mai, June, July 587.8 41848 0 35
September, October,
November, December 138.5 18111 2 20
Table 3: Time to switch from a value to another 5% larger
There were no values from 17th July to 24th September. Months might be split into two periods because
the bad data removing was done with Microsoft Excel that as a limited number of lines.
This analysis shows that changes in power occurs at less than 1 minute frequency.
Finally, it is considered that the mechanical inertia from components such as blades and rotor cancels out
changes in wind speed with higher frequency than a second.
3.2 Work with meteorologist centers data set
As explained in the part 2, national meteorological centers provide hourly wind data for every location
around the world and for the last 20 years. Thus, these data depicts already several wind power
fluctuations:
• Annual fluctuations
• Seasonal fluctuations
• Days fluctuations
• Diurnal fluctuation
Nevertheless, high frequency fluctuations are not revealed with these data. The overall idea is to process
measurements to assess the main characteristics of site specific high frequency fluctuations. This part is
called “Site characterization” and it is the first step of the wind profiles generation. Then, the 20 years
hourly data are filled to obtain 1 second granularity data.
-25-
3.2.1 Site characterization
Wind speed series with 10 minutes timescale provide information on how the wind fluctuates around its
hourly values. Every 10 minutes, the average, the standard deviation, the maximum and the minimum are
measured and recorded.
First, downscale from hourly values to values with a 10min granularity is studied. The goal is to
understand how 10min values are spread around the hourly mean value. Hourly average wind speed is
calculated. Then a standard deviation is calculated over the 10min average values for each hourly average
value. Every pair of mean and standard deviation are plotted (Graph 10).
Graph 10: Standard deviation of 10min values around their hourly means
Number of occurrences for each wind speed measured is added to the graph. For wind speed with enough
occurrences (more than 200), standard deviation can be considered as steady. The average value is 0.6
m/s. It means no matter the hourly average wind speed, 10min average wind speed are spread using the
same standard deviation. This value will be used to generate five values with a 10minutes granularity
between each hourly value.
Moreover, a second analysis is done. It aims to define wind speed values with a granularity under 10min.
Measurements associate a standard deviation for each 10min mean value recorded. For each 10min
average wind speed measured, the average of standard deviations is calculated. As the graphic 11 shows, in
this case, standard deviation is a linear function increasing as higher wind speed are measured. In other
words, the turbulence intensity is steady (Graph 12).
0
200
400
600
800
1000
1200
0.000
0.500
1.000
1.500
2.000
2.500
0 2 4 6 8 10 12 14 16
Num
ber
of
occ
urr
ence
s
Sta
nd
ard
Dev
iati
on
[m
/s]
average wind speed over 10min
-26-
Graph 11: Standard deviation as a function of the wind speed - 1s granularity
Graph 12: Intensity of turbulence as a function of the wind speed
y = 0.1321x + 0.0235R² = 0.9415
0
100
200
300
400
500
600
700
800
900
1000
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12 14 16 18
Num
ber
of
occ
urr
ence
s
Sta
nd
ard
dev
iati
on
[m
/s]
Mean wind spead over 10min [m/s]
0
100
200
300
400
500
600
700
800
900
1000
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 2 4 6 8 10 12 14 16 18
Num
ber
of
occ
urr
ence
s
Inte
sity
of
turb
ule
nse
Wind speed 10min average
-27-
NH�?HOC�DA"�EFPE@?HB? = Q�GH-GF-R?ICG�CAHS?GH
We obtained the following relation with a correlation coefficient of R² = 0.9415. Q- = 0.1321 ∗ %?GH + 0.0235
This analysis clearly shows two features of the wind speed. 10min averages are spread over hourly
averages with a steady standard deviation, such value is around 0.6 m/s for the location considered. 1s
values measured are spread over 19minutes averages with a standard deviation raising as the wind speed
increases. Standard deviations for 1sec values are 50% larger than the steady deviation for 10min averages:
0.93 m/s (mean value calculated for wind speeds that occur more than 200 times). This matches the Van
der Hoven’s wind power spectrum showed previously.
3.2.2 Comparison between measurements and meteorological centers
data sets
Before using meteorological centers data sets, it is important to compare them to measurements made on-
site. Indeed, data sets with large spatial resolution often have inherent bias (see Annex 2).
As an example, data set from MERRA is used here. It contains hourly values from January 1981 to August
2015. Because data have been measured on-site at 50meters and during the entire year 2013, MERRA data
are download for the same height and the comparison is done over 2013.
69 days are missing from the measurements, they are also removed from MERRA data. Then both are
plotted in order to check their global outlook. As the graph 13 shows, MERRA and measured data look in
line.
Graph 13: Sample of MERRA and measured data
0
2
4
6
8
10
12
14
1
25 49 73 97 121
145
169
193
217
241
265
289
313
337
361
385
Win
d s
pee
d [
m/
s]
Time [hour]
Sample of MERRA and measured data
MERRA Measurements
-28-
Then, sum of squares (to be proportional to an energy) and means over month are calculated. November
and December are not considered because too many data are missing.
Sum of squares [kJ/kg] Annual mean [m/s]
MERRA 360 6.92
Measures 369 6.98
Deviation -2.4% -0.8% Table 4: MERRA and Measurements annual parameters
January February March April May June July August September October
MERRA 7.96 7.74 5.75 7.73 7.10 8.14 6.90 6.73 5.34 5.86
Measures 8.03 7.66 5.90 7.40 7.08 8.22 7.05 6.68 5.71 6.08
Deviation -0.9% 1.0% -2.5% 4.5% 0.3% -0.9% -2.2% 0.8% -6.5% -3.7%
Table 5: MERRA and Measurements monthly parameters
Annual values clearly shows that MERRA underestimate wind power at the location considered. However,
monthly results shows that there is no inherent annual bias because deviation might be equally positive
than negative.
Annex2 introduces a method to calibrate satellite measurements for a given location with ground
measurements. It is develop for solar irradiation but it can be extended to wind speed dataset. This has
not been done in this work because it is already mainly developed by specialized companies (as shown in
the part 2). However further developments for automating wind speed time series generation include this
work.
3.3 Filling hourly values
3.3.1 From hourly values to 10minutes granularity values
As explained in the previous part. First, 10min granularity values are generated between each hourly value
(using the steady standard deviation). As the sample of MERRA values shows, hourly values are strongly
linked with a trend over several hours. To comply with these trends, 10min values are spread considering
a linear regression between every two hourly values.
Graph 14: Evolution of hourly average wind speed
4
5
6
7
8
9
10
11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Win
d s
pee
d [
m/
s]
Hours
-29-
A linear regression is done between every two hourly values. Then, the 10 minutes value is calculated
thanks to an inverse normal distribution with the following parameters:
- Probability: random number between 1 and 0
- Expectation: value from the linear regression
- Standard deviation: from the relationship calculated in the site characterization part, 0.6 in this
example.
For the same period plotted above, the graph 15 shows hourly values, the linear regression and the 10min
granularity values.
Over one year this method gives the following deviations:
10min Hourly Deviation [%]
Sum [kWh/kg] 457.2 454.9 0.51
Average [m/s] 6.951 6.952 -0.01
Table 6: Deviation of the 10min granularity values generation
3.3.2 From 10minutes values to 1 second values
Moving from 10min granularity values to 1second granularity values is done in two step. First, each 10
minutes value is filled with a random number of points: they are spaced out from each other with a time
period between 3 seconds and 30 seconds. Then a linear regression is added to these “targets”. The linear
regression gives the trend for the 1second points. This method is completely new and only developed for
this work.
Graph 15: Linear regression and 10min granularity values
-30-
The graph 16 shows random points spread between two 10min values.
Then each one second point is calculated thanks to an inverse normal distribution with the following
parameters:
- Probability: random number between 0 and 1.
- Expectation: Value from the linear regression.
- Standard deviation: from the site calculation done before (as a function of the wind speed)
This gives the following results, where the red line is the 10minutes value.
Graph 16: Filling the 10min value with a random number of points
Graph 17: Filling with 1sec granularity points
-31-
3.4 Conclusion
This method allows the user to create wind speed time series with a 1 second timestamp for every location
around the world. Every peak depicted at the beginning of this part is visible in the final time series. The
first two, the synoptic peak and the diurnal peak, are already depicted in the hourly input. Then the large
turbulent peak is created between each 10min value thanks to a very wide distribution for the 1sec point.
The graph 18 shows a typical distribution of wind speed for a very short period. It comes from Wind
Energy Explained, a reference book in the wind energy field (McGowan, 2009). It clearly shows variations
over 30sec and turbulence every second as it was represented in the model developed in this part.
For further validation of this model, time series generated will be converted into power time series using a
power curve for a given wind turbine. These results will be compared with measured power. Indeed, wind
speed time series with 1 second timescale are not easily available and it is more convenient to compare
turbine output power.
Graph 18: Typical Distribution of Wind Speed for a very short period
-32-
4 Solar energy: state of the art
4.1 Basis
First, as a reminder, the solar power, understood as instantaneous density of solar radiation incident on a
given surface, is called irradiance. It is typically expressed in W/m². The solar energy i.e. the sum of
irradiance over a time period (e.g. 10min, 1 hour, 1 day or more) is called irradiation. It is expressed in
Wh/m² in this document.
The solar irradiance is produced by the sun in the form of electromagnetic radiations. Passing through the
atmosphere, the irradiance diminishes due to atmospheric absorption and scattering and cloud reflection.
Figure 4: Solar losses through the atmosphere
On the ground, solar irradiance can be divided into three components: the global horizontal irradiance
GHI, the direct horizontal irradiance DHI and the diffuse horizontal irradiance DIF. They are linked with
the following relation: XYN = RYN + RN3
The direct radiation is the part of the solar radiation that comes straight from the sun to the ground
without any atmospheric losses. DIF is the irradiation component that reaches a horizontal Earth surface
as a result of being scattered by air molecules, aerosol particles, cloud particles or other particles. In the
absence of an atmosphere there would be no diffuse horizontal irradiation.
GHI is the most important parameter for calculation of PV electricity yield because PV panels generate
electricity from both direct and diffuse radiations. Thus, when it is written irradiance or irradiation in this
document, it means global irradiance or global irradiation.
-33-
Graph 19: Clear sky irradiance daily profiles
In order to get the maximum power from the sun, solar panels are tilted. So it is important to calculate the
global tilted irradiance. Unlike a horizontal surface, a tilted surface also receives small amount of ground-
reflected radiation.
Most of the PV modules are installed on fixed tilted construction but it also exists construction with 1-axis
tracking or 2-axis tracking as the figure 5 shows.
