Modeling the Future Wind Production in the Nordic Countries924504/FULLTEXT01.pdf · F or ar 2040 skapas en ny upps attning vindproduktionsserier d ar h ansyn tas till teknologisk

INOM EXAMENSARBETE ELEKTROTEKNIK, AVANCERAD NIVÅ, 30 HP

, STOCKHOLM SVERIGE 2016

Modeling the Future Wind Production in the Nordic Countries

VIKTOR GRANBERG

KTHSKOLAN FÖR ELEKTRO- OCH SYSTEMTEKNIK

Abstract

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.

Sammanfattning

Vindkraften i Norden har haft en snabb utveckling under de senaste aren, vilket

staller hoga krav pa bra vindkraftmodellering. Detta examensarbete undersoker

hur tidsserier for vindkraftproduktion kan skapas for att sedan anvandas i el-

marknadssimuleringar. Examensarbetet bestar av tva huvuddelar. Den forsta ar

att skapa tidsserier av vindkraftproduktion for det nuvarande systemet med in-

stallerad vindkraft i Norden. Den andra delen ar att skapa framtida tidsserier som

ska motsvara vindkraftproduktionen for ar 2040.

Den foreslagna modellen anvander sig av historiska tidsserier av vindhastighet fran

ERA-Interim som omfattar tiden fran 1979 fram till idag. De nuvarande vindkraft-

parkernas position matchas med sina respektive narmsta geografiska punkter med

vindhastighet i ERA-Interim. En effektkurva anpassas for att ge den basta match-

ningen med historiska vindproduktionsdata. Tidsserierna med vindhastighet om-

vandlas med hjalp av effektkurvan till vindkraftproduktionsserier vilka sedan slas

samman till en serie per prisomrade. Vindproduktionsserierna jamfors sedan med

historisk vindkraftproduktion och anvands slutligen i elmarknadssimuleringspro-

grammet EMPS.

For ar 2040 skapas en ny uppsattning vindproduktionsserier dar hansyn tas till

teknologisk utveckling samt okad geografisk utbredning. De framtida vindproduk-

tionsserierna anvands sedan i elmarknadssimuleringar tillsammans med serierna

som motsvarar dagens installerade system dar viktfaktorn andras for varje ar fran

dagens serier till 2040-serierna.

Vindproduktionsserierna for dagens installerade system visar sig ha hog korrela-

tion och lag avvikelse jamfort med historisk vindkraftproduktion. Effekten av att

anvanda de framtida 2040-serierna visar sig genom att vardefaktorerna for vind

okar, mer energi kan produceras for samma installerade kapacitet samt variationen

i vindkraftproduktion minskar mellan varje timme.

Acknowledgements

I would like to thank my supervisor at Vattenfall Jussi Makela 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

Contents

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

Contents vi

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

Contents vii

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

List of Figures

2.1 The Nordic price regions. Image courtesy: Nord Pool Spot. . . . . . 8

2.2 PDFs for wind power production during 2014 in Sweden’s priceregions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 typicalriver 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 genericpower 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 windspeed for a wind park in northern Norway. . . . . . . . . . . . . . . 36

4.7 Wake effect visible at the offshore wind park Horns Rev near thecoast 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 butseveral 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

List of Figures x

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 allgrid 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 allgrid 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 allgrid 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

List of Tables

2.1 Hourly correlation in wind power production between Swedish priceregions for 2012. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Hourly correlation in wind power production between Swedish priceregions 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 forSweden 2012. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3 Errors and hourly correlations in wind energy production in Finlandand Norway between the model data utilizing all the grid pointswith equal weight factors and historical production data for 2012. . 46

4.4 Errors and hourly correlations in wind energy production in Swedenbetween the model data utilizing all the grid points in Sweden withequal 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 2015profiles and 2040 profiles. Positive values meaning higher valuefactors for the 2040 profiles. . . . . . . . . . . . . . . . . . . . . . . 56

xi

Abbreviations

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

Chapter 1

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

1

Chapter 1. Introduction 2

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


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


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 6 will summarize the results

and conclusions from the previous chapters and give some ideas of possible future

studies.

Chapter 2

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

5

Chapter 2. Wind Power Modeling 6

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


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.


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


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 Kraftnat [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


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

two years.

