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STOCKHOLM SVERIGE 2016,

Modeling the Future Wind Production in the Nordic Countries

VIKTOR GRANBERG

KTH

SKOLAN FÖR ELEKTRO- OCH SYSTEMTEKNIK

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In recent years there has been a rapid expansion in wind power production within the Nordic countries which creates a demand for accurate wind power models.

This thesis looks into how to create accurate time series of wind power production that can be used in energy market simulations. The thesis has two main parts where one is to create time series of wind power production based on the currently installed wind parks in the Nordic system and the second is to create future time series corresponding to year 2040.

The suggested model uses gridded wind speed time series from 1979 and onward coming from the meteorological model ERA-Interim. The locations of currently installed wind power capacity are matched with their corresponding ERA-Interim wind speed. A power curve is optimized to give the best fit with historical wind power production. The wind speeds time series are transformed into wind power production series by applying the power curve and finally aggregated into one wind energy production series per price region. These wind power production time series are then compared to historical wind power production data and later used for electricity market simulations in a program called EMPS.

For the year 2040 a new set of wind power production series are produced. The dif- ference is that technological development and increased geographical distribution are taken into account. The resulting series are then used in long term market simulations together with the wind power production series that represents the current system by shifting the weight factor each year from the current series to the 2040 series.

The final series for the current system provides high hourly correlation and low errors compared with historical wind power production. The effect of the 2040 series gave higher wind value factors, higher power output in relation to installed capacity and a reduced variability in hourly wind power production.

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Vindkraften i Norden har haft en snabb utveckling under de senaste ˚aren, vilket st¨aller h¨oga krav p˚a bra vindkraftmodellering. Detta examensarbete unders¨oker hur tidsserier f¨or vindkraftproduktion kan skapas f¨or att sedan anv¨andas i el- marknadssimuleringar. Examensarbetet best˚ar av tv˚a huvuddelar. Den f¨orsta ¨ar att skapa tidsserier av vindkraftproduktion f¨or det nuvarande systemet med in- stallerad vindkraft i Norden. Den andra delen ¨ar att skapa framtida tidsserier som ska motsvara vindkraftproduktionen f¨or ˚ar 2040.

Den f¨oreslagna modellen anv¨ander sig av historiska tidsserier av vindhastighet fr˚an ERA-Interim som omfattar tiden fr˚an 1979 fram till idag. De nuvarande vindkraft- parkernas position matchas med sina respektive n¨armsta geografiska punkter med vindhastighet i ERA-Interim. En effektkurva anpassas f¨or att ge den b¨asta match- ningen med historiska vindproduktionsdata. Tidsserierna med vindhastighet om- vandlas med hj¨alp av effektkurvan till vindkraftproduktionsserier vilka sedan sl˚as samman till en serie per prisomr˚ade. Vindproduktionsserierna j¨amf¨ors sedan med historisk vindkraftproduktion och anv¨ands slutligen i elmarknadssimuleringspro- grammet EMPS.

F¨or ˚ar 2040 skapas en ny upps¨attning vindproduktionsserier d¨ar h¨ansyn tas till teknologisk utveckling samt ¨okad geografisk utbredning. De framtida vindproduk- tionsserierna anv¨ands sedan i elmarknadssimuleringar tillsammans med serierna som motsvarar dagens installerade system d¨ar viktfaktorn ¨andras f¨or varje ˚ar fr˚an dagens serier till 2040-serierna.

Vindproduktionsserierna f¨or dagens installerade system visar sig ha h¨og korrela- tion och l˚ag avvikelse j¨amf¨ort med historisk vindkraftproduktion. Effekten av att anv¨anda de framtida 2040-serierna visar sig genom att v¨ardefaktorerna f¨or vind

¨

okar, mer energi kan produceras f¨or samma installerade kapacitet samt variationen i vindkraftproduktion minskar mellan varje timme.

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I would like to thank my supervisor at Vattenfall Jussi M¨akel¨a and the people at Vattenfall Long Term Market Outlook for helping me develop the idea for this thesis as well giving valuable opinions and support during the work process. I would also like to thank Egill Tomasson for supervising the project at KTH.

iii

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Abstract i

Sammanfattning ii

Acknowledgements iii

Contents iv

List of Figures ix

List of Tables xi

Abbreviations xiii

1 Introduction 1

1.1 Background . . . 1

1.2 Problem Definition . . . 2

1.3 Objectives . . . 3

1.4 Overview of the Report . . . 3

2 Wind Power Modeling 5 2.1 Wind Power . . . 5

2.1.1 Wind Turbine Technology . . . 5

2.2 Wind Power Modeling Techniques . . . 6

2.2.1 The Value of Accurate Wind Series . . . 6

2.3 Price Regions . . . 7

2.4 Wind Characteristics . . . 8

2.4.1 Correlation Between Price Areas . . . 9

2.4.2 Wind Data for Sweden . . . 9

2.5 Interconnections. . . 11

3 Theory 13 3.1 Statistics . . . 13

v

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3.1.1 The Probability Density Function . . . 13

3.1.2 The Weibull Distribution . . . 13

3.1.3 Mean Absolute Error . . . 14

3.1.4 Root Mean Squared Error . . . 14

3.1.5 Pearson’s Correlation Coefficient . . . 14

3.1.6 Standard Deviation . . . 14

3.1.7 Interquartile Range . . . 15

3.2 EMPS . . . 15

3.2.1 Configuration . . . 16

3.2.2 The Strategy Part . . . 17

3.2.3 The Simulation Part . . . 18

3.3 ERA-Interim . . . 20

3.3.1 Interpolation . . . 21

3.4 Power Curve . . . 23

3.5 Wind Value Factor . . . 24

4 Creating Wind Energy Production Series for the Current Situa- tion in the Nordic Countries 27 4.1 Introduction . . . 27

4.2 Method . . . 28

4.2.1 Wind Park Data Gathering . . . 28

4.2.2 Get relevant ERA-Interim data . . . 28

4.2.3 Regions . . . 29

4.2.4 Finding a Power Curve . . . 31

4.2.4.1 Weighting . . . 31

4.2.4.2 Using a Generic Power Curve for all Regions. . . . 32

4.2.4.3 Finding an optimized power curve . . . 33

4.2.5 Scaling . . . 35

4.2.6 Verification of Method . . . 36

4.3 Results . . . 38

4.3.1 Denmark. . . 39

4.3.2 Finland . . . 39

4.3.3 Norway . . . 42

4.3.4 Sweden . . . 42

4.3.5 Perfect Distribution. . . 43

4.4 Discussion . . . 46

5 Making the Future Wind Series 51 5.1 Future Trends in Wind Turbine Technology . . . 51

5.1.1 Capacity Factor . . . 53

5.1.2 Wind Value Factor . . . 54

5.2 Method for Creating Future Wind Series . . . 54

5.2.1 Choosing Grid Points . . . 54

5.2.2 Choosing the Power Curve . . . 55

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5.3 Results . . . 55 5.3.1 Effect on Value Factors . . . 55 5.4 Discussion . . . 56