Graph 20 : Clear sky irradiance daily profile on a 30° tilted plane in La Réunion, France, 1st January
0
100
200
300
400
500
600
700
6:40
7:10
7:40
8:10
8:40
9:10
9:40
10:1
0
10:4
0
11:1
0
11:4
0
12:1
0
12:4
0
13:1
0
13:4
0
14:1
0
14:4
0
15:1
0
15:4
0
16:1
0
16:4
0
17:1
0
17:4
0
18:1
0
18:4
0
19:1
0
Irra
dia
nce
[W
/m
²]
Time
GHI [W/m²]
DHI [W/m²]
DIF [W/m²]
0
100
200
300
400
500
600
700
800
900
1000
6:40
7:10
7:40
8:10
8:40
9:10
9:40
10:1
0
10:4
0
11:1
0
11:4
0
12:1
0
12:4
0
13:1
0
13:4
0
14:1
0
14:4
0
15:1
0
15:4
0
16:1
0
16:4
0
17:1
0
17:4
0
18:1
0
18:4
0
19:1
0
19:4
0
Irra
idan
ce [
W/
m²]
GHI [W/m²]
GTI [W/m²]
-34-
Figure 5: Solar panel tracking systems
4.2 Data available
4.2.1 Measurement
As for a wind farm project, the first step of the PV project’s development is the implementation of
sensors. For solar potential assessment, pyranometers are implemented at the location. A first
pyranometer is placed on a horizontal surface. A second one is placed on a tilted surface. The tilted angle
is equal to the planned tilted angle of the solar panels.
Pyranometers measure solar irradiance every 5 seconds. If the pyranometer stands alone, it stores average
values every minute. If the pyranometer is linked to a SCADA, all data can be stored.
The minimum acquisition time is one year because it has to reflect the seasonality changes.
4.2.2 Clear sky model
For a given location, it is possible to get the theoretical irradiance if there is no cloud: the clear sky
irradiance. It is mainly based on the sun path geometry described by mathematic formulae. However, it
also includes several losses: from Ozone, air molecules, aerosols and water vapor. These parameters come
from other atmospheric models. They can be static (one clear sky model per site per day for all the years)
or dynamic (all these parameters are calculated every time new data are available from NOAA or
ECMWF).
For this work two clear sky models were used: one static from software PVSYST and one dynamic from
MACC-Clear database (Armines, 2015).
The clear sky index is defined as the ratio between the irradiation measured and the clear sky irradiation
for the same time period.
Z@?GFO;DCH-?["AF�ℎ?-GDC = -GC@DCFFG-CG�CAH?[(?B�?-CFFG-CG�CAHA"�ℎ?B@?GFO;D-GDC
4.2.3 Data from satellite outputs
It exists different satellite programs for weather and environmental observation. All of them are based on
geostationary satellites that cover part of the globe (see picture 6).
Meteosat is the satellite program of the European Union. Satellites are operated by EUMETSAT
(EUMETSAT, 2015). Meteosat-10 is the Prime operational geostationary satellite. Meteosat-7 is the
IODC operational geostationary satellite.
-35-
GOES is the US satellite program (NOAA, 2015). There are two geostationary satellites: GOES-EAST
and GOES-WEST.
Last, several other countries have their own program: Russia, Japan (MTSAT covers the pacific area on
the picture below), China, India.
Figure 6: Coverage of several satellites
Numerous meteorologist companies or public research centers process satellite outputs to provide free
and/or commercial dataset of solar parameters (depending on the size and the granularity of the dataset)
(MESOR, 2009).
The table 7 presents the main datasets and their characteristics:
*Depend on the location
Table 7 : Main datasets for satellite imagery -1
Product Provider Area Time period
NASA SSE NASA World 1983/7/1 – 2005/6/30
Meteonorm Meteotest World 1981 - 2000
Solemi DLR (Germany) Europe/Africa/Asia From 1991
EnMetSol Univ of Oldenburg Europe/Africa From 1995
Satel-light ENTPE (EU) Europe 1996 - 2001
PVGIS JRC (EU) Europe/Africa 1981 - 1990
Helioclim Armines Europe/Africa From 2004 to last month
MACC RAD Armines Europe/Africa From 2004 to last month
SolarGIS GeoModel World From 1994/1999/2007 to last month*
-36-
Temporal and spatial resolutions also differ from sources. The best satellite temporal resolution is 15min
(IEA, Geneva University, 2013). Below 15min, data are recovered with regressions based on the clear sky
profile and stochastic algorithms.
Product Provider Temporal
resolution
Spatial
resolution Price
NASA SSE NASA Daily 100km Free of charge
Meteonorm Meteotest Up to 1min NA 115€/site
Solemi DLR (Germany) Hourly 3km On request
EnMetSol Univ of Oldenburg Up to 15min 1-3km On request
Satel-light ENTPE (EU) Up to 30min 5-7km Free of charge
PVGIS JRC (EU) Daily NA Free of charge
Helioclim Armines Up to 1min 5-7km Subscription
MACC RAD Armines Up to 1min 5-7km Free of charge
SolarGIS GeoModel Up to 15min 1-3km 1000€/site
Table 8 : Main datasets for satellite imagery -2
4.2.4 Data from meteorological ground stations
Numerous database from measurements are also available. First of all, the World Radiation Data Center
(World Radiation Data Center, 2015) that provides ground measurements of 1195 stations from 1964 to
1993. Moreover some national centers have their one database (USA, Canada, Australia, Switzerland,
France). PVGIS and Meteonorm use these databases and combine them with satellite data. It is the reason
why they do not have a spatial resolution in the table above.
If the planned site’s location is very close to the station, it is possible to make a direct use of their data. If
not, data might be used to control on-site measured values.
4.3 Photovoltaic power plant sizing
The first step is to calculate the total energy the location gets over a year.
On-site measurements are the most reliable source. However it covers only a short period of time. Thus,
satellite data are compared to measurements to correct errors from satellite data. It might remove an
inherent bias as well as introduce shadow losses specific to the site (for example, a faraway mountain
might block the sun every morning). When the correction is satisfactory overall, it is applied to the whole
satellite data.
A method of satellite data calibration with ground measurement is depicted in Annex 2.
As soon as data are checked, they are summed over the year to obtain a total annual horizontal resource in
kWh/m2.
Solar panel are oriented with a tilted angle and an azimuth angle to get the maximum solar energy. For
example, in the northern hemisphere, solar panels are mainly oriented south (azimuth equal to 180°). In
practice, a trade-off is found between space available and tilted angle because tilter are the panels larger
the distance between rows to avoid shadowing is needed. Several set of possibilities are evaluated (type of
panels, number of panel, azimuth, tilt…). For each, it is possible to see the sun path as the figure 7 shows.
-37-
It takes into account losses due to surrounding relief. The total annual horizontal resource is converted
into a total tilted resource peculiar to the project.
The last step is to get the expected electricity production from solar resource. Every loss is considered:
shadow due to external obstacle to the sun radiation, shadow between panels, losses in electrical devices
(inverters, transformers) and losses due to performance degradations, soil and down time.
Figure 7 : Sun path
The final results are the overall efficiency of the photovoltaic park also called performance ratio (around
80%), the specific efficiency and the expected annual production. The specific efficiency is the ratio of the
energy installed over the power installed.
-38-
5 Irradiance profile generation
5.1 Data used
Depending on the location and the means, the amount and the type of data developers get might be very
different. First, yearly or monthly or daily irradiance averages might be available. For each average the
standard deviation might be available. The size of dataset widely vary from a source to another. Last but
not least, sample of days and explanation of the specific features of the location’s weather are very useful.
The solar time series generator is developed in order to be efficient even with very few inputs. More
inputs it gets more accurate it is. Each parameter has a default value that can be optimized using the data
measured on-site.
Clear sky and diffuse profiles are extracted for the software PVSYST. They have a temporal resolution of
1min mean.
Brief calculations give values with the following temporal resolutions: 1month, 1day, 10minutes.
5.2 From yearly average to daily averages - Methodology
This part presents how it is possible to down scale inputs from annual irradiation to daily irradiation.
5.2.1 From annual irradiation to monthly irradiation
In cases in which only yearly averages are available, they are spread over months using the clear sky
profile. Monthly clear sky irradiation give the distribution of solar irradiation over the year (see example in
graph 21). Each month obtains a weight ri, corresponding of its importance in the annual sum:
∀C ∈ _1; 12a,F� = Z@?GFO;DCFFG-CG�CAHA"%AH�ℎCZ@?GFO;DGHHEG@CFFG-CG�CAH
0%
2%
4%
6%
8%
10%
12%
14%
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11 12
% o
f an
nual
irr
adia
tio
n -
ri
Irra
dia
tio
n [
kWh
/m
²]
Month
Monthly irradiation ri
Graph 21: Monthly clear sky irradiation in Sevilla - Spain
-39-
The annual energy is distributed over each month according to its weight found from the clear sky profile:
∀C ∈ _1; 12a,�H?FcD%AH�ℎ� = F� ∗ GHHEG@CFFG-CG�CAH
This case is very simple because it is also very uncommon. Most of the time, monthly irradiations are
available, it is the case of most of national centers.
5.2.2 Create several months
Most of the datasets presented in the part 4.2.3 provide monthly data. According to the means of the
project, it is possible to get several monthly irradiations each month i.e. several years of monthly
irradiance. Graphs 22 shows monthly averages in La Reunion, French island from few data sets. Monthly
average from measured data is added. First, one can see that all of these curves have the same shape:
winter’s irradiations are lower than summer’s irradiation (the considered location is in the Southern
hemisphere). However, there is important biases between the different curves. Based on data measured on
site, data from NASA, PVGIS and Clima SAF are removed. Thus averages of monthly irradiance values
used in the following part are averages of only Kilowattsol, Helioclim and measured data.
3,000
3,500
4,000
4,500
5,000
5,500
6,000
6,500
7,000
7,500
8,000
1 2 3 4 5 6 7 8 9 10 11 12
Mo
nth
ly i
rrad
iati
on
[kW
h/
m²]
Month
KWS - 2012 KWS - 2013 Helioclim - 2004 Helioclim - 2005
NASA - 1983-1993 PVGIS - 2001-2012 Clima SAF 1998-2011 Measures - 2005
Graph 22 : Monthly averages from datasets
-40-
These considerations are kept when evaluating deviations, mean deviation and standard deviation. These
are calculated for each month using only Kilowattsol, Helioclim and measured data.
Month Mean
deviation [W/m²]
Standard deviation [W/m²]
Sum [W/m²] Average [W/m²]
January 363 533 180 871 5 835
February 241 361 161 437 5 766
March 103 132 162 462 5 241
April 178 248 144 056 4 802
May 208 284 127 210 4 104
June 240 324 114 436 3 815
July 140 210 120 987 3 903
August 137 158 136 638 4 408
September 170 234 149 093 4 970
October 164 205 166 597 5 374
November 231 341 173 092 5 770
December 382 407 181 085 5 841 Table 9 : Monthly parameters
A second option is possible in order to create several months. It implies a very large sample of monthly
irradiation. For each month, every monthly irradiation is divided by the clear sky monthly irradiation.
Monthly clear sky index is get. It is rounded and placed into one of the ten bins (0-10% of the clear sky
irradiation, 10%-20%, ..., 90%-100%). It gives a probability for each value of monthly irradiation to occur.