SE1 SE2 SE3 SE4SE 0.500 0.641 0.922 0.803SE1 1 0.758 0.311 0.121SE2 1 0.447 0.229SE3 1 0.667SE4 1

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

SE1 SE2 SE3 SE4SE 0.558 0.699 0.931 0.772SE1 1 0.768 0.352 0.095SE2 1 0.496 0.172SE3 1 0.736SE4 1

Table 2.2: Hourly correlation in wind power production between Swedish priceregions 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 Kraftnat,

it is possible to look at the wind power production distribution for each price

region. Figure 2.2 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.


MWh/h0 100 200 300 400 500

Pro

babi

lity

0

0.002

0.004

0.006

0.008

0.01SE1

MWh/h0 200 400 600 800 1000 1200 1400

Pro

babi

lity

×10-3

0

0.5

1

1.5

2

2.5

3SE2

MWh/h0 500 1000 1500 2000

Pro

babi

lity

×10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6SE3

MWh/h0 200 400 600 800 1000 1200 1400

Pro

babi

lity

×10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8SE4

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

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.


Production [MWh/h]0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pro

babi

lity

×10-4

0

1

2

3

4

5

6

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

Chapter 3

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) =

∫ b

a

f (x) dx (3.1)

where f (x) >= 0 and∫∞−∞ 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

(xc

)k−1e(−(x

c ))k

(3.2)

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

13

Chapter 3. Theory 14

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, x 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, x) =1

N

N∑i=1

|xi − xi| . (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, x) =

√√√√ 1

N

N∑i=1

(xi − xi)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 =

∑Ni=1 (xi − x) (yi − y)√∑N

i=1 (xi − x)2√∑N

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 =

√∑ni=1 (xi − x)2

n− 1. (3.6)


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.


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.


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 Figure 3.2. 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


Figure 3.1: Diagram of installed power plants and hydro reservoirs of a typicalriver 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


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


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 −RRmax

· 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


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,


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.


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− vp1

)+ 1

)(exp

(v − coutp2

)+ 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, cout sets the cut out wind speed, p1 and p2 are shape

parameters. The four parameters can be set by creating an optimization problem


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 = (pᵀt) / (tᵀt) (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 = (pᵀg) / (gᵀt) (3.11)


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 pᵀg is the annual revenue and gᵀt 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.

Chapter 4

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

Chapter 4. Creating Wind Energy Production Series for the Current Situation inthe Nordic Countries 28

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. Figure 4.1 shows 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


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 Chapter 3.3.1.

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


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.


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

Kraftnat. 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


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.

Figure 4.4 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.


Wind Speed [m/s]0 5 10 15 20 25 30

Cap

acity

util

izat

ion

fact

or

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


Production [MWh/h]

0 500 1000 1500 2000 2500 3000

Pro

babl

ity

#10-3

0

0.5

1

1.5

2

2.5

3

PDF SE3 With Generic Power Curve

TSOModel

Figure 4.4: Comparison of PDFs in SE3 between the model data with ageneric 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


Time [h]1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

Pro

duct

ion

[MW

h/h]

0

500

1000

1500

2000

2500

3000

3500SE3 Generic Power Curve

TSOModel

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

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


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

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

k =

∑ETSO∑EModel

. (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.


Figure 4.7: Wake effect visible at the offshore wind park Horns Rev near thecoast of Denmark. Photo courtesy: Vattenfall Wind Power.

Wind Speeds 1

Wind Speeds 2

Wind Speeds n

Power Curve

Weighting and

summing

Scaling to TSO data

Optimal parameters

?

No

Yes

Final wind energy production series

Adjust parameters

Figure 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.


Production [MWh/h]0 200 400 600 800 1000 1200 1400 1600

Pro

babi

lity

#10-3

0

0.5

1

1.5

2

2.5PDF SE3 With Optimized Power Curve

Figure 4.9: Comparison of PDFs in SE3 between the model data with anoptimized power curve and TSO data.

4.3 Results

Here the results from the comparison between the created wind energy produc-

tion series and historical data are presented. The model is compared against year

2012 to give a more fair verification since it was trained to year 2013. The results

are presented for each Nordic country with statistical evaluation of the error met-

rics MAE (3.3), RMSE (3.4) and correlation (3.5) and comparing the standard

deviation (3.6), median, minimum and maximum value as well as the interquar-

tile range. These results are presented in Table 4.1 for FI, NO, DK1, DK2 and

DK which is the aggregated wind energy production series for Denmark. The

MAE and RMSE are given in percent of the installed capacity in the region. The

Swedish results are presented in Table 4.2. The hourly error distributions are also

presented in histograms where there in each figure are the same number of bars

and the same scale on the error axis to help to make the comparison.