6 The Finished Wind Profiles 63

6.1 Summary . . . 63 6.2 General Conclusions . . . 64 6.3 Future Studies. . . 65

Bibliography 67

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2.1 The Nordic price regions. Image courtesy: Nord Pool Spot. . . 8 2.2 PDFs for wind power production during 2014 in Sweden’s price

regions. . . 11 2.3 PDF for entire Sweden’s wind power production during 2014.. . . . 12 3.1 Diagram of installed power plants and hydro reservoirs of a typical

river in Sweden. . . 18 3.2 How EMPS simplifies each area’s power plants and hydro reservoirs. 19 3.3 Map over the Nordic countries with ERA-Interim grid points. . . . 22 4.1 Interactive map with installed wind power in Norway. . . 29 4.2 The ERA-Interim map with the Nordic countries’ regional splitting. 30 4.3 The generic power curve used in the example calculations. . . 33 4.4 Comparison of PDFs in SE3 between the model data with a generic

power curve and TSO data. . . 34 4.5 Hourly production for SE3 with a generic power curve. . . 35 4.6 Curve fitting to a scatter plot of wind power production vs wind

speed for a wind park in northern Norway. . . 36 4.7 Wake effect visible at the offshore wind park Horns Rev near the

coast of Denmark. Photo courtesy: Vattenfall Wind Power. . . 37 4.8 Flow chart that illustrates the principles of the power curve op-

timization when there is only one historical series per region but several grid points. . . 37 4.9 Comparison of PDFs in SE3 between the model data with an opti-

mized power curve and TSO data. . . 38 4.10 Hourly production for SE3 with an optimized power curve. . . 39 4.11 The error distribution for the modeled wind energy production dur-

ing 2012 for Denmark compared to historical data from the TSO. . 40 4.12 PDFs of the modeled wind energy production during 2012 for Den-

mark and historical data from the TSO. . . 41 4.13 PDFs of the modeled wind energy production during 2012 for Fin-

land and historical data from the TSO. . . 42 4.14 The error distribution for the modeled wind energy production dur-

ing 2012 for Finland compared to historical data from the TSO. . . 43 4.15 PDFs of the modeled wind energy production during 2012 for Nor-

way and historical data from the TSO. . . 44

ix

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4.16 The error distribution for the modeled wind energy production dur- ing 2012 for Norway compared to historical data from the TSO. . . 44 4.17 PDFs of the modeled wind energy production during 2012 for Swe-

den and historical data from the TSO. . . 45 4.18 The error distribution for the modeled wind energy production dur-

ing 2012 for Sweden compared to historical data from the TSO. . . 45 4.19 PDFs of the modeled wind energy production during 2012 for Fin-

land and the modeled wind energy production for 2012 utilizing all grid points in the country with equal weight factors. . . 47 4.20 PDFs of the modeled wind energy production during 2012 for Nor-

way and the modeled wind energy production for 2012 utilizing all grid points in the country with equal weight factors. . . 48 4.21 PDFs of the modeled wind energy production during 2012 for Swe-

den and the modeled wind energy production for 2012 utilizing all grid points in the country with equal weight factors. . . 49 5.1 PDFs of the modeled wind energy production during 2012 for Den-

mark using the 2015 profiles and the 2040 profiles. . . 57 5.2 PDFs of the modeled wind energy production during 2012 for Fin-

land using the 2015 profiles and the 2040 profiles. . . 58 5.3 PDFs of the modeled wind energy production during 2012 for Nor-

way using the 2015 profiles and the 2040 profiles. . . 59 5.4 PDFs of the modeled wind energy production during 2012 for Swe-

den using the 2015 profiles and the 2040 profiles.. . . 60

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2.1 Hourly correlation in wind power production between Swedish price regions for 2012.. . . 10 2.2 Hourly correlation in wind power production between Swedish price

regions for 2014.. . . 10 4.1 Comparison between model data and historical data for Denmark,

Finland and Norway 2012. . . 40 4.2 Statistical data comparing the model data with the TSO data for

Sweden 2012. . . 41 4.3 Errors and hourly correlations in wind energy production in Finland

and Norway between the model data utilizing all the grid points with equal weight factors and historical production data for 2012. . 46 4.4 Errors and hourly correlations in wind energy production in Sweden

between the model data utilizing all the grid points in Sweden with equal weight factors and historical production data for 2012. . . 46 5.1 Statistical data for the 2040 series compared with the 2012 series.

All values have the unit MWh/h. . . 56 5.2 Difference in percentage points for value factors when using 2015

profiles and 2040 profiles. Positive values meaning higher value factors for the 2040 profiles. . . 56

xi

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CHP Combined Heat and Power

DE Germany

DK Denmark

ECMWF European Centre for Medium-Range Weather Forecasts EFI Elektrisitetsforsyningens ForskningsInstitutt

EMPS EFI’s Multi-area Power-market Simulator

FI Finland

FLH Full Load Hours IQR Inter-Quartile Range MAE Mean Absolute Error

ME Mean Error

NL Netherlands

NO Norway

PDF Probability Density Function RMSE Root Meab Squared Error SD Standard Deviation

SE Sweden

TSO Transmission System Operator

UK United Kingdom

xiii

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Introduction

1.1 Background

Over the last ten years we have seen a rise in electricity produced by renewable energy sources. Especially in electricity coming from wind turbines. Wind power has gone from being a very small and negligible energy source to a moderate size energy source generating around 8 % of the total yearly electricity production in Sweden 2014 [1] and 39 % in Denmark [2]. In Finland, wind power production is still only at 1.3 % of their electricity production [3] with 627 MW installed capacity, but there is an aim to install much more the coming years. The goal for 2020 is to have around 2500 MW of installed wind power capacity in Finland [4]. While other resources like nuclear and coal power plants can provide a very stable and constant electricity production over time, wind power production will vary due to the stochasticity in the wind. And while hydro power can vary its production over short periods in time to compensate and keep production and consumption in the market equal at all times, wind power will have large variation in its production with almost no controllability which will make it harder to keep power production and consumption at the same level. This is seen as one of the problems with a rapidly increasing share of wind power production in a power system since there must exist some regulatory power source that is large enough to compensate for the variability in the wind power production.