This method is also presented for the days generation.
5.2.3 Create days from monthly irradiation
5.2.3.1 1st method
The monthly energy is distributed over every day according to an inverse normal distribution with the
following parameters:
- Probability: random number between 0 and 1.
- Esperance: RGC@DGI?FGc?CFFG-CG�CAH = defghij�kk)l�)g�efm)jneofg
- Standard deviation: the monthly standard deviation After the normal distribution a second processing is added to make sure no day has an energy higher than
the clear sky day or smaller than the diffuse day.
5.2.3.2 2nd method
Otherwise it is possible to use a probability distribution. This method is based on data from Helioclim.
Daily irradiance is compared with Clear Sky values. These values are placed into 10 bins (Table 10). The
bin 1 is smaller because it has very few values and the bin 10 is larger because it has to represent only
completely sunny days.
Bins 1 2 3 4 5 6 7 8 9 10
Interval 0% to
15% 15% to
25% 25% to 35%
35% to 45%
45% to 55%
55% to 65%
65% to 75%
75% to 85%
85% to 95%
95% to 100%
-41-
Table 10 : Bins separations
Counting the number of occurrences into each bins and transforming this result as a percentage of the
total number of occurrences, one gets the probability distribution.
It is possible to calculate a probability distribution over the entire year (graph 23). However, it is more
accurate to calculate probability distributions for every month to get the difference between months.
Indeed, a summer month do not have the same amount of sunny day (with a Clear Sky index between
0.95 and 1) than a winter month. This gives the graph 24.
Graph 23 : Days distribution over the year
Graph 24 : Day distribution over each month
For further development, it is possible to give a probability distribution distinct for every day. These ones
would be calculated over the surrounding days.
For example, the probability distribution of the 1st March is calculated using the clear sky indexes of days
from 15th February to 15th March.
According to the probability distribution obtained previously, N clear sky indexes are calculated for each
month (N is equal to the number of days of this month). Then daily irradiations are calculated using Clear
Sky values. This is done in a loop while the sum of every daily irradiations is not included in the interval
0%
5%
10%
15%
20%
25%
30%
35%
1 2 3 4 5 6 7 8 9 10
Ind
ex o
f th
e C
lear
Sky
Bins
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
1 2 3 4 5 6 7 8 9 10 11 12
Ind
ex o
f C
lear
Sky
Distributions for every months
-42-
[monthly average – deviation; monthly average + deviation]. The deviation comes from the previous
analysis. In order to avoid infinite loop, every 5s the deviation increases by 0.1%. The tolerance range is
getting larger and eventually the sum of every daily irradiations is included. Thus final deviation is
controlled in the Table 11 below that shows final deviation gotten after one year of daily irradiation
calculated.
Original values Generated values
Deviation of
the mean [%]
Deviation of
the mean
deviation
[%]
Month Mean [W/m²]
Mean
deviation
[W/m²]
Mean [W/m²]
Mean
deviation
[W/m²]
1 5834.5 362.9 5833.92 363.7 0.2% 0.0%
2 5765.6 240.6 5773.64 240.6 0.0% 0.1%
3 5240.7 102.7 5238.45 103.6 0.9% 0.0%
4 4801.9 178.2 4797.94 178.6 0.2% -0.1%
5 4103.5 208.1 4100.36 210.1 1.0% -0.1%
6 3814.6 239.7 3808.79 239.7 0.0% -0.2%
7 3902.8 139.9 3902.99 140.6 0.5% 0.0%
8 4407.7 136.5 4404.62 136.5 0.0% -0.1%
9 4969.8 169.8 4966.24 171.8 1.2% -0.1%
10 5374.1 164.4 5371.39 167.0 1.6% -0.1%
11 5769.7 230.5 5771.93 237.0 2.8% 0.0%
12 5841.5 381.7 5833.35 384.0 0.6% -0.1%
Mean 4985.5 212.9 4983.6 214.4 0.7% 0.0%
Table 11 : Final monthly deviations
With this method, the average mean deviation (i.e. the average of every monthly deviation) is equal to
4.26% of the average daily irradiation (4985 W/m²) for the original values. After generating daily
irradiation for each months, the average mean deviation is equal to 4.29% of the average daily irradiation
(4983 W/m²). Thus the method is validated.
5.3 Sub-daily profiles
Daily irradiance time series are already well defined with the alternation of day and night. It is not possible
to spread the daily irradiation over every minute or second of the day equally. It has to follow the trend of
the clear sky day and the next value is strongly correlated with to the previous one. It is very difficult to
reveal a law between every values of a daily profile with a 10min temporal resolution. Even if, obviously it
follows the clear sky profile part of the time, two unknowns remains: when does it stop to follow the clear
sky profile and, if it is not on the clear sky profile, how much is the irradiance?
The first step of this work was the study of several timescales to determine if one of them looks more
predictable. Three of them were studied: 10min timescale, 1min timescale and 1second timescale. The
same day is plotted below with the three different resolution. It appears 10min and 1min timescales
smooths the shadow occurs because of clouds. The 1second timescale is the most relevant because, when
clouds pass by, the irradiance measured drops to an irradiance value around the diffuse value (which is
-43-
calculated using the sun path geometry described by mathematic formulae). Eventually, smaller timescales
than 1sec need too large computational resources.
Then, larger timescales are only mean of 1second values.
Graph 25: One day irradiance with a 10min timescale
Graph 26: One day irradiance with a 1min timescale
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Graph 27: One day irradiance with a 1second timescale
Note: with the 1sec timescale, it is even possible to see albedo effects: when a cloud passes by, both sun
rays reflected by the cloud and direct rays reach the solar panel. Very high irradiation is captured. This
effect will not be modeled in this work. Indeed, most of the irradiance due to albedo effect is curtailed by
the inverter in order to ensure stable generation.
5.3.1 Methodology
Several parameters are needed to create a day. First, the daily irradiation expected is compared to the clear
sky irradiation for the same day i.e. the clear sky index for the day is calculated. It gives us the type of day
(see the six types of day below).
Then, the two main parameters are the probability of fall and the probability of return. The first depicts
the likelihood the profile switches from a clear sky state to a cloudy sky state. The second depicts the
opposite: the likelihood the profile switches from a cloudy sky state to a clear sky state. Higher
probabilities values means faster change between the Clear Sky State and the Cloudy Sky State.
Finally, last two parameters are added: the fall factor f, and the fall interval ∆. The first gives the irradiance
of the cloudy sky state. It is a percentage of the clear sky irradiance. It depicts the cloud optical depth. The
second add a random feature to the fall factor: more important the fall interval, more important the
irradiance of the cloudy sky state might varies around the values defined by the fall factor.
Each day generated must have the energy determined in the previous part. Parameters briefly described
previously must change over the day to ensure the energy of the entire day is equal to the one expected.
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Time (local time)
-45-
To reach this objective a shape curve is created for each day. This shape curve has the exact expected
irradiation (which is the integral of the shape curve over the day). The profile generated is going to follow
the trend of this curve: the energy contained in the profile which is generating is compared to the energy
contained in the shape curve at the same point of the day. According to the result of this difference,
parameters’ values are modified. This is done with every 10minutes average values.
The graph 28 below gives an example. The shape curve is red and the generated daily profile is blue. At
the beginning of the day, the daily profile is above the shape curve: its irradiation (purple curve) is higher
than the irradiation of the shape curve (beige curve). Then, parameters are modified, the daily profile falls
and both irradiations are equal. This occurs several times per day in order to obtain the same irradiation in
the daily profile than in the shape curve (which is the expected irradiation).
Graph 28 : Shape curve and comparison of irradiations
Note: for further understanding, the reader might refer to the part 5.5 Generation and computing code
that explains the process for the creation of one day with an expected irradiation.
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The previous example shows the basis shape curve. It is uniform over the day. Several shape curves are
created to obtain different profiles of day:
• Sunny,
• Sunny/cloudy,
• Cloudy/sunny,
• Sunny/cloudy/sunny,
• Cloudy/sunny/cloudy,
• Very cloudy.
Each profile is defined in the following section.
First, as before, the clear sky index is defined for the day:
��� = �������� ��������������������������
������������������ = 16���(�)������
CS is the clear sky irradiance value as timescales of 10min. The division by 6 converts the irradiance to
irradiation (from W to Wh with 10min granularity values).
5.3.1.1 Sunny day, and cloudy day
It is the simpler shape curve. It is uniform over the day as a percentage of the clear sky. �ℎ����!�"�(�) = ��� ∗ ��(�)
5.3.1.2 Dual profiles
Cloudy/sunny and Sunny/cloudy curves are the dual profiles, they have two parts. The sunny part is
follow 90% of the clear sky profile. The cloudy part is below the clear with a percentage obtained as
explained below.
-47-
5.3.1.2.1 Cloudy/sunny
The following equation expresses that the energy in the shape curve must be equal to the expected energy.
$����������� = �� ∗ � ��(�)/6&'���� + �) ∗ � ��(�)/6*
��&
M is the middle of the day. It is calculated with the formula:
+ = �����,-. + ���,-.2
• �����,-. is the first index value for which CS is different from 0.
• ���,-. is the last index value for which CS is different from 0.
Because the shape curve is stuck between the clear sky and the diffuse curves, we have the following
conditions:
0�� ∗ � ��(�)&'���� ≥ � 2�33!��(�)&'�
����) ≤ 1
The previous system gives limitations for the expected energy: this type of profile may be used only if the
expected energy is lower than the clear sky energy and higher than half of the clear sky energy plus half of
the diffuse energy.
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Time
Clear sky profile Cloudy/Sunny Sunny/Cloudy Very cloudy shape
Graph 29 : Uniform and dual shapes of day
-48-
5� = 16 6� 2�33!��(�)&'���� + ���(�)*
��& 7 ≤ $����������� ≤ 16 6���(�)*��� 7
We choose to set the value r2. Thus the value for r1 is:
8�� = 6 ∗ $����������� − �) ∗ ∑ ��(�)&��&;�∑ ��(�)&����) = 0.9
5.3.1.2.2 Sunny/cloudy
This case is just the opposite of Cloudy/sunny.
$����������� = �� ∗ � ��(�)/6&'���� + �) ∗ � ��(�)/6*
��&
We have the following conditions:
0 �� ≤ 1�) ∗ � ��(�)&'�
��� ≥ � 2�33!��(�)&'����
5) = 16 6� ��(�)&'���� + �2�33!��(�)*
��& 7 ≤ $����������� ≤ 16 6���(�)*��� 7
We choose to set the value r1. Thus the value for r2 is:
8 �� = 0.9�) = 6 ∗ $����������� − �� ∗ ∑ ��(�)&'����∑ ��(�)*��&
5.3.1.2.3 Interval for the expected energy
As the profiles were defined, the value CS(M) (clear sky irradiance at noon) is part of the second part of
the day. It is the highest value of the CS profile. So, we have: 5� > 5)
-49-
5.3.1.3 Three-part profiles
A third class of profile was designed. They have three parts: morning, noon and afternoon.