Time [h]1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

Pro

duct

ion

[MW

h/h]

0

200

400

600

800

1000

1200

1400

1600SE3 Optimized Power Curve

Figure 4.10: Comparison of hourly production for SE3 with an optimizedpower curve.

4.3.1 Denmark

Figure 4.11 shows the hourly error distribution between the model and TSO data

for 2012. As mentioned before, matching the PDFs of the modeled data and the

historical data is important to get a good match of the statistical metrics shown

in Table 4.1. Figure 4.12 shows the PDF of the model data and the historical data

for Denmark using 2012 data.

4.3.2 Finland

Figure 4.14 shows the error distribution for Finland and Figure 4.13 shows the

comparison between the PDF of the model and TSO data.


DK DK1 DK2 FI NOMAE 4.1% 4.5% 5.8% 6.3% 6.7%RMSE 5.7% 6.1% 8.3% 8.6% 9.0%r 0.965 0.959 0.949 0.91 0.837SD [MWh/h]Model 856.5 618.5 265.1 49.9 111.2TSO 876.2 652.4 260.9 43.5 109.2Median [MWh/h]Model 953.5 674.9 239.9 38.0 147.0TSO 946.1 680.5 253.2 44.6 153.3Max [MWh/h]Model 3634 2659 975 217 507TSO 3773 2799 975 183 570Min [MWh/h]Model 4.3 4.1 0.0 2.6 10.1TSO 0.0 0.0 0.0 0.3 0.5IQR [MWh/h]Model 1256 889 421 62.4 168TSO 1316 959 434 66.3 169

Table 4.1: Comparison between model data and historical data for Denmark,Finland and Norway 2012.

Error [p.u.]-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Cou

nt

0

100

200

300

400

500

600

700

800

900

1000

Figure 4.11: The error distribution for the modeled wind energy productionduring 2012 for Denmark compared to historical data from the TSO.


SE SE1 SE2 SE3 SE4MAE 2.7% 4.5% 6.6% 4.3% 3.4%RMSE 3.6% 6.4% 8.8% 5.8% 4.5%r 0.961 0.855 0.895 0.950 0.949SD [MWh/h]Model 505.6 54.8 103.7 253.4 203.4TSO 506.0 57.6 116.1 267.2 195.8Median [MWh/h]Model 731.5 45.8 117.0 311.8 193.6TSO 745.5 47.1 113.4 316.4 199.7Max [MWh/h]Model 2539 228 469 1231 838TSO 2454 300 533 1179 936Min [MWh/h]Model 75.7 2.8 10.0 23.9 5.7TSO 27.0 0.0 0.5 1.8 0.6IQR [MWh/h]Model 713.2 74.3 145.3 377.2 299.5TSO 724.1 86.1 167.5 407.7 281.0

Table 4.2: Statistical data comparing the model data with the TSO data forSweden 2012.

Production [MWh/h]0 500 1000 1500 2000 2500 3000 3500 4000

Pro

babi

lity

#10-4

0

1

2

3

4

5

6

7

8

TSOModel

Figure 4.12: PDFs of the modeled wind energy production during 2012 forDenmark and historical data from the TSO.


Production [MWh/h]0 50 100 150 200 250

Pro

babi

lity

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

TSOModel

Figure 4.13: PDFs of the modeled wind energy production during 2012 forFinland and historical data from the TSO.

4.3.3 Norway

In Norway, there was a problem finding historical wind production data on a price

region level. There were only historical data available for the larger wind parks.

Also the wind energy production series were created for regions that are different

from the Norwegian price regions which would make it difficult to compare on price

region basis. The results for Norway are for these reasons presented on a country

level, where the historical data for the entire Norway was created by aggregating

all the historical wind production series for the wind parks. Figure 4.15 shows the

comparison between the PDF of the model data and the PDF of the historical

data. Figure 4.16 shows the error distribution for Norway.

4.3.4 Sweden

The Swedish results are presented in Table 4.2 for all the price regions as well as

total Sweden. Figure 4.17 shows the PDFs of Swedish model data and historical

data. Figure 4.18 shows the error distribution between the two series.


Error [p.u.]-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Cou

nt

0

200

400

600

800

1000

1200

Figure 4.14: The error distribution for the modeled wind energy productionduring 2012 for Finland compared to historical data from the TSO.