For TSOs it is important to have information about future wind power impact on the power system so that they at an early stage can simulate and test that the power system will remain stable or else they will have to take different measures

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to make sure that stability is achieved in the long term. Electricity producing companies, investors and electricity retailers want to have information about the future electricity price development to estimate future revenues. The CO2 emis- sions and other pollutants are also connected to the variability in the wind power production. What is important to remember is that the energy production of a wind turbine is proportional to the cube of the wind speed, making it important to have accurate measurements of models of the wind behavior. Wind power has a very low cost to produce energy and when a system has a large share of installed wind power capacity then the electricity prices can drop significantly. The wind power is said to cannibalize itself, meaning that the more wind power that is in- stalled in a system, the lower the electricity price gets which in turn decreases the profit.

The idea for this thesis originates from a study at Uppsala University [5] which was picked up by Vattenfall who wanted to improve their current wind energy production series to better be able to cope with the rapidly increasing impact of wind power in the power system. The reason for modeling the whole Nordics is because the countries are tightly interconnected and no country within the Nordics can be seen as an isolated system. I also want to state that even though that Iceland is part of the Northern countries, it will not be included in this thesis due to not being interconnected to the other countries’ power system. It is therefore not interesting to include it in the power system simulations. I will for simplicity’s sake still refer to Denmark, Finland, Norway and Sweden as the Nordic countries throughout the thesis.

1.2 Problem Definition

The wind power production should be modeled well enough so that it can as exactly as possible describe the behavior that is seen in the system today. By using as many historical years as possible describing the wind speeds, the model should be able to “capture” many different weather scenarios. These weather scenarios can describe how high and low the expected future production can get for the coming years or the mean value and variance of the weather years. It is important that the historical wind data is represented for as many historical hydro inflow years as possible since the hydro inflow is correlated to the wind speeds. It is also

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important that the historical wind data can accurately describe the variations in wind speeds of all the countries in the Nordic region.

Since wind power is steadily increasing in all the Nordic countries and the wind turbine technology is constantly developing, it is necessary to make the model able to handle these factors as well. The idea is to create another wind power production series that represents the year 2040 where the wind farms cover a larger land area within the country and the wind turbines are more efficient. The series representing the current situation will gradually for each year be phased out at the same rate that the 2040 series are gradually phased in.

1.3 Objectives

The wind series shall be created by using a meteorological model that covers the years 1979 to 2013. The main objectives of the thesis are:

• Study and describe the principles of the simulation model used at Vattenfall and the meteorological model from where the wind speeds are acquired.

• Create wind energy production series that matches the current situation of installed wind power within the Nordic countries.

• Verify the new wind energy production series against historical data.

• Create a future wind energy production series for year 2040 where the geo- graphical wind park distribution and turbine technology has changed from the current situation.

• Implement the new wind energy production series in Vattenfall’s simulation model and analyze the impact on the simulation results.

1.4 Overview of the Report

Chapter 2 gives further introduction into the field of wind power and mentions wind characteristics, modeling techniques, price regions and interconnections. In Chapter 3 the theory of the simulation model EMPS, the meteorological model

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ERA-Interim, the wind value factor and the power curve are explained. Such as the simulation model EMPS and the ERA-Interim meteorological model. The main method for the creation of the current situation wind energy production series are described in Chapter 4. The future series representing the year 2040 with more distributed wind parks and better wind turbine technology taken into account are described in Chapter 5. Finally Chapter 6will summarize the results and conclusions from the previous chapters and give some ideas of possible future studies.

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Wind Power Modeling

2.1 Wind Power

The idea to harvest the wind for energy goes back a long time. In the beginning it was only used for pumping water, grinding grains, cutting wood at saw mills and pushing the sails on boats. Already in the 1940s a wind turbine of 1.25 MW was constructed and powered a local utility network. However, due to high availability of cheap oil and low energy prices wind turbines were sidelined by other energy sources [6]. In the 1970s, oil crisis with increasing oil prices due to shortages created an interest in alternative energy sources where wind power was again seen as an interesting energy source.

2.1.1 Wind Turbine Technology

A wind turbine basically consists of a tower with a rotor on top that captures the kinetic energy in the wind and converts it to rotational energy by accelerating the rotor. This rotational energy is absorbed by the wind turbine’s generator which converts it to electrical energy. The rotor on wind turbines in 2015 could have a diameter of 90 m and a tower height (hub height) of 80 m [7]. The wind turbine also has motors to control the yaw, which makes sure that the turbine is always facing the wind. There is usually also a pitch control in the wind turbines which adjusts the pitch of the rotor blades to keep the rotor speed within operating limits.

Once the turbine generates at its rated power, the rotor blades are adjusted to

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keep the output at the rated power. In case of potentially harmful wind speeds the blades are feathered meaning that almost no wind energy is captured by the rotor. The speed at which this occur is usually referred to as the cut-out speed and is typically around 25 m/s depending on the type of wind turbine used. There is also a cut-in speed at which the wind turbine starts to generate power. The cut-in wind speed is typically between 3-4 m/s [8].

2.2 Wind Power Modeling Techniques

There are different methods to model wind power production. One way to do it is by using statistical models based on e.g. autoregressive methods such as ARMA [9]. The advantages of using statistical models are that the length can be decided arbitrarily and that they can be simple to use due to not needing any physical data except historical data. Another way to model wind power is to use physical models that are based on actual physical data in the system together with the laws of physics. Unfortunately, a physical model cannot produce data of arbitrary length but is dependent of the length of the input data. One can for example make a physical model for wind power production basing it on very accurately describing the installed capacity and using very sophisticated physical formulas for the conversion of wind speeds to wind power. But still the model is dependent on the wind speed data for length, accuracy and temporal as well as geographical resolution. The good thing with the physical model is that it can be more accurate and capture system losses as well as being controllable where the physical parameters can be changed and the consequences evaluated e.g. adding more wind power capacity in a region or increasing the efficiency in the turbines.

For this work the a physical model will be developed since the simulation benefits by using historical wind speeds that correlates with other historical data used in the model, such as hydro inflow, temperature, insolation etc.

2.2.1 The Value of Accurate Wind Series

Since this thesis is about creating reliable time series for wind energy production based on physical and historical data it is interesting to think about why it is of value to measure and model wind production. In the context of Vattenfall, it is very important to have a good wind energy time series to use in their simulation

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model because wind is becoming a larger part of the total energy production and is growing rapidly. It is of importance that the variability in the wind becomes well represented so that the simulation can show how much the hydro power needs to regulate the variations in power output. It will also affect the import and export of the countries. If one looks at a critical connection like the one between Norway and the UK, it is very important to take into account the wind production in the UK so that the power flows between the two countries are well represented. Heavy winds in southern Norway might lead to high export to northern England, but the heavy wind in Norway might correlate with high winds in northern England which decreases the needed export from Norway.