5.3.1.3.1 Sunny/cloudy/sunny
$��� �������� = �� ���(�)/6�∈A + � ∗ B/6
With the following parameters:
- U is the interval that contains the sunny values
- l is the number of cloudy values
- Y is the irradiation level during the cloudy time
We have the following conditions:
C �� ≤ 1B ∗ �6 ≥ 0.15 ∗ max(��) ∗ �
Study of diffuse irradiation profiles shows that diffuse irradiation is around 10% of the global irradiation
at noon. A higher value (15%) is kept because the daily profile may fall under the shape profile.
As before, this profile can be used only with expected energy that satisfies these conditions:
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Clear sky profile Cloudy/Sunny/Cloudy Sunny/Cloudy/Sunny
Graph 30: Three-part profiles
-50-
5H = 16 6�����(�) + 0.15 ∗ max(��) ∗ ��∈A 7 ≤ $����������� ≤ 16 6���(�)�∈A + B ∗ �7
We choose to set the value r1 and l. Thus the value for Y is:
0 �� = 0.9� = 20B = 6 ∗ ($����������� ) − ��∑ ��(�)�∈A�
5.3.1.3.2 Cloudy/sunny/cloudy
$��� �������� = �� ���(�)/6�∈A + �) ���(�)/6�∈AI
Where U is the interval that contains the sunny values and JI is the interval that contains the cloudy
values.
We have the following conditions:
8 �� ≤ 1�) ���(�)�∈AI ≥�2�33!��(�)�∈AI
As before, this profile can be used only with expected energy that satisfies these conditions:
5� = 16 6�� ���(�)�∈A +�2�33!��(�)�∈AI 7 ≤ $����������� ≤ 16 6���(�)�∈A + �) ���(�)�∈AI 7
We choose to set the value r1. Thus the value for r2 is:
8 �� = 0.9�) =6 ∗ ($����������� ) − ��∑ ��(�)�∈A∑ ��(�)�∈AI
-51-
5.4 Solar generation parameters set up
Multiple combinations of parameters have been evaluated to set them up to their best value (see results
pp54-61).
For each combination of parameters, two analysis were done. The first one checks statistical parameters’
values. For the difference between the energy of the day created and the energy expected, it calculates
mean, median and bias over 30 days. The second one is a visual check: do the created days look like real
days? The appreciation is let to the user. The result is a mark out of 2 (see Table 12).
Mark Appreciation
0 Don’t look like real days
1 Might look like real days
2 Look like real days
Table 12 : Appreciations for solar generated profiles
To test multiple combinations of parameters, a special code was written. Its input is a matrix of
parameters and it generates 15 days for each combinations. For each combination days are plotted and the
median error, the mean error, and the error’s standard deviation are calculated.
If the irradiation of the day being generated is below the irradiation of the shape curve, probability of fall
inf and probability of return inf are used. On the contrary, if the irradiation of the day being generated is
above the irradiation of the shape curve, probability of fall sup and probability of return sup are used.
Parameters Type
Solar energy Interval
Fall interval, ∆ Interval
Fall factor, f Value
Probability of fall inf Value
Probability of return inf Value
Probability of fall sup Value
Probability of return sup Value
Table 13 : Parameters for the solar irradiance profile generation
-52-
5.5 Generation and computing code
According to the previous considerations, the generating code is an up-grading process: it computes 1sec
granularity values that are aggregated while 10min granularity values are get. It is divided into 3 steps:
create a 1minute mean value from sixty 1second values (1); create a 10min average value with ten 1minute
average (2); create a day with one hundred forty four 10minutes average values (3).
5.5.1 Create a 1minute mean value from sixty 1second values
60 times loop:
TEST: is the previous value equal to the clear sky value?
If YES:
Next value has the probability 1-Pfall to be equal to the clear sky value.
Else next value is calculated using a normal distribution with the fall interval and the fall
factor as parameters
If NO:
Next value has the probability Preturn to be equal to the clear sky value.
Else next value is calculated using a normal distribution with the fall interval and the fall
factor as parameters
It returns the average of the 60 values obtained.
The two plots below show every 1seconde value in a 1minute value. The red line is the clear sky value that
is considered steady during this small time period. It shows the two cases where it starts on the clear sky
value or not. The fall factor is equal to 0.5 and the fall interval is equal to 50W. These plots clearly show
that two states of irradiance value exist: the clear sky value and the “out of clear sky value”. Moreover the
correlation between two following values is depicted: there is a trend that the next value will be around the
previous value. Exactly, in this case, the probability that the next value will be around the previous one is
90%.
Graph 31: Examples of 1sec granularity profiles
-53-
5.5.2 Create a 10min average value with ten 1minute average
Calculate the average of ten 1minute averages.
Note: it is important to create two different functions for 1minute mean and 10minutes mean because the
Clear Sky profile has a 1minute temporal resolution. Each time this function call the first function, it gives
a new Clear Sky value as input.
5.5.3 Create a day with one hundred forty four 10minutes average
values
For a given value of energy expected, it generates a shape curve.
144 times loop:
Calculate the energy of the part of the day created.
Calculate the energy of the part of the shape function.
TEST: Does the part of the day created have a larger energy than the shape function?
If YES
Pfall gets the value Pfall_sup and Preturn gets the value Preturn_sup
If NO
Pfall gets the value Pfall_inf and Preturn gets the value Preturn_inf
Note: Pfall_inf and Pfall_sup and Preturn_inf and Preturn_sup are linked with the following relations:
KL-MM_�OL < KL-MM_QRS
KTUVRTO_QRS < KTUVRTO_�OL
5.6 Results and final set up
More than 200 combinations was processed. Here are the main features obtained:
• Probabilities strongly control the shape of the day: larger the probability longer the phases of the day. With high probabilities (larger than 1%), the day can be divided into several phases (sunny or cloudy). With small probabilities (smaller than 1%) the day is very intermittent.
• Fall interval is used to control the deviation. Larger the interval, more intermittent the day.
• The fall factor does not have influence on the daily profile. It is always set up to 10%.
Next pages sum up results obtained. For each type of days, parameters have been set up to default values.
These values are presented and few day profiles are shown.
Clear sky time series are also drawn in black. Generated irradiance time series are potted in red.
0200
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Examples of Cloudy/Sunny/Cloudy
-62-
5.7 Conclusion
The generation of solar irradiance time series is strongly based on the clear sky profile. It exists two main
state during the generation: to be on the clear sky or to be below the clear sky. Alternations between these
two states with a 1Hz frequency give profiles with a similar shape than measured time series (see the two
plots below that are not supposed to be similar but only have the same shape in the alternations of clear
sky value and non-clear sky values). In order to obtain the expected daily irradiation, alternation between
these two states are guided by two distributions of probabilities. Finally, it is possible to obtain different
types of days using different objective shapes.
Graph 32 : Typical days generated
Graph 33 : Typical days measured
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6 Forecasting
6.1 Introduction
Renewable energy power plants are essential to see a sustainable electrical system in the 21st century. First
because electricity is nowadays a primary resource and second because we cannot produce electricity from
fossil fuels anymore without strongly distort the earth's climate. However, these energies are intermittent
and thus it is impossible to totally rely on them. Storage medium are part of the solution but they also
have their drawbacks: large costs and important carbon footprint. The best solution would be to know
exactly when energy from sun or wind is available. Knowing the electricity generation from renewable
energy power plants in advance influences the way power plants of the whole mix are managed. For this
purpose, power plant operators and grid operators buy forecasts from specialized companies.
When sizing new power plants, it is essential to analyze the forecast’s accuracy. First to know if it will be
useful and, in case of a positive answer, to evaluate its influence over the management of the power plant.
This part explains how it is possible to generate forecast data. It is important to notice that the forecast
generation presented in this document is absolutely not related to the forecast generation done by
specialized companies called forecasters. The work done by forecasters is quickly described here. It used
large physical models and statistic post-processing to generate weather forecast for the next hour to the
next weeks.
The work presented in the following parts 7 and 8 aim to generate forecasts for the special use of the
sizing of power plants. Wind speed and irradiance time series are first generated using methods explained
in the previous two parts 4 and 5. These time series are inputs of Akomis, the Akuo’s model briefly
described in the introduction. They are also used to generate forecasts time series which are another input
of Akomis. Methods used for forecasts generation does not use neither physical model nor statistical post
processing with historical data. It only consists of applying an error onto the wind speed or irradiance time
series.
To give the reader an overview of the forecast sector, forecasting methods used by specialized companies
are presented first. Then, analysis of historical forecast data is explained. Results from the latter part are
used to generate forecasts. Methods and results from are both detailed.
6.2 Forecasting methods
Diverse resources are used to generate solar and wind forecasts. The physical prediction is mainly based
on Numerical weather prediction (NWP). Then satellite imagery might be used as well as observations
from on-site devices (H.M. Diagne, 2012) (IEA, 2013).
Every forecasting company develops its own combination of these inputs. Results are corrected using
statistical models.
The usefulness of each resource depends on the location studied and the forecast horizon considered.
Five types of forecasts are studied: very short term forecast (to 1 hour ahead), short‐term forecasts (to 6
hours ahead), day ahead forecast, long term forecast (to weeks ahead) and very long term forecast (to
months ahead). The first three are used to monitor power plants and sell and buy on market places. The
last two are used to plan maintenance.
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6.2.1 Physical Models: NWP models and MOS Correction
NWP models use the physical equations of the atmosphere to generate global weather prediction. They
have a very large number of outputs describing the weather of a wide area in 3 dimensions. They are very
computational resource intensive and thus they are developed by national or international centers. The
most used are from the NOAA (US National Oceanic and Atmospheric Administration) and the ECMWF
(European Center for Medium range Weather Forecasts). Their forecast horizon is around 10 days with a
spatial resolution between 2 and 50 km and a temporal resolution larger than or equal to 1 hour. They are
updated twice to four times a day.
NWP models are essential for forecast horizons beyond six hours. NWP have error patterns that are
corrected using MOS (Model Output Statistics) technics. Observed weather elements are compared to
NWP outputs using statistical approach. MOS correction reduces especially NWP inherent bias.
6.2.2 Satellite imagery
Images from geostationary satellites are used to predict weather up to few hours ahead. Clouds reflect
light into the satellite leading to detection and the ability to calculate the cloud optical depth i.e. the
amount of light transmitted through the cloud. Using two consecutive images, a motion vector is then
applied to each cloud. It gives its direction and velocity. Assuming the persistence in the opacity, direction
and velocity, satellite image analysis give forecasts up to 5 hours ahead.
The accuracy of this method depends on the location. Indeed it predicts only cloud movement and not
the cloud formation. Satellite imagery is not used in regions of world with a lot of convective phenomena
like mountainous islands.