4.3.5 Perfect Distribution

Results for the case of perfect distribution, meaning utilization of every grid point

within a country with equal weights, are presented below for all the Nordic coun-

tries except Denmark. Table 4.3 shows the errors and the correlation for Finland

and Norway during 2012 between the model data assuming perfect distribution

and the historical data with the number within the parenthesis representing the

difference in percentage points when comparing to the model data using weighted

distribution as shown in the results above. In Table 4.4 the same results are shown

for Sweden and its price regions.

Figure 4.17 shows the distribution curves for Sweden where the grid points are

chosen to match current installed wind parks and the other where all grid points

of Sweden are used. The same comparison is done for Norway in Figure 4.15.

Denmark already has installed wind parks at each grid point which is why it is

not shown here.


Production [MWh/h]0 100 200 300 400 500 600

Pro

babi

lity

#10-3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

TSOModel

Figure 4.15: PDFs of the modeled wind energy production during 2012 forNorway and historical data from the TSO.

Error [p.u.]-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Cou

nt

0

200

400

600

800

1000

1200

Figure 4.16: The error distribution for the modeled wind energy productionduring 2012 for Norway compared to historical data from the TSO.


Production [MWh/h]0 500 1000 1500 2000 2500 3000

Pro

babl

ilty

#10-3

0

0.2

0.4

0.6

0.8

1

1.2

TSOModel

Figure 4.17: PDFs of the modeled wind energy production during 2012 forSweden and historical data from the TSO.

Error [p.u.]-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Cou

nt

0

100

200

300

400

500

600

700

800

900

Figure 4.18: The error distribution for the modeled wind energy productionduring 2012 for Sweden compared to historical data from the TSO.


FI NOMAE 6.2% (-0.1) 5.0% (-1.7)RMSE 8.1% (-0.5) 6.6% (-2.4)r 0.889 (-2.3%) 0.918 (-9.7%)

Table 4.3: Errors and hourly correlations in wind energy production in Finlandand Norway between the model data utilizing all the grid points with equal

weight factors and historical production data for 2012.

SE SE1 SE2 SE3 SE4MAE 3.0%(+0.3) 5.1%(+0.6) 6.9%(+0.3) 5.1%(+0.8) 3.4%(+0.0)RMSE 3.9%(+0.3) 7.3%(+0.9) 9.2%(+0.4) 6.8%(+1.0) 4.6%(+0.1)r 0.953(-0.8%) 0.822(-3.9%) 0.886(-1.0%) 0.931(-2.0%) 0.952(+0.3%)

Table 4.4: Errors and hourly correlations in wind energy production in Swedenbetween the model data utilizing all the grid points in Sweden with equal weight

factors and historical production data for 2012.

Figure 4.19 to 4.21 show the PDF of the model data for wind energy production

compared with the PDF of the model data with perfect distribution for Finland,

Norway and Sweden.

4.4 Discussion

Looking at the performance of the model shown in Table 4.1 and 4.2 in terms

of correlation, error, and statistical metrics the wind series are very capable of

describing the current installed wind turbine fleet in the Nordic countries. The fit

of the PDFs in Figure 4.12, 4.15 and 4.17 confirms this. The only PDF that did

not seem to fit well with historical data was the PDF of the Finnish wind energy

production shown in Figure 4.13. A small wind turbine fleet for 2012 and training

the model to 2013 data where further big installations in wind power capacity was

made might be the explanation. High correlations were reached in each country,

with some regional variations that might be explained by turbulent wind areas

that the meteorological model does not capture, or very low amount of installed

wind power in a region which makes it harder to model with accuracy.

We can see that the minimum production are a bit too optimistic compared to

TSO data. This effect could be due to the smooth power curve which does not

have a value of zero below e.g. 3 m/s but has a small value which with large

amount of installed capacity might lead to almost 50 MWh too high production.


Production [MWh/h]0 50 100 150 200 250

Pro

babi

lity

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

ModelModel utilizing every grid point

Figure 4.19: PDFs of the modeled wind energy production during 2012 forFinland and the modeled wind energy production for 2012 utilizing all grid

points in the country with equal weight factors.

A contribution to the error could also come from the fact that the model does not

take into account possible temporary shutdown of wind turbines or complete wind

parks.