Another reason is that investors want to know historical wind data so that they can get an estimate of annual wind energy production. Investors want to mini- mize their cost of producing energy and since the variable cost of a wind turbine is negligible it means that the wind turbine should at all times maximize its produc- tion. To get the highest profitability from a wind location, one must also choose a suitable wind turbine that operates efficiently for the wind speeds in that location.

2.3 Price Regions

Each country in the Nordic countries is divided into price regions or bidding areas [10]. The local TSO decides how many and where the bidding areas should be. In Norway there are five price regions, four in Sweden, two in Denmark and Finland does only have one at the moment. The map in Figure 2.1 shows the Nordic countries’ price regions with the name of each price region, e.g. SE1 for northern Sweden.

The price regions’ borders are set near constraints in the transmission system to get regional system conditions reflected in the price. For the Nordic market, a system price is calculated without taking available transmission capacity between bidding areas into account. Inside each price region an area price is calculated. The area prices may be different from each other, due to bottlenecks in the transmission system, which makes the power flow from the low price region to the high price region.

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Figure 2.1: The Nordic price regions. Image courtesy: Nord Pool Spot.

2.4 Wind Characteristics

When looking at historical wind speed data one can see trends in the wind speeds that there is seasonality in the wind. The wind speeds tend to be higher during winter and lower during summer. This is in general a good effect since it correlates with higher demand during wintertime, especially in the Nordics where there is a fair share of electric heating in houses and cold winters. It is sometimes misunder- stood that renewable energy is producing the most when the demand is the lowest, and for some types of renewable energy this is true. Solar power in the Nordic countries is a good example of this since there are many more sun hours during the summer than during the winter. This leads to very low or almost zero production in winter which gives a negative correlation between solar power production and demand when looking at seasonality.

On diurnal basis it is different since solar power has higher production during the day when the sun is up, which correlates with high demand since the industries consume a lot of power during daytime. Wind power tends to produce less during daytime and more during night when looking at the average. This means that on

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average the wind and solar power are negatively correlated on a yearly and diurnal basis. That means that a combination of the two can reduce the variability and intermittency in the renewable energy power output [11].

2.4.1 Correlation Between Price Areas

The correlation between wind speeds at different locations decreases rapidly with distance. In Sweden the correlation drops significantly when the distance is 1000 km between the measured points. This means that geographically spread out wind parks will most likely not produce at maximum power or have zero pro- duction at the same time. When there is no wind at one wind park there will most definitely be production somewhere else if wind parks are many and spread out. The result of this is that there is less need for regulation in the electric- ity production when wind parks are spread out since the wind energy production curve will be smoother and have less volatility compared with when the wind parks are located closer together. This does however require that enough transmission capacity is available in the transmission grid to have distant wind parks balance the production. If not, then there will be a need to locally balance the energy production with e.g. hydro power or gas turbines when a local wind park varies its power output.

2.4.2 Wind Data for Sweden

It is interesting to look at the typical wind characteristics for Sweden and see if there are any patterns which should be represented in the time series. The hourly correlations in wind power production for 2012 and 2014 between Sweden’s four price regions are shown in Table 2.1 and 2.2, where the data comes from the Swedish TSO Svenska Kraftn¨at [12]. We can see that there is a clear trend where the correlation decreases with increased distance. SE1 has a strong correlation of 0.758 to SE2 during 2012 and 0.768 during 2014 to SE2, but only 0.121 (2012) and 0.095 (2014) to SE4. As described in the section above, this is beneficial for wind power production. If there is zero production due to low wind speeds in SE4, there might still be a substantial amount of wind power production in SE1 and vice versa. The tables also show that the hourly correlation has not changed drastically from 2012 to 2014 despite large wind power installations during the

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period. The small differences could be due to different weather conditions for the two years.

SE1 SE2 SE3 SE4

SE 0.500 0.641 0.922 0.803 SE1 1 0.758 0.311 0.121

SE2 1 0.447 0.229

SE3 1 0.667

SE4 1

Table 2.1: Hourly correlation in wind power production between Swedish price regions for 2012.

SE1 SE2 SE3 SE4

SE 0.558 0.699 0.931 0.772 SE1 1 0.768 0.352 0.095

SE2 1 0.496 0.172

SE3 1 0.736

SE4 1

Table 2.2: Hourly correlation in wind power production between Swedish price regions for 2014.

It is interesting to see how the distributions look for wind power production in the different price regions. Using wind power production data from Svenska Kraftn¨at, it is possible to look at the wind power production distribution for each price region. Figure2.2 shows that there is a quite high probability of having zero wind power production within each price region. This can be regarded as expected as wind speeds quite often are lower than the cut-in wind speed of the wind turbines and since the wind parks experiences almost the exact same winds within each price region due to the wind parks being relatively close to each other. If we however also look at the aggregated wind power production in the whole Sweden shown in Figure 2.3 we can see that there is almost no time with zero wind power production. This is due to the low hourly wind correlation between the wind parks in the north and the ones in southern Sweden. It can be interpreted as if larger wind areas are used, the so called smoothing effect for the wind power production increases. The smoothing effect increases the minimum production and decreases the peaks in wind power production compared to if all wind power capacity would be located at the same spot.

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MWh/h

0 100 200 300 400 500

Probability

0 0.002 0.004 0.006 0.008

0.01 SE1

MWh/h

0 200 400 600 800 1000 1200 1400

Probability

×10-3

0 0.5 1 1.5 2 2.5

3 SE2

MWh/h

0 500 1000 1500 2000

Probability

×10-3

0 0.2 0.4 0.6 0.8 1 1.2 1.4

1.6 SE3

MWh/h

0 200 400 600 800 1000 1200 1400

Probability

×10-3

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

1.8 SE4

Figure 2.2: PDFs for wind power production during 2014 in Sweden’s price regions.

2.5 Interconnections

When looking at the Nordic region, it is also important to take wind in the UK, Netherlands and Germany into account, due to the large impact the connections between UK and NO, NL and NO, NE and DK, DE and DK, DE and SE can have on the prices. If for example Sweden has a surplus of power and wants to export hydro power to Germany, then depending on if there are high winds and therefore high wind production in the area of the connection point in Germany, this could “push” the hydro export back towards Sweden. It is not a push per se, but a consequence of the low prices that emerges from large wind production in a region. The low prices in turn make the hydro producing companies want to save the water in their reservoirs to dispatch the production when prices have risen.

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Production [MWh/h]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Probability

×10-4

0 1 2 3 4 5 6

Figure 2.3: PDF for entire Sweden’s wind power production during 2014.

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Theory

3.1 Statistics

3.1.1 The Probability Density Function

The PDF can be seen as the shape of the distribution of a variable.

P (a < X < b) = Z b

a

f (x) dx (3.1)

where f (x) >= 0 and R

−∞f (x) = 1.