GOES and MTSAT from the US agency NOAA and Meteosat (MSG and MFG) from the EU agency
EUMETSAT are the most two used programs. Each one has several satellite. As shown in figure 8, it is
necessary to use at least 5 satellites to cover the entire world with a good resolution.
Figure 8 : Satellites placements
6.2.3 Devices on-site
It is important to compare macro data with on-site measurements. This can be done live to correct the
next forecast or a posteriori to correct model outputs for a specific location.
For wind forecast, it is possible to use the anemometer put on the hub. However it measures wind after
the blades so important corrections has to be applied to obtain a reliable average. A mast might be put on-
site at least at 80% of the hub height. Wind speed values are mainly used for post-processing.
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For solar forecast, camera might be used. As the satellite imagery, images from a camera installed on the
ground are processed to obtain a cloud cover and a cloud optical depth. Irradiance is predicted for the
current cloud shadow and then the cloud shadow is moved forward in time based on cloud velocity and
direction. Fisheye cameras detect clouds within a 5km radius. It implies a very short forecast horizon (up
to 30min). Today, the use of on-site camera is very limited but it is growing fast thanks to prototypes
developed by several private companies.
6.2.4 Statistical Models
Statistical models consist in finding a relationship between the inputs and the outputs data which allows to
predict the future time step. The underlying assumption is that future irradiation can be predicted by
training the algorithms with historical patterns. Several statistical models have been developed for the last
10 years. The simplest stochastic learning technique is the persistence forecast which is based on current
or recent measurement and extrapolated to account for changing sun angles. It is worthwhile to
implement and run a more complex statistic model only if it is able to clearly outperform the persistence
model.
Learning algorithms used for irradiance forecasting include pattern recognition methods (k-nearest
neighbors, Artificial Neural Network), regression methods (AutoRegressive Moving Average,
AutoRegressive Integrated moving Average) and more recently algorithms using a Master Optimization
Process.
Inclusion of data from sky imagery, satellite imagery and NWP can significantly increase accuracy and
forecasting skill (M. Journée, 2010). More than the inputs, it is the ability to set up MOS and statistical
models and to combine the different inputs that allow one forecaster to be better than another.
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6.3 Metrics used for solar irradiance forecasting error
Three metrics are mainly used to evaluate the forecast error: the RMSE (Root Mean Square Error), the
MAE (Mean Average Error) and the Bias. They are obtained with the following formulae:
���� =�1�( �������� − ��������)�����
� � =�| �������� − ��������|����
"#$% = �( �������� − ��������)����
Notice that these indicators can be calculated over different time period: θforecast can be the signal
measured over 1sec, 1min, 10min etc.
These indicators are only the most used. As explained in the Annex 1, it is important to design indicators
for every special needs.
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7 Wind speed forecasting
Wind speed forecast are widely used for wind farms. Long term forecasts are important for maintenance
planning as well as short term and very short term forecasts are used for production forecasts and to take
decision on energy markets. In this document, two types of forecasts are considered: Day Ahead forecasts
and up to 7 days forecasts.
Akuo are already using forecasts to plan maintenance and a project of wind turbine associated with battery
is developed. Studies have already been done to assess forecast errors. It exists two different types of
errors, temporal gaps and quantitative gaps. The first exists because forecasters do not know exactly when
wind speed changes occurs. The second exists because they do not know exactly which the wind speed
value are over the time. Smaller the timestamp, more important are these errors.
7.1 Basis
Wind speed forecasts are generated from hourly profiles as used for wind speed time series. This time, it is
not relevant to consider a very small timescale: hourly forecasts are the main used because they are the
best trade-off between accuracy and current needs. Thus temporal errors and quantitative errors are
implement directly on hourly values from satellite data.
7.2 Temporal errors
The first temporal error is implemented on every value of the daily forecast. It expresses a global temporal
bias. For the day ahead forecast, this gap is calculated thank to a normal distribution with the following
parameters:
- Expectation: 0
- Standard deviation: 0.5hour (i.e. 30minutes)
For the next day the daily bias is calculated with another normal distribution with following parameters:
- Expectation: bias of the previous day
- Standard deviation: 0.5hour
The image 31 shows this deviation:
Graph 34: Daily temporal deviation
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Then another temporal deviation is added to each hourly value. Its value calculated thanks to a normal
distribution with the following parameters:
- Expectation: 0
- Standard deviation: 0.2hour (i.e. 12 minutes).
The image 32 shows the previous two deviations:
7.3 Quantitative errors
The most important deviation is still missing: does the forecaster forecast the good wind speed value? A
quantitative deviation is added to each hourly value. It has the following parameters:
- Expectation: 0
- Standard deviation: 0.1m/s
Graph 35 : Daily and hourly temporal deviations
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Then a moving average on 5hours is added to smooth the output. The graph 36 shows the final forecast
and the real data:
7.4 Results and comparison
This model of forecast was applied on one year of hourly values. RMSE was calculated for different
parameters. The table 14 below shows the average results (10 calculations were done for each set of
parameters).
Quantitative sd 0.05 0.1 0.15 0.2 0.5 1 1.5 2 10
Temporal sd
1 – 0.75 2.18 2.17 2.13 2.17 2.16 2.17 2.27 2.36 4.97
1 – 0.5 1.81 1.76 1.81 1.78 1.82 1.95 1.77 1.90 4.85
0.5 – 0.1 0.92 0.89 0.89 1.05 0.81 1.04 1.06 1.20 4.58
0.2 – 0.1 0.79 0.82 0.69 0.75 0.87 1.02 4.55 4.56 4.55
Table 14 : RMSE for wind speed for different set of errors
RMSE result has the same unit as the input: m/s. It appears that the quantitative parameter has not a
significant impact if it is between 0.05m/s and 2m/s. Larger deviation were not considered than 2m/s
because typical wind speed are around 10m/s. Smaller the temporal deviations, smaller the RMSE.
The important result of this study is that it is possible to obtain very different error with the parameters
selected. According to a given location, it will be possible to set the parameter in order to generate
forecasts with the expected error. Moreover, it will be possible to test forecasts with different errors very
easily by changing these three parameters.
Graph 36 : Wind speed forecast
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Research studies calculate RMSE of forecast models only in kW: they compare the wind farm power
forecasted to the wind farm power measured. A last study was done to evaluate RMSE in power. The
wind turbine used has a rate power of 3.3kW. Its power curve is plotted below.
RMSE calculated with turbine power output with 10 different forecasts. Results are in the table 15.
Parameters:
Temp1 – Temp2 -
Quant
Wind speed RMSE
[m/s] Power RMSE [kW] Ratio
1-0.5-1 1.62 0.68 2.37
1.05.1 1.67 0.69 2.40
0.5-0.1-0.2 1.02 0.49 2.08
0.5-0.1-0.2 1.18 0.55 2.13
0.2-0.1-0.5 0.61 0.33 1.86
1-0.75-0.2 2.25 0.92 2.46
1-0.75-0.2 2.13 0.89 2.40
1-0.5-1 1.89 0.76 2.49
1-0.5-1 1.66 0.71 2.34
0.5-0.1-0.1 0.72 0.37 1.97 Table 15 : RMSE for wind power with different set of errors
As the scatter plot shows (Graph 38), there is a linear relation between wind speed error and power error
with an average ratio of 2.24 (this ratio strongly depends on the turbine). It is possible to obtain average
error for power forecasts in a region. This value will be in kW. Using the power curve of the wind turbine
used for the project, the regression between wind speed RMSE and power RMSE is calculated. The
expected error can be transpose from kW to m/s. Finally, forecast model parameters are set up to obtain
the expected error.
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15 20 25 30
Po
wer
[W
]
Wind speed [m/s]
Graph 37 : Power curve
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Graph 38 : Wind speed RMSE versus Power RMSE
7.5 Conclusion
Wind speed forecast generation is based on three different errors. Two are temporal, a daily one and an
hourly one and one is quantitative. They can be easily adjusted to obtain the error expected. Thanks to a
linear relation between power error and wind speed error, the switch from one to another is also easy in
case of the expected error is given as a power. Last, it is possible to analyze how the power plant reacts to
an increasing forecast error (temporal, quantitative or both) by generating years of forecast very easily.
y = 0.3519x + 0.1205R² = 0.995
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.00 0.50 1.00 1.50 2.00 2.50
Po
wer
RM
SE
[kW
]
Wind speed RMSE [m/s]
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8 Irradiance forecasting
As for the profile generation, it is first important to characterize the forecast before generating it. Part of
my work at Akuo was dedicated to the solar forecast analysis. Because of the more and more important
use of solar power plants with storage and constrains from the grid, a special look has to be given to the
forecast. A benchmark was done and more than 20 companies were asked to explain their forecasting
services. Then a trial period was set up with half of them for 4 locations where Akuo already operates a
solar power plant. It included forecasters Akuo already has a contract with. After one month, a short list
of 4 forecasters was drawn and after three months, 2 companies were chosen and a contract was signed
with each of them. From this work a large database of forecasts is available. It is used to evaluate forecast
accuracy and obtain trends for the forecast generation. Annex 1 introduces this work.
8.1 Pre analysis
First of all, during the two months of the trial, numerous of irradiance forecasts were seen. It leads to two
qualitative remarks:
- Forecasters are not able to forecast precisely the irradiance over a day even one hour ahead
- The main action of the forecasters involves the adjustment of the clear sky irradiance curve
- Intra-day forecast is not better than day ahead forecast
Database used for this analysis includes all day ahead forecasts sent to Akuo during the second month of
the trial (so only with the best four companies) for the 4 locations. There are compared with measures
made on-site.
The comparison is the difference between the total energy forecasted for a day and the energy measured
for the same day.
Every day is classified into 10 bins according to its energy compared to the clear sky energy (from 0%-
10% to 90%-100%).
As the graph 39 shows, the deviation strongly depends on the type of day. Clearer the day, smaller the
deviation (it even becomes negative). There is no inherent bias in the forecasts. Moreover, for each bin,
the interval where the deviations are included has a constant length (expect for 30% of clear sky but there
is not enough value to conclude).
-180
-130
-80
-30
20
70
120
170
220
-4
-3
-2
-1
0
1
2
3
4
5
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Num
ber
of
occ
urr
ence
s
Dev
iati
on
[kW
h]
BinsNote: each black point is a deviation and red histogram shows the number of values considered for each bin
Graph 39: Deviations as a function of the Clear sky percentage
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Bins Mean Standard deviation
0.1 2.02 1.44
0.2 2.04 1.07
0.3 2.40 0.50
0.4 1.73 1.04
0.5 1.45 0.96
0.6 0.90 0.84
0.7 0.40 0.78
0.8 -0.07 0.75
0.9 -0.55 0.72
1 -0.77 0.59
Table 16 : Deviations as a function of the Clear sky percentage
The table 16 bears out the observation made on the graph 39. The mean decreases as the standard
deviation is steady. It seems forecasters always forecast between 70% and 80% of the clear sky daily
irradiation. The deviation is positive if the day has less energy than 80% of the clear sky and the deviation
is negative if the day has more than 80% of the clear sky.