Looking at the error distributions for Denmark and Sweden in Figure 4.11 and

4.18 respectively shows a narrow band for the errors, especially for Sweden. These

errors are more widely distributed for Finland and Norway shown in Figure 4.14

and 4.16.

The most difficult country to model is according to Table 4.1 Norway. It has

the highest errors and the lowest correlation. Looking at the error distribution for

Norway in Figure 4.16 it is also clear that Norway has the widest error distribution.

There is quite a good fit for the PDF of the model as shown in Figure 4.15. The

rough terrain in Norway as well as the long shoreline towards the sea might make

it hard for the ERA-Interim model to capture the correct wind speeds. Another

explanation is also that the historical data for Norway might not be completely

reliable, it is only the best available data that was found. This leaves an open end


Production [MWh/h]0 100 200 300 400 500 600 700

Pro

babi

lity

#10-3

0

1

2

3

4

5

6

ModelModel utilizing all grid points

Figure 4.20: PDFs of the modeled wind energy production during 2012 forNorway and the modeled wind energy production for 2012 utilizing all grid


which makes it hard to determine if it is the model that is performing poorly or

if it is only the verification that is the troublesome part. Perhaps in the future

Norway will release historical data that has the resolution of one series per price

region.

An improvement to the model would be to look at the connections of the wind

parks. If a wind park is in price region 1 on the border to region 2 it is counted

as being part of region 1. However, if the wind park has its connections going to

a substation in region 2 it should be counted as belonging to region 2.

Another limitation is that the ERA-Interim dataset, as with all reanalysis models,

cannot capture details of topology as in mountainous regions. If a grid point

is located in an area with complex terrain the wind speeds are most probably

underestimated, since in reality the wind turbines would be placed at a location

chosen for its favorable local wind conditions.


Production [MWh/h]0 500 1000 1500 2000 2500 3000

Pro

babi

lity

#10-3

0

0.2

0.4

0.6

0.8

1

1.2

ModelModel utilizing all grid points

Figure 4.21: PDFs of the modeled wind energy production during 2012 forSweden and the modeled wind energy production for 2012 utilizing all grid


Seeing the effects of using all the grid points in an area versus only a few proved to

increase the errors for Sweden as seen in Table 4.4. However, the errors were not

that much larger meaning that Sweden already has fairly well distributed wind

power production and might not need to focus on increasing the geographical

distribution, if not other effects such as transmission constraints are taken into

account. We can also see that there are close to no difference in SE4. In SE4 all the

grid points are currently already used in the model and the wind power generation

are well distributed among the grid points. The two datasets for Sweden are

correlated to 95.3 % and had distribution curves that were almost perfect matches

as shown in Figure 4.21. This could be seen as a simulation that if Sweden would

have had a perfect distribution of wind power in the country we would see the same

effect as we have observed here. For Norway, the distribution curves are also very

similar as shown in Figure 4.20. It is a big difference in the maximum production

for which there is a small probability of production in the range 500-600 MWh in

the series assuming perfect distribution. If we on the other hand look at the PDFs

for Finland shown in Figure 4.19 one can see a big difference if using every point


versus only the few where current capacity is installed. The reason could be that

Finland at this point in time does not have a lot of wind power installed, hence

very few grid points in the first dataset. A simple conclusion that could be drawn

from this is that Finland would benefit the most to try to distribute their wind

power production geographically much more than they have at current stage. The

benefit is due to the peak of the PDF is shifting to the right which gives a higher

expected wind power production.

What is also most interesting are the results shown in Table 4.3. There the errors

actually decrease with the assumption of perfect distribution. The correlation gets

lower on the other hand, but still these are interesting results. For Norway there

is quite a large decrease in the error which might make it better to use the series

with perfect distribution. These results are taken into account for creating the

future wind energy production series described in the next chapter.

Chapter 5

Making the Future Wind Series

5.1 Future Trends in Wind Turbine Technology

To create wind series that represent the future wind energy production, one of the

things that are necessary to look at is the future wind turbine technology. A clear

pattern that can be seen when looking at trends in wind technology is that the

blades of the wind turbines have been increasing in length the last decades. There

are several reasons for this. One reason is to be able to install capacity at regions

with lower wind speeds that are located closer to where the demand is, since longer

blades capture more wind energy and therefore can produce electricity for lower

wind speeds. A second reason for this is that the blades reach winds higher up in

the air which usually have higher speed and are less turbulent than winds at lower

altitudes. One would also think that by increasing the blade length that the wind

turbines cover a larger area and can extract more energy from the wind for each

wind park. This is only partly true for a wind park. The power per wind turbine

can be described as

Power per turbine = CBetz1

2ρv3

π

4d2, (5.1)

where CBetz = 16/27 is the Betz limit, ρ is the air density, v the wind speed and

d the rotor diameter. Here it is clear that the power per turbine increases with

the rotor diameter. There are though some limitations to increasing the rotor

diameter of all the wind turbines at a wind park. To not have significant power

loss in a wind park coming from wind-shadow effects the rule of thumb is to place