The PDFs shown in this thesis are created by making a histogram of the data series where the height of each bar is equal to (number of observations in the bin)/(total num- ber of observations × width of bin). The sum of all bar areas is 1.

3.1.2 The Weibull Distribution

The Weibull distribution is a popular distribution in the wind industry since it seems to be a good description of locally measured wind speed distributions. It can be written as

f (x) = k c

x c

k−1

e((xc))k (3.2)

where k is the shape parameter and c is the scale parameter.

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3.1.3 Mean Absolute Error

Three error estimates are used for the model verification. In the following equa- tions, x represents the observed time series, ˆx represent the predicted time series and N is the number of data points.

The mean absolute error gives the average of the absolute value of forecast errors

MAE (x, ˆx) = 1 N

N

X

i=1

|xi− ˆxi| . (3.3)

3.1.4 Root Mean Squared Error

The root mean squared error compared to the MAE, amplifies large errors and gives them a higher weight, i.e. being off by 4 is more than twice as bad as being off by 2. The RMSE is always larger than or equal to the MAE.

RMSE (x, ˆx) = v u u t

1 N

N

X

i=1

(xi − ˆxi)2. (3.4)

3.1.5 Pearson’s Correlation Coefficient

Pearson’s correlation coefficient measures the extent to which two variables, here x and y, tend to change together. It is defined as

r =

PN

i=1(xi− ¯x) (yi− ¯y) q

PN

i=1(xi− ¯x)2 q

PN

i=1(yi− ¯y)2

(3.5)

where ¯x is the mean value of x and ¯y the mean value of y.

3.1.6 Standard Deviation

The standard deviation (SD) is a way to describe the variability or the spread of data. It is calculated as

SD = s

Pn

i=1(xi− ¯x)2

n − 1 . (3.6)

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3.1.7 Interquartile Range

The IQR gives the range of the middle 50% of data in a distribution and also gives an indication of the variability. It is calculated by subtracting the 25th percentile of data from the 75th percentile.

3.2 EMPS

In this project, the market simulations are done with a simulation software called EMPS (EFI’s Multi-area Power-market Simulator) which is a market simulator with a focus on optimizing the hydro power production. The model gives insight to price formation, energy economics, energy transmission, environmental effects and quality of power delivery. EMPS is a multi-area model, where the user creates a data model that can consist any number of areas. It was developed in the 1960’s at EFI in Norway, or SINTEF as it is now called, and is still under continuous development. Originally designed to model hydro dominated regions, but it can model other types of regions as well. It is mostly used among major market players in the Nordics with almost no users among non-Nordic companies. The information for this section mainly comes from the EMPS manual [13] and the course material from Hydro Power Scheduling at NTNU [14].

EMPS consists of two parts, a strategy part and a simulation part. The strategy part computes the water value based on stochastic dynamic programming as a function of reservoir level and time. Water value is the expected value of the water in the hydropower plants’ water reservoirs. The calculation of the water values takes a lot of computing capacity which is why the calculation is done on a very simplified model representation of the hydropower system. All the hydropower plants in each area are aggregated into one equivalent power plant with a single reservoir. The time resolution is up to two hours and the planning horizon is 1-25 years.

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3.2.1 Configuration

In each area, production can be modeled as hydro, thermal or wind power. Con- sumption are modeled with demand contracts. Each area has connections to sur- rounding areas to model the transmission lines. These connections are described with their Net Transmission Capacity (NTC), electric loss and transmission fees.

Thermal power plants are specified by their bid price, capacity and availability profile. There are however no ramping constraints, which means that the pro- duction can go from zero to maximum capacity from one hour to another. The thermal power plants model nuclear power, CHP and various condensing thermal plants.

Hydro power plants are specified by their minimum and maximum allowed reser- voir levels, their historical inflow levels as well as their minimum and maximum production. Ramping restrictions and water run times are not modeled. Especially the lack of including water run times in the model gives too high flexibility in the hydro system since the delay for the water to flow from one hydro power station to another will not be represented, i.e. a water volume in a hydro power station will immediately after being dispatched be available at the next hydro power station further down the stream even if in reality the water run time between those two stations could be one hour.

The wind and solar power are modeled as must run with historical production levels that correlates to the hydro production levels. It is these historical wind production levels that this project focuses on a great deal.

What also is important to specify are the transmission and the demand. The transmission is modeled with capacity on a weekly level and with losses and costs.

The demand has both a profile for fixed consumption and one for price-dependent consumption like electric boilers as well as one for rationing.

On the supply side the degrees of freedom are the management of the time-variant water inflow, renewable energy with its variable production, thermal production and import from other areas.

The demand side’s degrees of freedom are purchase of power for flexible consump- tion like electric-boilers, rationing, export to other areas, possible reductions in delivery contracts when power supply is critically low.

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3.2.2 The Strategy Part

One complex task when simulating power markets with a lot of hydro power is to determine the water value at any given point in time for each hydro reservoir. In the strategy part, EMPS calculates the water values by using Stochastic Dynamic Programming which will not be explained here. What is always an important part when one wants to solve optimization problems is to have a clear problem definition. For the water value computation, EMPS has formulated the problem in their manual as “Given a forecast for future price trends, it is necessary to find a strategy that maximizes the expected profit”. Using a setup which includes the whole Nordic region with all the installed hydro power results in very complex and time consuming calculations. That is why all the installed hydro power for each area is aggregated into one station with one reservoir as shown in Figure3.2. When comparing Figure 3.1 and 3.2 it is clear that this is a very large simplification.

The energies of the water reservoirs are calculated by multiplying each reservoir’s water volume with the energy equivalent of letting one m3 of that water pass through all the plants in that river, ending up at sea level. All the energies of the reservoirs in the area are then added to one equivalent reservoir. The equivalent plant is calculated by adding the maximum capacity for all plants and the minimum and maximum constraints of production.

But these simplifications are not enough. Having only a ten area model would result in unacceptable computation times. The limit is in practice only three ar- eas. The calculations are therefore done as an iterative procedure. But because the water value in one area depends on all the other areas in the power market, the information regarding the opportunities for exchange with other areas must somehow be supplied in the water value calculations. This is handled by having parameters in the calculation which has to be manually calibrated. The most important calibration factor is the feedback factor which model the feedback from demand in other areas than the one in which the water values are calculated. It controls how much firm demand is taken into account for the water value calcu- lation. The second most important calibration factor is the form factor which changes the annual distribution of firm demand. For example a larger value in- creases the winter load and reduces the summer load and a lower value has the opposite effect. The third and final calibration factor is the elasticity factor of price flexible demand. It controls the size of the price elastic market by affecting

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Figure 3.1: Diagram of installed power plants and hydro reservoirs of a typical river in Sweden.

the quantity that is available at each price level of the demand curve. The cali- bration could be a demanding process which requires the user to have experience to get high quality in the results. There is currently no automatic calibration that gives sufficient quality in the results.