Indeed, on average, 77% of the clear sky daily irradiation is forecasted with a mean deviation under 10%
whereas on average 73% of the clear sky daily irradiation was measured with a mean deviation of 18%.
According to the type of day, the forecast error will be positive or negative. Because there are more sunny
days than cloudy days (especially where solar power plants are built), the final bias of the forecasting error
is negative.
8.2 Generation
The general idea is that forecasters know the global trend of a day one day ahead. Moreover, they can even
know the shape of the day: will it be sunnier on the morning or on the afternoon? Nevertheless, they do
not know faithfully how much time will last a specific sunny time or a specific cloudy time.
From the day generated, the daily energy is calculated and it is compared with the clear sky irradiation over
the same day of the year. According to the percentage of Clear sky calculated (the clear sky index), an
error is generated.
Then, the day profile is completely converted into a “percentage of clear sky over the time” profile or a
clear sky index profile (example Graph 40). Please notice than the vertical scale is the clear sky index:
when the profile has a clear sky index equal to 1, it is equal to the clear sky. During the night, the clear sky
value is zero as the profile value so the clear sky index is always equal to 1. In the example below, the
sunrise is at 5:40 and the sunset at 19:10.
The daily part of the profile (from the first value where the clear sky value is different from 0 to the last
one) is divided into N parts. N represents the accuracy of the model: larger N, more accurate is the model
because intervals are smaller and small changes can be detected (see Graph 41).
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Graph 40 : A day of clear Sky index
Graph 41 : Examples of forecast shapes
Two errors are put on this profile. First, it is a temporal error because the duration of each part is
changed. If the clear sky index generated has an error2 superior than the one expected, parts with a high
index are shortened and parts with a small index are lengthened. In other words, sunny parts are
shortened and cloudy parts are lengthened. It might even lead to the removal of a part.
In the example below, the error of the first index generated was 1.7% (every error is a percentage of the
energy of the clear sky profile) with N=4 whereas the expected error is 24.6%. Parts with larger indexes
2 Here, error is the difference between the daily energy of the forecast and the daily energy of the real profile.
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are lengthened and part with smaller indexes are shortened in order to increase the error. This process
stops when the error generated is included in +/- 10%. In this example, the error after temporal changes
is 14.7%. The Graph 42 shows the result on a clear sky index scale.
Second, every index is changed to reach the error expected +/- 1%. It is the same logic than before: if the
clear sky index generated has an error superior than the one expected, every part is lowered. On the
contrary, if the clear sky index generated has an error inferior than the one expected, every part is raised.
In other words, it gets sunnier or cloudier. The index max is 1 and the index min is 0.1.
In the example below, every parts of the profiles are raised to reach a final error of 24.0%. The Graph 43
shows the result on a clear sky index scale.
From these processing, a forecast profile is obtained. It consists of several clear sky indexes with a
duration for each of them (Graph 43). Then, clear sky indexes are transposed to irradiances using the clear
sky values (Graph 44).
Graph 42 : Temporal error
Graph 43 : Power error
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In the example below, the different parts of the day are clearly represented. At the very beginning of the
day and at the end of the day, the sky is clear whereas it is partly cloudy during the day. However clear sky
parts are larger in the forecast than in the real profile because of the high error expected. In the same way,
cloudy parts have an higher index in the forecast than in the real profile.
Graph 44 : Solar irradiance forecast profile
It is important to note that this process cannot be used for the sunrise and the sunset values. Indeed,
variation in the CS index are too much important. Thus clear sky values are used for the sunrise and the
sunset.
Another methodology was developed to generate forecast profiles. It involves the detection of large
variations of clear sky indexes. In this process, separations between each parts that divide the day are get
from the detection of a large variation of the clear sky index. This method was not as accurate as the one
developed previously in this document.
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8.3 Conclusion
Thanks to a large database of forecasts, an analysis was done to assess the forecast accuracy. Then, day
were processed one by one in order to produce a forecast with a given error. First the day is divided into
N parts – N is a parameter that represents the frequency of changes the forecaster can detect. Each part
of the day has an average irradiance and then, two errors are applied. The first is a temporal error that
changes the length of the part. The second is a quantitative error that changes the irradiance value. This
method has very reliable results because the daily error of the forecast generated is equal to the error
expected +/- 1% and the error expected come from large database of forecasts.
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9 Conclusion
The work presented in this document describes current methods used for renewable energy resource
assessment. The output of these methods is a yearly amount of energy available. This value is enough if
there is neither storage nor action taken for grid balancing. Otherwise, it is necessary to have time series of
the resources: wind speed and solar irradiance. Thus, methods have been developed to generate these time
series using measurements available. It is possible to create profile with the expected averages and a shape
very similar to on-site measurements’ shape. Last, these profiles have been modified in order to create
other time series taken as forecast time series. Temporal and quantitative errors were applied and thanks
to a preliminary study of the current forecast accuracy, it is possible to achieve forecast with the expected
deviation.
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Annex 1: Results Irradiance forecasting benchmark
This analysis identifies the most accurate forecast related to Akuo’s special needs: hybrid solar plants with
storage. A special attention is dedicated to the improvement of the Intra-Day forecast. This paper explains
the methodology and it reports the results.
Phase 1: Forecast qualification form
The first step of the forecast analysis was a benchmark of more than 20 companies. They received a
forecast qualification form to fulfill. It contained the following parts:
- Company information (revenues, number of employees, income distribution)
- Historical (does the company already deliver Day Ahead/Intra day forecast, in which area…)
- Data sources (NWP, satellite imagery, statistical models)
- Cost estimations (for a trial period and for operation)
Thirteen companies fulfilled the form. The global idea was to test every model or combination of models
available. Three companies were removed because they sent us back only costs without explanation of
their model. A fourth was removed because of its lack of experience and the very common models it uses.
Forecaster NWP Satellite Imagery
Forecaster1 WRF (Hirlam, GFS) Meteosat, GOES
Forecaster2 GFS, CMC Meteosat
Forecaster3 ECMWF, GFS
Forecaster4 ECMWF, GFS, AROME, ARPEGE
Forecaster5 NEMS-G, NEMS4, NEMS12, NMM-SA01 Meteosat, GOES
Forecaster6 GFS, ICON
Forecaster7 GFS
Forecaster8 IFS, GFS Meteosat
Forecaster9 ARW 3.6 Meteosat, GOES
Forecaster1 and Forecaster5 were taken for the trial period first because there were Akuo’s actual
providers. A VB script was written to convert their file into the format asked for the trial. Because
Forecaster5 data was not used at all for SiteR1 and SiteR2, there were not tested. Moreover, Forecaster5
do not provide intra-day forecasts. For all these reason, Forecaster5 is not shown in the results part.
Phase 2: Trial period
Specifications and preparation
The trial period had the following specifications:
• 4 sites: Olmo1 (called SiteC), Bardzour (SiteR1), Les Cèdres (SiteR2), Sainte Marguerite (SiteG)
They were chosen because their location is close to the sites proposed of the AO CRE ZNI II
Call for tenders and because they have historical GHI data.
• Forecasts for Global Horizontal Irradiance and Temperature
• 1 Day ahead forecast per day sent at 15:30 local time
• 24 Intraday forecasts per day sent every hour HH:30
• Granularity: 10min average
• The timestamp indicates the beginning of the forecast
• Example: The GHI value in front of 10:50 is the forecast from 10:50 to 11:00.
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Historical data were sent to the forecasters. It is very important to check and correct data before sending
them to the forecaster. The methodology to check data is as follow:
• Clear the timestamp: check if there are 144 values per day (except day with daylight saving time
changes)
• Check local time/GHI: at which time start every day?
• Compare measurements with clear sky profile from PVSYST (it might be useful to correct the
PVSYST profile).
A routine with measurement from each sites was computed (Visual basic request on the ICONICS or
SQL databases, scheduled task on Windows, and FTP transfert with Syncback Pro).
Process
Nine forecasters were tested during one month. According to their result, only four of them were tested
another month. The next part present results for both months.
Numerous forecasters were not able to send us every forecast on time. To detect a problem, a daily check
was done to ensure every forecast was sent the day before. Missing forecasts, reactivity and availability of
the forecaster service were taken into account in the evaluation.
Metrics
First, the forecast accuracy was evaluated with usual metrics: RMSE, MAE and bias for every 10 minutes
point. However, these indicators are not relevant because the storage is able to cope with short period
errors. Thus we have considered RMSE for the difference between the energy forecasted and the energy
measured on site for the entire day. To identify a trend between the Day Ahead and the Intra-Day, the
same indicators has been applied to the Intra-Day forecast sent at 3:30. Moreover, box plots were drawn
for the Day ahead forecast, and intra-day forecasts sent at 3:30, 9:30 and 13:30 (which are the intra-day
forecasts we will use for the AO CRE ZNI II).
In addition, battery state of charge has been simulated based on forecasted solar power production: the
production planned is the one the forecaster gives. Batteries are used to compensate gaps between
forecasted power and in live power production (plot 1).
Plot 1: State of charge for one day
-600
-400
-200
0
200
400
600
800
1000
En
ergy
[W
h]
Measured [W] Forecast [W] Battery charge max min
Battery size for this day
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On the provided example:
• At the very beginning of the day: forecasted irradiance is below measured irradiance,
consequently, batteries are charging energy.
• Then forecasted irradiance is mainly below measured irradiance, consequently batteries are
discharging energy.
For the considered period, difference between max of charge and min of charge is calculated on a daily
basis. It provides an optimized battery sizing for every single day.
Battery max sizing, mean and bias calculated over the benchmark period were reported. For the previous
example, the battery sizing is 0.5kWh battery sizing with a bias of -0.2kWh.
Last indicators are sum of improvements and sum of step backwards between the Day Ahead and the
Intra-day forecasts: does the forecaster reduces the error between day ahead forecast and intra-day
forecast? For both forecasts, difference between forecasted energy and measured energy is calculated
following the below formulae:
Sumofimprovements = � (|�34 − ����5|−|�63 − ����5|)7���������58��
Case in which the energy in the Intra–Day is closer to the energy measured than the energy in the Day Ahead
Sumofstepbackwards = � (|�34 − ����5|−|�63 − ����5|)?�@�������58��
Case in which the energy in the Intra–Day is further from the energy measured than the energy in the Day Ahead
• EDA: energy of the Day Ahead forecast
• EID: energy of the Intra-Day forecast
• Ereel: energy measured on site
The Intra-day forecast used is an aggregation of every Intra–Day forecasts: only values from H to H+1
from the Intra-Day forecast sent at H-30minutes have been considered.
The more improvement the better and the less step backwards the better.
Other tests
Detection of cloudy days
A forecasting error does not have the same impact is it underestimates or overestimates the irradiation of
the day: if the forecast underestimates the irradiation of the day, Akuo will announce less energy than the
power plants will get and the surplus is curtailed. In this case, the power plant earns less than it is possible.