51

Chapter 5. Making the Future Wind Series 52

the wind turbines at least 5 times their diameter from each other in the prevailing

downwind direction and 2-5 rotor diameters in the crosswind direction [24]. In

the following example the turbines are spaced 5 rotor diameters away in both the

downwind and crosswind direction. This means that each wind turbine uses (5d)2

of land area. Combining this with (5.1) we get

Power per turbine

Land area per turbine=CBetz

12ρv3 π

4d2

(5d)2=CBetz

12ρv3 π

4

25(5.2)

which is independent of the rotor diameter [25]. This means that each wind

turbine per land area unit should not produce more power from increasing the

rotor diameter, but still they do due to the fact that they can reach the winds at

higher altitude. Having a larger rotor diameter can also result in a higher capacity

factor by faster reaching their rated power for lower wind speeds, i.e.the same as

shifting the power curve to the left. They might still have the same maximum

capacity, if the same turbine is used, but will have higher Full Load Hours (FLH).

And given that winds are not very regular, the total efficiency is increased.

What also is important to consider when looking at trend in blade lengths is the

cost side. Costs for operating and maintaining one larger wind turbine is lower than

operation and maintenance for several smaller ones. However, the installation cost

of a large wind turbine is usually much higher than that compared with installing

smaller turbines. The transportation costs are higher since the blades are made

in one piece and require vehicles and roads able to transport them. Recently

blades has started to be sent piecewise and put together at the wind park site.

Manufacturing costs are also higher since this kind of large objects require special

machines and manufacturing techniques. The fundament must be larger to be

able to hold larger mass and handle higher forces since the towers are catching

more wind and gets a larger momentum due to increased height. All in all one can

say that the blade length will increase in the future simply because it is already

increasing. The reason why it is increasing is because the demand for them is

high, meaning that investors find it profitable.

This chapter describes how the future wind series are created. The year that the

future wind series are representing is the year 2040. The 2040 wind series are

used in the simulation together with the current 2015 wind series by adjusting

the weight factor of the two so that year 2015 uses 100% 2015 wind series and

decreases each year until the year 2040 where the 2015 wind series have 0% weight


and the 2040 wind series have 100% weight. At the end of the chapter the impact

of the 2040 series is evaluated in an EMPS simulation by comparing the simulation

result when scaling from 2015 wind series to 2040 wind series and by only using

the 2015 wind series.

5.1.1 Capacity Factor

A term that is constantly brought up when deciding which wind turbine to use at

a future wind park is the capacity factor. The capacity factor tells the percentage

of rated power that the wind turbine delivers over the course of a year. It is

calculated as CF = Average powerRated peak power

where Average power = Energy productionAmount of hours

. The

capacity factor is of course mainly dependent on the wind resources at the location

of the wind turbine, but the power curve of the wind turbine is also of great

importance and will have a big impact on the power output.

In Global Wind Energy Outlook 2014 from GWEC and Greenpeace [26] it is stated

that the average capacity factors globally today are about 28 %, varying widely

from region to region. It is also assumed that they will stay at the same value

until 2030 after which they are assumed to rise to 30 %. They are however stating

that in reality the capacity factors will probably be greater than that value.

It is worth noticing that a capacity factor of 100 % is not something to strive for.

Since the wind is varying that would mean the generator is under-dimensioned.

Think as an example of having a very large rotor of 150 m in diameter with a very

small generator, e.g. an dynamo found on bicycles. This setup would probably

have a capacity factor of 100 %, but it would not be profitable since the small

generator would produce such low quantities of electricity that the payback for the

investment would be too small. The costs could have been reduced by decreasing

the rotor size, even if that means the capacity factor goes down. It is important not

to make the confusion between having a high capacity factor and a high efficiency.