3.2.3 The Simulation Part

The strategy part provided the water value decision table. In the simulation part the system operation states are obtained for different inflow scenarios. The

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Figure 3.2: How EMPS simplifies each area’s power plants and hydro reser- voirs.

simulation does not give an accurate optimal solution, due to the fact that future inflow is unknown. Instead the aim is to achieve an optimal system utilization in the long run based on expected inflow and the economic impact of extreme conditions. The simulation logic is based on two steps: [14] Optimal decision on the aggregate area level using a network algorithm based on the water values computed in the strategy phase, i.e. area optimization. Detailed reservoir drawdown in a rule based model to distribute the optimal total production from the first step between the available plants. In this step it is verified if the desired production is obtainable within all constraints at the detailed level. When simulating on the aggregate area level a total production for each area is calculated. This production is in the drawdown model distributed between the modules within the areas. The distribution is not calculated by a formal optimization, but by a rule based strategy which is explained below. First a distinction is made between buffer reservoirs and regulation reservoirs. A buffer reservoir is typically small and has little regulation capability. This gives a ratio between reservoir volume and annual inflow which is fairly low, making an empty buffer reservoir fill up in the course of one to two weeks. A value below 2-3 % is regarded as low. Regulation reservoirs are all the reservoirs that are not buffer reservoirs. In the reservoir drawdown model the year is divided into two seasons with different strategies. A filling season with

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inflow larger than discharge and a depletion season with discharge larger than inflow. The expected time for the different seasons are important parameters for the simulation. In the filling season the main objective is to avoid spilling. A way to solve this is to try having the reservoirs at a level which make them have equal relative damping D, which can be seen as a simplified expression for the risk of spillage [14]. The damping is defined as

D = Rmax− R

Rmax · α, (3.7)

where Rmax is the maximum water level in the reservoir, R the actual water level in the reservoir and α the degree of regulation which is defined as α = Rmax/Qa, where Qa is the annual inflow. The depletion season has two objectives: [14]

1. The rated plant capacity must be available as long as possible to avoid emptying some reservoirs too early and causing a capacity deficit.

2. At the end of the depletion season the reservoirs should have equal relative damping according to (3.7) to minimize spillage in the coming spring inflow period.

EMPS is under continuous development that is taking place at SINTEF Energy Research. Despite its weaknesses, EMPS strengths are its potential for realistic simulation of hydro power dominated systems and its robustness as a model.

3.3 ERA-Interim

ERA-Interim is a global atmospheric reanalysis produced by the European Cen- tre for Medium-Range Weather Forecasts (ECMWF). It covers the period from January 1 1979 onwards and is continuously extended. The data products are gridded and include a range of surface parameters describing weather as well as ocean-wave and land-surface conditions. The grid has a resolution of 80 km and a temporal resolution of three hours [15] at 60 vertical levels starting at surface level and going up to 0.1 hPa.

Reanalysis is a relatively young field. The advantage of using reanalysis data is that it provides a spatially complete and coherent data set. If one would use

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archived weather analyses from operational forecasting systems the forecast model is most likely changed over a large time span. The reanalysis is produced with a single forecast model and therefore changes in methods over different years can be ruled out when analyzing the data. The reanalyses have improved in quality over the years due to better models, better input data and better assimilation methods. The data products are constantly improving in spanning longer time periods, higher spatial and temporal resolutions. For multivariate reanalysis it is required that there is a physical coherence so that the estimated parameters are consistent with the laws of physics and observations. This is different from other estimation methods of geophysical parameters from observations. A forecast model unifies observations of various types that stem from different sources. A meteorological model extrapolates the information from observed parameters to unobserved parameters located nearby to get a full coverage of an area, meaning that each grid point in the specified grid will not have any lack of information.

3.3.1 Interpolation

Since the ERA wind data only gives three hour wind speed estimates and there is need for one hour resolution, the data needs to be interpolated. There are several methods to interpolate missing data. Two common methods are linear interpolation and last observation carried forward. LOCF copies the last known data point to fill in the gaps which means it doesn’t catch the trends in the dataset and is therefore not suitable for this application. Linear interpolation is an interpolation method that simply makes a straight line between each known data point and the next coming known data point. If just one more data point needs to be interpolated the new data point will have a value which is right in between the previous and the following. When only every third data point is known, which is the case in this work, the linear interpolation formula is

y2 = (x2− x1)(y3− y1)

(x3 − x1) + y1. (3.8)

The chosen interpolation method was however cubic spline interpolation which creates a smoother interpolation than the linear interpolation and uses some more sophisticated methods to interpolate the data points. It sets its conditions so that the first and second derivatives of the interpolation formula are continuous,

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Figure 3.3: Map over the Nordic countries with ERA-Interim grid points.

which makes a smoother curve compared to piecewise linear interpolation. The interpolation was performed in MATLAB [16] which has built-in functions for making cubic splines [17].

While there exist many different sources for acquiring good wind speed data with high spatial and temporal resolution, some with even higher resolution e.g.

MERRA [18], ERA-Interim was chosen mainly since it was used previously for the continental wind series in EMPS. Another reason is due to the fact that data acquisition would be easier since data tools for this was already created, meaning only minor adjustments had to be made to acquire the data. The continental wind series are however not modeled in the same manner as described in this report, but the underlying data source for the continental wind speeds is still ERA-Interim.

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ERA-Interim was therefore chosen to get a more consistent wind power part of the EMPS simulation by using the same data source.

3.4 Power Curve

A power curve shows the relation between the wind speed that a wind turbine

‘receives’ and the power it produces for that wind speed. Wind turbines typically have a cut-in wind speed which is the lowest wind speed the wind turbine can operate at. It is important to represent the cut-in wind speed in the model since it shifts the weight of the distribution curve towards zero. Every wind turbine also has a cut-out wind speed at which it angles the ‘blades’ to stop rotating and producing energy. After stopping the wind speed is monitored and the wind turbine does not start to operate again until the wind speed has been lower than the cut-out wind speed for some 10 minutes. The cut-out wind speed exists because of safety reasons and reduces the risk of damage to the equipment.

A way to perform this curve-fit is to create a scatter plot with wind power produc- tion to wind speed. The problem here is that the measured production data must be available for each wind park to capture the wind parks power curve. This is no problem when there is wind power production data available for each wind park as in Norway, but for Sweden, Denmark and Finland when wind power production data is only available for each price region, which in turn consists of several differ- ent wind parks with different wind speeds and different wind turbines. Another issue is that the available wind speed data comes from ERA-Interim which is not the real wind speed data but the modeled and also lacks one hour resolution. A positive aspect when applying a fitted curve is that it includes both the array losses (due to wake effects) and electric collecting system losses of the wind park.