However, if the forecast overestimates the irradiation of the day, Akuo will announce a larger production
than the power plant will be able to do. In this case, the power plant might lose money because of
penalties. These considerations show it is important the forecaster detects the cloudy days. A special
attention was given to these days and a mark over 5 was given. The mark is given according to three
points:
- Is the forecasted irradiation over the day close to the measured irradiation?
- Does the shape of the day forecasted look like the measured day?
- Does the intra-day forecast improve the previous result?
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Tables of results are given in the next part.
Mix of several forecasts
It came out that some set of forecasts (from one forecaster and for one location) have an inherent bias.
Average of forecasts with bias were also tested: the box plots present the results.
Today, this method does not appear as a solution. A further analysis need to be down to combine two
forecasts in the best way. The average reduces the bias only for one site between two forecasters. In other
cases, it only smooth the result.
Comparison with Meteo France forecast
Free day ahead forecast is available on Meteo France website. Its granularity is far smaller than the one
expected from specialized companies: the day is divided into 3 parts for La Réunion and Guadeloupe and
in 4 parts for Corsica. This test was done during one month and the results are mitigated because of the
very small sample of cloudy days available. It was impossible to say forecasters are really better than Meteo
France for cloudy day forecasting while MeteoFrance did not detect as well all bad weather times.
A further comparison could be done in a next analysis.
Comparison with an average day
Measurements from the month of September 2014 were used to generate an average day (its irradiation is
one 30th of the irradiation of the month September 2014). The metric Battery State was calculated with
this day as a forecast (and repeated every day of the month).
Results are included in the next part as a base for comparison.
Results
This part sums up results from the trial period.
RMSE for Day RMSE for Day Ahead and Intra-Day 3:30 forecasts on a day
basis
September
First results are RMSEs on a daily basis i.e. we took the total irradiation of the day in the following
formula:
���� = 1A�BCDD��� − CDDE���8���F�
SiteC SiteG
DA 3:30 DA 3:30
Forecaster1 1.142 1.058 4.419 5.308
Forecaster8 0.567 3.083
Forecaster2 1.636 1.168 2.711 2.683
Forecaster3 0.999 0.937 2.122 1.985
Forecaster4 0.735 0.649 2.400 1.845
Forecaster9 1.317 2.865
Forecaster6 1.172 1.031 1.879 1.873
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SiteR1 SiteR2
DA 3:30 DA 3:30
Forecaster1 1.233 1.347 2.342 2.108
Forecaster8 2.492 2.517
Forecaster2 1.104 0.942 1.642 1.338
Meteocontrol 0.896 0.767
Forecaster3 1.296 1.306 0.972 1.221
Forecaster4 0.982 0.951 1.061 0.865
Forecaster9 2.263 2.184
Forecaster6 1.766 1.715 1.494 1.401
Chart 1: RMSE for Day Ahead and Intra-Day 3:30 forecasts on a day basis for September
From these results and the box plots attached, Forecaster4 obtains the best results for SiteC and Site R1
and very good result for SiteG. Forecaster6 obtains the best result for SiteG with good results for the
other locations. Forecaster1 obtains the best result for SiteR2 with average results for the other locations.
Forecaster2 obtains good results for every site whereas Forecaster9 obtain bad results for every sites.
Forecaster8 and Meteocontrol obtains good results as well.
October
SiteC SiteG
DA 3:30 DA 3:30
Forecaster1 1.069 1.234 1.381 2.473
Forecaster3 0.838 0.713 1.336 1.328
Forecaster4 0.808 0.648 1.202 1.229
Forecaster6 1.007 0.915 1.087 1.083
SiteR1 SiteR2
DA 3:30 DA 3:30
Forecaster1 2.010 1.773 1.992 2.128
Forecaster3 1.658 1.658 1.497 1.497
Forecaster4 1.307 1.324 1.292 1.300
Forecaster6 1.693 1.714 1.324 1.158
Chart 2: RMSE for Day Ahead and Intra-Day 3:30 forecasts on a day basis for October
From these results and the box plots attached, Forecaster1 clearly obtains the worse results. Forecaster6
have still the best results for SiteG and Forecaster4 has the best results for the other three. Forecaster3
obtains good results.
-84-
Battery sizing based on Day Ahead forecasts
September
This indicator evaluates the ability of the company to forecast accurate irradiance profile.
SiteC SiteG
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Forecaster1 2.79 1.01 -0.22 5.79 1.75 0.15
Forecaster8 1.92 0.84 -0.12 5.79 1.32 -0.48
Forecaster2 3.69 1.09 -0.49 5.63 1.31 -0.17
Forecaster3 2.19 0.90 -0.22 4.37 1.08 -0.33
Forecaster4 2.19 0.91 -0.01 3.81 1.44 0.07
Forecaster9 2.77 1.11 -0.10 4.91 1.25 -0.14
Forecaster6 2.60 0.96 -0.29 4.10 1.10 0.04
Average day 2.35 1.20 NA 4.94 1.47 NA
SiteR1 SiteR2
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Forecaster1 2.33 1.16 -0.01 3.55 1.45 -0.31
Forecaster8 4.37 1.39 -0.44 4.77 1.32 -0.49
Forecaster2 2.95 1.18 0.10 4.19 1.21 -0.05
Forecaster3 3.06 1.13 -0.31 2.50 1.05 0.02
Forecaster4 2.78 1.08 -0.13 2.23 1.06 -0.02
Forecaster9 3.91 1.45 -0.48 3.46 1.22 -0.44
Forecaster6 2.75 1.27 -0.42 2.63 1.10 -0.11
Average day 4.51 1.37 NA 4.98 1.16 NA
Chart 3: Battery sizing based on Day Ahead forecasts for September
Best results are obtained by by Forecaster3 and Forecaster4. Forecaster1, Forecaster8, Forecaster2 and
Forecaster9 obtains the worse results.
-85-
October
SiteC SiteG
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Forecaster1 2.81 0.85 -0.04 2.76 1.33 0.07
Forecaster3 1.85 0.74 -0.11 2.86 1.13 -0.31
Forecaster4 1.90 0.71 -0.10 2.53 1.26 0.28
Forecaster6 2.35 0.87 -0.13 2.42 0.99 -0.18
SiteR1 SiteR2
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Max of battery size
[kWh]
Mean of battery size
[kWh]
Bias [kWh]
Forecaster1 4.93 1.84 -0.51 4.01 1.72 -0.72
Forecaster3 4.13 1.55 -0.30 3.85 1.35 -0.07
Forecaster4 2.69 1.33 -0.11 2.55 1.26 0.22
Forecaster6 2.95 1.65 -0.39 3.03 1.27 -0.04
Chart 4: Battery sizing based on Day Ahead forecasts for October
As for the first metric, Forecaster4 obtains the best results and Forecaster1 the worse. Forecaster6 is still
the best for SiteG and Forecaster3 obtains good results.
Comparison between Day – Ahead and Intra – Day forecasts
September
SiteC SiteG
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Forecaster1 11.0 2.1 11.6 7.3
Forecaster2 6.2 3.7 1.5 2.2
Forecaster3 6.8 2.5 3.6 2.5
Forecaster4 3.8 1.0 6.1 0.7
Forecaster6 3.1 6.1 7.4 6.7
SiteR1 SiteR2
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Forecaster1 12.6 8.7 6.5 5.4
Forecaster2 4.3 4.5 4.1 3.4
Forecaster3 1.7 2.6 4.9 3.4
Forecaster4 1.5 1.1 2.6 1.2
Forecaster6 7.5 1.9 11.6 2.1
Chart 5: Comparison between Day – Ahead and Intra – Day forecasts for September
-86-
This indicator shows how much it is difficult for forecasters to improve their forecast between one day
ahead and few hours ahead. Two different types of intra-day forecasts are distinguished: Forecaster1 and,
even less so, Forecaster6 change a lot their forecast: they obtain the larger improvements but also large
step backwards. Forecaster3 and Forecaster4 have a more conservative intra-day forecast.
For further analysis, comparison of day ahead and intra-day forecasts are plotted over the month. If there
is no change, the value is 0. If there is an improvement, the value is positive and if there is a step
backward, the value is negative. However a positive value means a good result only if the day ahead
forecast was already good. Thus, day ahead error and intra-day error are plotted as well: the first with
diamonds and the second with circles. An example is shown below.
October
SiteC SiteG
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Forecaster1 11.4 4.1 10.7 5.3
Forecaster3 7.0 3.3 4.5 3.4
Forecaster4 4.3 1.5 3.5 4.4
Forecaster6 11.4 3.7 3.6 3.0
SiteR1 SiteR2
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Sum of improvements
[kWh]
Sum of step backwards
[kWh]
Forecaster1 16.8 6.6 3.4 4.0
Forecaster3 5.2 2.8 6.3 2.8
Forecaster4 2.6 3.8 2.1 2.0
Forecaster6 19.2 2.2 11.9 2.5
Chart 6: Comparison between Day – Ahead and Intra – Day forecasts for October
The trend depicted for September is still valid for October. However, Forecaster6 has strongly improved
its intra-day forecast with large improvements and step backwards close to Forecaster3 and Forecaster4’s
step backwards.
-87-
Forecaster1
Forecaster2
Forecaster3
Forecaster4
Forecaster6
-88-
Detection of bad days
September
Site Date Forecaster1 Forecaster8 Forecaster2
SiteC 20150903 1 1 1
SiteC 20150911 1 1 1
SiteC 20150913 4 4 3
SiteC 20150914 5 2 1
SiteC 20150918 5 2 1
SiteC 20150919 4 3 1
SiteC 20150923 5 4 2
SiteC 20150928 2 2 1
SiteC 20150929 2 2 1
SiteC 20150930 3 2 2
SiteG 20150911 1 1 1
SiteG 20150912 2 1 1
SiteG 20150915 2 1 1
SiteG 20150930 5 1 1
Site Date Forecaster3 Forecaster4 Forecaster9 Forecaster6
SiteC 20150903 2 NA 1 1
SiteC 20150911 1 3 1 1
SiteC 20150913 5 4 1 3
SiteC 20150914 2 3 1 1
SiteC 20150918 2 3 1 1
SiteC 20150919 5 4 2 2
SiteC 20150923 3 3 4 1
SiteC 20150928 2 1 2 1
SiteC 20150929 2 2 1 1
SiteC 20150930 4 5 5 1
SiteG 20150911 1 2 2 1
SiteG 20150912 1 1 1 1
SiteG 20150915 2 4 1 1
SiteG 20150930 1 2 1 1
Site Date Forecaster1 Forecaster8 Forecaster2
SiteR1 20150903 4 1 2
SiteR1 20150904 4 2 2
SiteR1 20150913 4 1 3
SiteR1 20150916 3 3 1
SiteR1 20150926 2 1 4
SiteR1 20150929 2 1 2
SiteR1 20150930 4 1 1
-89-
SiteR2 20150913 4 1 2
SiteR2 20150915 2 1 1
SiteR2 20150917 1 1 1
SiteR2 20150929 2 2 3
Site Date Forecaster3 Forecaster4 Forecaster9 Forecaster6
SiteR1 20150903 1 NA 1 1
SiteR1 20150904 3 NA 1 2
SiteR1 20150913 1 2 1 2
SiteR1 20150916 3 2 1 1
SiteR1 20150926 2 4 2 1
SiteR1 20150929 1 3 2 1
SiteR1 20150930 1 4 1 2
SiteR2 20150913 3 4 4 2
SiteR2 20150915 3 1 1 1
SiteR2 20150917 3 2 1 1
SiteR2 20150929 3 4 2 2 Chart 7: Bad days detection for September
Forecaster1 and Forecaster4 obtain the best result in the detection of bad days. Forecaster3 has the third
rank. Others and especially Forecaster6 and Forecaster2 have very bad results.