On the other hand a very low capacity factor would not be good either, since it

implies that the generator is over-dimensioned in relation to the wind speeds and

rotor size. This means that the turbine will not produce for most of the hours it is

used, which leads to smaller revenues due to zero production the majority of the

time.


5.1.2 Wind Value Factor

Looking at the trends for the wind value factors there is typically a negative trend.

This is the result of that wind power cannibalizes its own profit [27]. It means

that the more wind power that is installed in a system the lower the market price,

which in turns lowers the profit. This is of course true for every market when the

production of a good is increased, but there is a difference for variable renewable

energy sources. The difference is that wind is typically highly correlated within

e.g. a price region meaning that when a wind turbine is producing and has a

chance to make profit, then most probably all the other wind parks in that region

is producing simultaneously and giving a large boost in energy production. Due

to wind having a negligible marginal cost of energy the market price decreases

rapidly and hence also the profit for that wind turbine. And as the wind speeds

gets lower the market price increases with the decrease of wind power production.

The wind value factors described in Chapter 3 can be used to describe this effect.

5.2 Method for Creating Future Wind Series

The method is a bit different for the future wind series. The chosen grid points’

wind speeds are not weighted individually inside the price regions but all grid

points receive an equal weight factor of 1.0. One reason for this is due to the

results in Chapter 4 but also the uncertainty of estimating capacity for future

wind parks would be too high, hence a uniform capacity distribution is chosen

where each future wind park’s wind speed will have an equal impact on that price

region’s wind series. The wind speed altitude for the 2040 profiles is 120 m since

larger rotor blades require a higher tower with a higher hub height. The wind

speeds are also for the 2040 profiles acquired from ERA-Interim.

5.2.1 Choosing Grid Points

In 2040, all the current installed wind turbines will be phased out. Assuming

that wind power will still be an attractive energy source, then current wind parks

will most probably still be used but with new wind turbines or with the old wind

turbines repowered. Apart from the current wind parks new ones will also be

built at other locations, further increasing the distribution of the wind parks. As


seen in the results in Chapter 4 an increased distribution of wind power will not

provide a big difference from the current situation. Therefore every grid point in

Sweden is part of the 2040 wind series. If one looks at northern Finland instead

it is a rather big difference from the current situation to utilize every grid point

in the 2040 wind series. Given the results from Chapter 4 it shows that northern

Finland converges quickly to be close to the perfect geographical distribution by

only utilizing a few more grid points in the simulation. This result is the basis

for also using every grid point for Finland and Norway part of the 2040 wind

series. As said before Denmark already utilizes every grid point for the current

wind series.

5.2.2 Choosing the Power Curve

The aim for choosing a future power curve is to have a higher capacity factor

somewhere near 0.35. Denmark had a capacity factor of 0.31 for 2014, Finland

0.27, Norway 0.31 and Sweden 0.27 [28]. Vestas V136 [29] was used as a typical

future low wind speed wind turbine and for regions where it gave too low or high

capacity factor, the power curve was adjusted by changing c in (3.9) to get a

resulting capacity factor of 0.35.

The other parts of the process to create future wind series are done analogously

to the method of producing the wind series for the current situation in Chapter 4.

5.3 Results

Table 5.1 shows descriptive statistics for the 2040 wind series as well as the statis-

tics for the wind series describing the current situation.

Figure 5.1, 5.2, 5.3 and 5.4 shows the comparison of the 2015 and 2040 PDFs for

Denmark, Finland, Norway and Sweden respectively for the wind year 2012.

5.3.1 Effect on Value Factors

The results from the EMPS simulation is shown in Table 5.2 where the difference in

the wind value factors between the 2015 wind series and the wind series that scales


DK FI NO SESTD2040 series 882.6 36.62 103.0 511.82015 series 856.5 49.9 111.2 505.6Median2040 series 986.7 49.1 159.1 746.42015 series 953.5 38.0 147.0 731.5Max2040 series 2813 154 454 22282015 series 3634 217 507 2539Min2040 series 3.2 1.0 6.7 17.92015 series 4.3 2.6 10.1 75.7IQR2040 series 1601 54.2 158 7832015 series 1256 62.4 168 713

Table 5.1: Statistical data for the 2040 series compared with the 2012 series.All values have the unit MWh/h.

the 2015 series to the 2040 series are presented. The numbers are in percentage

points with positive values meaning higher value factors for the 2040 profiles. Note

that the wind series that scales the 2015 series to the 2040 series is almost 100%

weighted to the 2015 series for year 2016 and for the years 2040 to 2050 completely

consisting of the 2040 series.