The power curve will be based on following equation which is occasionally used at Vattenfall

y = k



exp c − v p1

 + 1

 

exp v − cout p2

 + 1

 , (3.9)

where v is the wind speed, k is the maximum efficiency, c the parameter which can control the cut in wind speed, coutsets the cut out wind speed, p1 and p2 are shape parameters. The four parameters can be set by creating an optimization problem

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to minimize the objective function being the mean absolute error MAE of the historical wind energy production series and the modeled wind energy production series, which is described in Chapter 4.

3.5 Wind Value Factor

The market value of a variable renewable energy source depends on its relative price compared to the base price. To decide this market value we introduce the value factor. It can be described as the wind value factor compares the market value of power with time-varying winds and the value that would be expected if winds were invariant [19], or the value factor is a metric for the valence of electricity with a certain time profile relative to a flat profile [20]. In this thesis the wind value factors short-term variations are neglected and instead we focus on the longer term. Let’s say that a wind park tends to produce most of its annual energy output when electricity prices are high, then that wind park has a higher market value compared with a wind park that typically produces most of its annual energy output when prices are low.

The value factor can have a value larger than 1.0. The base price in Germany was 51AC /MWh in 2011. Solar power has a positive correlation with demand, people are awake and industries are working during the day when the sun is up. In Germany in 2011 this led to solar power receiving an average price of 56AC /MWh which gives a solar value factor of 1.1 [21]. Wind has a positive seasonal correlation with demand which can lead to wind value factors being above 1.0 as well.

Mathematically we can define the base price ¯p as

¯

p = (p|t) / (t|t) (3.10)

where p[T ×1] is a vector of hourly spot prices and t[T ×1] a vector of ones. The two vectors do both have the dimension T × 1 where T is number of hours. The average revenue of wind power ¯pw can be written as

¯

pw = (p|g) / (g|t) (3.11)

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where g[T ×1] is the generation profile, i.e. a vector of hourly generation factors that sums up to the full load hours (FLH) for that year. It is worth mentioning that p|g is the annual revenue and g|t the annual production. Combining (3.10) and (3.11) we can express the wind value factor vw as

vw = ¯pw/¯p. (3.12)

The definition ignores future and intraday markets and relies only on day-ahead prices.

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Creating Wind Energy

Production Series for the Current Situation in the Nordic Countries

4.1 Introduction

This chapter describes the process to create wind energy production series to match the current wind energy production in the Nordic countries. It is perhaps the largest part in this project and also the most important since it includes de- veloping a method for creating the wind series as well as produces the final wind series that Vattenfall will use in their model. In the next chapter, the method described in this chapter will be used once more to create the 2040 series with the difference of using different input data hence producing wind series with different properties as well as another evaluation method. The current situation in the sys- tem regarding installed wind power must be investigated, the necessary data must be acquired and processed, the different regions must be defined, power curves must be specified and after creating the wind series the result must be evaluated and verified against real historical production data. There are unfortunately no single data source for historical production data and it exists in different quality for each country.

27

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4.2 Method

This part describes the method how to create the wind energy time series. It is described with ERA-Interim as the data source but can be applied to other meteorological models as data source as well.

4.2.1 Wind Park Data Gathering

The first step can either be very quick or very time consuming depending on the data available. A list of existing wind parks needs to be compiled. The list should include position data for each wind park, the capacity of the wind park and the grid connection date as well as possible decommissioning date. What also can be regarded as useful data is the hub height, yearly energy production, number of wind turbines as well as turbine model. The latter ones can be of value for making an even more detailed modeling which will not be addressed in this thesis. Nowadays there are usually web services that can give interactive maps with the location and capacity of a country’s installed wind parks. Sometimes also planned wind parks can be visible on these maps. Figure4.1shows the Norwegian equivalent from NVE [22] of one of these types of maps with installed wind power.

4.2.2 Get relevant ERA-Interim data

Once the grid points of interest are acquired, it is time to extract the wind speed time series data from the meteorological model. Usually the data from these models are very large and can require some time to process. In the ERA-Interim database there are wind data available for 60 altitudes starting at surface level with the top level at 0.1 hPa atmospheric air pressure. The altitude used for creating the 2015 series is 90 m which is the near the typical hub height of today’s installed wind turbines. The wind speeds are downloaded as a u component and a y component, where u is the westerly wind blowing to the east and y is the southerly wind blowing to the north. By adding these two vector components and calculating the absolute value of the resulting vector we get the wind speed values that will be used, the total horizontal wind speed. These wind speeds are saved with a name according to their corresponding grid point (as shown in figure 3.3), e.g. FIN10262 for a grid point in northern Finland. There are two columns that

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Figure 4.1: Interactive map with installed wind power in Norway.

contains the two wind speeds at 90 and 120 m altitude. Once the wind speeds have been extracted they only have a temporal resolution of 3 hours which means that they should first be interpolated to 1 hour resolution. The interpolation is described in Chapter3.3.1.

4.2.3 Regions

If one wants to model Sweden’s wind power production using this method, the best thing to do would be to create wind series for each price area since the TSO offers historical wind production data for the price areas. But to make wind series for the price areas within Sweden one must first decide which grid points that belong in each price area. Finland and Norway are however split in a somewhat other manner. Finland only has one price region but the simulation taking part

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in EMPS has three areas for Finland. Norway has in reality five regions but here seven regions are created. The reason for having more areas in the EMPS simulation than existing price regions is because of how EMPS treats the rivers in the strategy part calculation described in Chapter 3. For large rivers it is simply beneficial from a modeling perspective to have one area per river. This gives higher accuracy and better controllability. Therefore more regions than price regions were created for the wind series as well. Figure 4.2 shows the final region splitting of the Nordic countries.

Figure 4.2: The ERA-Interim map with the Nordic countries’ regional split- ting.

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4.2.4 Finding a Power Curve

Even if a good correlation is reached for the wind series it does not mean that it will create a good match with measured data. This is why it is also very important to match the probability density function (described in (3.1)) of the created time series and the PDF of measured historical data from e.g. the Swedish TSO Svenska Kraftn¨at. A perfect match between the two PDFs would mean that the amount of any given production level is the same in the wind series, however not necessarily having equal levels at the same time. What heavily influences the shape of the PDF for the modeled wind series is the power curve. The power curve gives a relationship between the power output for each wind speed. One can describe it as the power curve sets the utilization of the installed wind power capacity for different wind speeds. Since the power curve is a non-linear function it will change the PDF of the power production from the PDF of the wind speeds.