October
Site Date Forecaster1 Forecaster3 Forecaster4 Forecaster6
SiteC 20151001 4 3 4 1
SiteC 20151010 1 4 3 3
SiteC 20151014 3 4 1 2
SiteC 20151020 1 3 2 4
SiteC 20151026 4 2 3 1
SiteG 20151002 2 1 3 1
SiteG 20151017 3 2 5 2
SiteG 20151031 1 2 1 3
SiteR1 20151002 1 1 3 1
SiteR1 20151003 2 1 3 2
SiteR1 20151023 2 2 2 2
SiteR1 20151027 1 2 2 2
SiteR1 20151028 3 2 3 2
SiteR2 20151003 1 1 3 2 Chart 8: Bad days detection for October
Even if its results is not perfect, Forecaster4 is the one that detects bad days on a regular and frequent
basis. Forecaster1 has as many good results as bad results and Forecaster6 strongly detect one bad day.
-90-
Results – conclusion
For the month of September, Forecaster4, Forecaster3 and Forecaster6 obtain the best results.
Forecasters that did not provide intra-day forecasts are strongly penalized and thus Forecaster8 is not
taken for the next month. Forecaster1 and Forecaster2 obtain average results. Because Forecaster1 is our
current provider, it is taken for the next month unlike Forecaster2. Last, Forecaster9 obtains the worse
results.
Results for October strongly shows that Forecaster1 provide less accurate forecasts than Forecaster3,
Forecaster4 and Forecaster6. Between the last three, results are very close. A cost estimate was asked for
the three. Here are the final costs after negotiations (prices for GHI, GTI, Temperature and Power):
- Forecaster3: 2 300€/site/year
- Forecaster4: 4 600€/site/year
- Forecaster6: >40 000€/site/year
Obviously, Forecaster6 was removed and a contract was signed with Forecaster3. Because Forecaster4 has
many trouble in data providing, a special point was insert to its contracts before
Conclusion
Important differences has been shown in forecasting accuracy between the companies.
First, numerous forecasters are not yet able to provide intra-day forecasts. Moreover, even if intra-day
forecast is available it is not very reliable: as many improvements as step backwards are seen between day
ahead and intra day forecasts.
Second, NWP models used do not seem to significantly influence the forecast accuracy: Forecaster4 uses
very specific model AROME while Forecaster3 uses only free models from NOAA and ECMWF and
Forecaster4 outperforms very slightly Forecaster3. It seems the internal resources to process
measurements (historical and in live) and the ability to set up internal statistical models are more
important than the input used.
This study clearly shows that it exists better forecasts supplier than the ones Akuo Energy works with.
Nevertheless, the trial lasts only two months that is not enough to surely assess forecasters. Forecaster3
and Forecaster4 will provide forecasts for Olmo1, Bardzour and Les Cèdres at the same time as
Forecaster1 during the next year.
-91-
Annex 2: Calibration of satellite data with ground
measurements
First considerations
Comparison needs high-quality ground measurements. This means first class or secondary standard
pyranometers according to the ISO 9060 classification and regular maintenance (research centers clean
their pyranometers every day or every week).
Then, ground measurements should be available for a period of at least one year, so that all seasons are
included. In case of a tight time schedule, a shorter period may be considered for on-site measurements
(half of year, several months), however such data may not be capable to cover all deviations.
Remove implausible ground measurements
Removing the implausible values is the first step of the calibration. It may be the most important one.
First of all, it is important to check the timestamp. It has to be regular. This might be done with a pivot
table that counts the number of values per day (or month).
Then, a visual check helps to remove irrelevant values such as steady values or ramp.
Filtering with solar angle (available in PVSYST), it is important to force all night values to zero.
Finally, it is compared with a clear sky profile. We advise to take the MACC – Clear model. It is a dynamic
model with atmospheric values (ozone, aerosols, water vapor…) from ECMWF.
Comparison and calibration for daily values
Ground measurements versus satellite data are plotted in a scatter plot in order to see bias (Scatter plot 1).
The calibration model is a linear combination of the Clearness Index Kt.
G� = HICJ4KKLM43HIC�8�����E
G���5������� = $ ∗ G�� O P ∗ G� O Q
-92-
The Clearness Index Kt is defined as the ratio of the horizontal global irradiance to the corresponding
irradiance available out of the atmosphere (i.e. the extraterrestrial irradiance multiplied by the sinus of the
sun height). The extraterrestrial irradiance is the Solar constant (1367 W/m²) corrected by a yearly sinus
function of amplitude 3.3% accounting for earth orbit ellipticity. It is available in PVSYST.
The optimization minimizes the absolute differences between the measured Kt and the calibrated Kt.
This method was used for Bardzour data calibration (Bardzour is power plants in La Réunion owned by
Akuo). MACC-RAD dataset is used (available for free on soda website). Data have been available since 7th
May 2015. Seven days were removed due to irrelevant data. Then a first comparison of MACC-RAD data
and measurements give the scatter plot 1. It clearly appears MACC-RAD has a positive bias: 11.5%.
Using the calibration explained before, we obtained the following coefficients:
• a = 0.7650
• b = 0.0091
• c = 0.2139
We finally obtained the scatter plot 2. The bias of the MACC-RAD data calibrated have a bias of 1.1%.
1000
2000
3000
4000
5000
6000
7000
8000
9000
1000 2000 3000 4000 5000 6000 7000 8000 9000
MA
CC
-RA
D I
rrad
iati
on
[W
h/
m²]
Measured Irradiation [Wh/m²]
Scatter plot 1: MACC-RAD versus Measurements
-93-
This calibration was validated checking the distribution of days (Distribution 1). MACC – RAD data set
overestimates the number of sunny days (with Clear Sky indexes in the bins 90% and 100%) whereas it
underestimates the number of cloudy days (with Clear Sky indexes below 60%). The graph below shows
the correction applied: points with small clear sky index and points with large clear sky index keep the
same Kt while other points have their Kt reduced.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 2000 4000 6000 8000 10000
MA
C C
-R
AD
Irr
adia
tio
n c
alib
rate
d [
W/
m²]
Measured irradiation [W/m²]
Scatter plot 2: MACC - RAD calibrated versus Measurements
0%
5%
10%
15%
20%
25%
30%
35%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120%
% o
f o
ccurr
ence
s
Bins - type of days with clear sky index
Distribution 1: Types of days
Measurements MACC - RAD MACC - RAD corrected
-94-
Calibration of sub daily profile
Once the daily irradiation has been calibrated, it is important to obtain sub daily profiles. It consists of
changing part of MACC-RAD irradiation profile with a timestamp of 15min. Please notice that 1min
profile from MACC-RAD model are only regression of the 15min profile because Meteosat provides data
every 15minutes.
First analysis
First we analyze measurements to reveal trend in intraday profiles. In the case of Bardzour, it clearly
appears that mornings are sunnier than afternoons. The graph below plots the average clear sky index for
each time during the day.
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2
Kt
valu
es
Kt values
Correction applied
Kt calibrated
Kt
40%
50%
60%
70%
80%
90%
100%
02:52:48 04:04:48 05:16:48 06:28:48 07:40:48 08:52:48 10:04:48 11:16:48 12:28:48 13:40:48
CS I
nd
ex
Time (UTC)
Evolution of the Clear Sky index
-95-
Raising the profile
In cases in which energy has to be added, there is two options according to the daily clear sky index.
If the clear sky index is higher than 40%, morning irradiance values are set to the clear sky values while the
energy of the day is below the energy expected. Last, a post processing is done: the last value modified
(which has the clear sky value) is set to the difference between the energy expected and the energy of the
profile. Thanks to this processing, the day has exactly the irradiation expected.
For example, in the following case the irradiation of the day is 4.123kWh and the irradiation expected is
4.489kWh. The clear sky has an irradiance of 8.046kWh. The clear sky index is 51%. It is necessary to
change the first ten values to obtain an irradiance larger than the one expected. Last the last modified
value is set to the difference between the expected irradiation and the daily irradiation with 9 values
modified.
0
200
400
600
800
1000
1200
Irra
dia
nce
[W
/m
²]
Time
MACC-RAD profile
0
200
400
600
800
1000
1200
Irra
dia
nce
[W
/m
²]
Time
MACC-RAD profile modified
-96-
If the clear sky index is lower than 40%, all the profile is raised. For example, in the following case, the
irradiation of the day is 1.878kWh and the irradiation expected is 2.132kWh. The clear sky irradiation is
8.000kWh. The clear sky index is 23%. The whole profile is raised by 113.6%.
Lowering the profile
In the case energy has to be removed. A starting point is randomly chosen from which irradiance is
lowered. If the starting point is equal to the clear sky, it is set to 80% of the clear sky (with a standard
deviation of 2% of the clear sky) and then, while the daily irradiation is higher than the irradiation
expected, following points are set to values around 55% of the clear sky (with a standard deviation of 5%
of the clear sky). The last value lowered is modified in order the daily irradiation equals the expected
irradiation.
For example, in the following case the irradiation of the day is 5.289kWh and the irradiation expected is
4.390kWh. The starting point is at 9:15am. It is not equal to the clear sky so it is straight changed to 55%
of the clear sky. Thirteen points have to be changed to be lower than the expected irradiation. The last
modified value is set to the difference between the daily irradiation with 12 values modified and the
expected irradiation.
0
200
400
600
800
1000
1200
Irra
dia
nce
[W
/m
²]
Time
MACC-RAD profiles
Clear sky MACC-RAD profile MACC-RAD profile modified
-97-
Conclusion
This method gives very accurate time series because it is based on real satellite measurements. However,
large dataset of ground measurement is needed in order to calibrate satellite data that overestimate the
potential of the location.
Last, the calibration obtains very good results but it cannot yet be completely automatic: visual check of
the distribution is very important.
0
200
400
600
800
1000
1200
Irra
dia
nce
[W
/m
²]
Time
MACC-RAD profiles
Clear sky MACC-RAD profile MACC-RAD profile modified
-98-
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