As described in Chapter 3 finding the power curve can be done in several ways.

Should each country have a generic power curve or should there be a power curve for each region? Maybe it can even be a specific power curve for every single grid point. This is something that needs to be evaluated and to look at the impact of choosing one option instead of another. If the turbine model for a wind park in a region is known, then it is usually easy to get the correct power curve from the manufacturer. These power curves have been created from real tests on the turbines and give the most exact representation of the wind turbine’s power curve.

This would however make the task unnecessarily complex and require a lot of time to go through each wind park to find the types of wind turbines installed. If there are several types of wind turbines, then the question remains how to determine the final power curve to be used for that wind park.

Before we start looking at how to find the power curve it is necessary to say a few words about weighting.

4.2.4.1 Weighting

The idea of the weighting is to make the installed capacity of a grid point decide the amount of impact that grid point will have on the final wind production series for that region. Let’s say that 90 % of the capacity in a region is located in the very south and the other 10 % of the capacity is located in the north of

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that region. Assuming especially that it is a quite large region with different wind characteristics in the north and south it would be unfair to have all the grid points with installed capacity to have equal weight and thus equal impact on the final wind production series for that region. This is especially important for regions with mountains and non-smooth terrain that can have large local variations of wind behavior.

It is now important to allocate each wind park’s aggregated capacity at the closest ERA grid point based on the position data of the wind park. In the ERA-Interim data there is a list available which states which coordinates the grid points have.

This made it simple to create an algorithm that calculates the nearest grid point from the position data of the wind park. After assigning capacity to the grid points the weights for the grid points can be calculated. The sum of all the installed capacity at each grid point should be computed so that a relative weight for each grid point compared other grid points is acquired. Here it is useful to have the data for grid connection date so that capacity development can be visualized and that the historical relative weights can be used to train the model to historical production data.

4.2.4.2 Using a Generic Power Curve for all Regions

We start by looking at the simplest alternative, i.e. to use a generic power curve in each region for the transformation. For the evaluation, a generic power curve that represents a typical high wind speed turbine today was used. The generic power curve had the parameters c = 9.8 m/s, cout= 22 m/s, p1 = 1.7 and p2 = 0.1 and is shown in Figure 4.3. The parameter k was set to 1 but is irrelevant to study since the series are scaled later in the process.

Figure4.4 shows the PDF of the modeled series generated using the generic power curve and the PDF of the historical production data from the TSO. It uses SE3 as an example for the year 2013. The same data is visualized in Figure 4.5 in a different way by taking a random sample of 3000 hours from year 2013 but instead showing the hourly production values. Here it can be seen that even if the data is well correlated it still has large errors. Figure 4.4 shows a large mismatch in the PDFs where the modeled series can produce more than twice as much energy per hour than the historical series which is limited to a bit more than 1500 MWh/h.

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Wind Speed [m/s]

0 5 10 15 20 25 30

Capacity utilization factor

0 0.2 0.4 0.6 0.8 1

Figure 4.3: The generic power curve used in the example calculations.

4.2.4.3 Finding an optimized power curve

When measured data for the wind power production of a specific wind park exists combined with available wind data then an equivalent power curve can be created by optimization. This can be done by making a scatter plot of wind speed and wind park power production for that specific wind park. The scatter plot typically shows a pattern similar to a power curve. If a curve fit is applied to the scatter plot one will get an equivalent power curve. This can be seen as an optimization problem where the objective function can be formulated as “minimize mean absolute error of the modeled hourly data minus the historical hourly data”. Possible outliers in the dataset should be removed e.g. having 500 MW production for 0.2 m/s wind speed might not be a trustworthy data point. These outliers can occur due to faults in wind speed measurements or due to the fact that this method does not take into account the information for when turbines are stopped for service. Figure 4.6 shows this where the method was applied to the wind park Smøla in northern Norway. A clear pattern is visible to the eye with the shape of a power curve. The curve fit shown in the figure is only performed up until 25 m/s and then a cut off is applied manually to the power curve. This solution can give a good power curve

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Production [MWh/h]

0 500 1000 1500 2000 2500 3000

Probablity

#10-3

0 0.5 1 1.5 2 2.5 3

PDF SE3 With Generic Power Curve

TSO Model

Figure 4.4: Comparison of PDFs in SE3 between the model data with a generic power curve and TSO data.

that will give accurate results in the model and also take into account so called hidden correlations like array losses, due to wake effects as shown in Figure 4.7, and electric collecting system losses [23].

If only historical wind energy production data exists on price region basis which is the case for the majority of the wind parks in the Nordic countries, then it is necessary to perform the optimization in a slightly different manner. In most cases it is hard to find real wind measurements for a wind park that covers at least a full year where also production data is available. In this project the real measured wind speeds were replaced with ERA-Interim wind speeds and the results were above satisfactorily. Figure 4.8 shows the principles of the optimization.

It is important to transform all of the grid point’s wind speeds with the power curve before weighting the time series. This is due to the fact that weighting and

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Time [h]

1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

Production [MWh/h]

0 500 1000 1500 2000 2500 3000 3500

SE3 Generic Power Curve

TSO Model

Figure 4.5: Comparison of hourly production for SE3 with a generic power curve.

summing wind speeds would not be an accurate way to model the wind energy production and since the power curve is a non-linear function it will give different results depending on at which stage the power curve is applied. If the optimized power curve is used instead of the generic power curve in Figure 4.3 the results look a bit different as shown in Figure 4.9 and Figure 4.10.

4.2.5 Scaling

The scaling of the wind energy production series is necessary if one wants to do a statistical comparison with the historical series. This is a very simple step that only consist of summing each individual series within the region. The result will give a smoother curve which with the correct scaling should be well correlated and have a very similar distribution compared with measured production data for that region.

The scaling is done so that annual production should be a certain amount of GWh.

This means that the scale factor k is the sum of the historical hourly production

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Figure 4.6: Curve fitting to a scatter plot of wind power production vs wind speed for a wind park in northern Norway.

divided with the sum of the model’s hourly production for a specific year

k =

XET SO

XEM odel. (4.1)

After calculating the scale factor k the model wind series are multiplied with k so that the modeled wind series produces the same annual energy as the historical data. The wind series are also scaled according to annual energy in EMPS, which is one of the reasons for using this method of scaling for verifying the wind series.

4.2.6 Verification of Method

What is interesting to test is the difference of making the time series with this method and simpler methods. If for example one would not add specific weights to each grid point but instead use a common weight factor of 1.0, would that have a large impact on the modeling? Another test that is interesting is what if not only specific grid points are chosen but choose all grid points within a price region. These two simplifications are evaluated separately. In case of simpler methods resulting in what is still regarded as good results, then the future wind series could be created using that simplified method.

References

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