DK1 DK2 FI NO SE1 SE2 SE3 SE42016 +0.10 +0.06 +0.08 +0.26 +0.01 +0.00 +0.00 +0.002020 +0.89 +0.75 +0.28 +0.61 +0.04 +0.02 +0.03 +0.032025 +0.90 +1.81 +1.02 +0.94 +0.16 +0.13 +0.27 +0.532030 +0.98 +2.72 +2.07 +1.43 +0.35 +0.27 +0.52 +1.092035 +0.91 +3.68 +3.35 +2.80 +0.36 +0.23 +0.70 +1.792040 +0.62 +3.93 +4.18 +2.54 +0.41 +0.12 +0.69 +2.042045 -0.19 +3.88 +5.74 +2.20 +0.29 -0.15 +0.35 +1.802050 -0.44 +4.36 +7.02 +2.11 +0.29 -0.25 +0.15 +1.70

Table 5.2: Difference in percentage points for value factors when using 2015profiles and 2040 profiles. Positive values meaning higher value factors for the

2040 profiles.

5.4 Discussion

It is clear from Table 5.1 and the figures that the 2040 wind series seem to have

a big impact on the wind energy production. Remember that the two series are


Production [MWh/h]0 500 1000 1500 2000 2500 3000 3500 4000

Pro

babi

lity

#10-3

0

0.2

0.4

0.6

0.8

1

1.2

2015 Model2040 Model

Figure 5.1: PDFs of the modeled wind energy production during 2012 forDenmark using the 2015 profiles and the 2040 profiles.

scaled to have equal annual energy production. With this in mind it is interesting

to see that the median production is higher for the 2040 series in all of the countries.

The mean production is equal per definition since the two wind series have the

same annual energy production. We can also see that the maximum production

is much lower for the 2040 series. This indicates that a lower amount of installed

capacity can give rise to the same amount of annual energy.

If we look at the PDFs for Denmark shown in Figure 5.1 we see that the 2040

model produce at maximum capacity for a much larger share of the time than the

2015 model. The curves look very different and here the only change is the power

curve since geographical distribution is almost the same.

In Finland there is clearly a large difference between the 2015 model and the 2040

model as shown in Figure 5.2. We see that the production is less variable with

a much smaller range between minimum and maximum production. One can say


Production [MWh/h]0 50 100 150 200 250

Pro

babi

lity

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Model2040 Model

Figure 5.2: PDFs of the modeled wind energy production during 2012 forFinland using the 2015 profiles and the 2040 profiles.

that the PDF for Finland in the 2040 model has a very similar shape to the PDF

of Sweden in the 2015 model. In this case the large impact in the change of the

PDF is not only due to the change in the power curve but due to the geographical

expansion of installed wind capacity as seen already in Figure 4.19.

For Norway, the change in the PDF is rather small which is shown in Figure 5.3.

We can see that the maximum production has decreased some 10 % but the shape

is almost the same having a slight shift to the right since the median production

has increased about 8 % with a constant mean value. For some regions in Norway,

the assumption to have a capacity factor of 0.35 was too low since in the very south

and very north the value factor was already higher than that. It could though be

possible that those regions will get a lower capacity factor in the future since the

currently installed wind power fleet in those regions are concentrated to locations

with very high mean wind speeds. Expanding the wind power production at more


Production [MWh/h]0 100 200 300 400 500 600

Pro

babi

lity

#10-3

0

1

2

3

4

5

6


Figure 5.3: PDFs of the modeled wind energy production during 2012 forNorway using the 2015 profiles and the 2040 profiles.

locations where the mean wind speeds are lower could then decrease the average

capacity factor in the region.

Sweden has not had a big change is the PDF shape either as shown in Figure 5.4.

There is a 12 % decrease in maximum production while the median production

has increased about 2 %, which shifts the weight of the PDF to the right. The

difference should mostly come from the changed power curve but the increased

amount of grid points might also affect the result in a negative way since these

new grid points could on average have less beneficial wind conditions, in other

words there might be a reason why these areas have no installed wind power.

There are some interesting results when looking at the wind value factors for

the different countries shown in Table 5.2. What is expected is the increase of

the wind value factors for Finland, since its wind power production becomes much

less variable due to increased geographical distribution and thereby should capture


Production [MWh/h]0 500 1000 1500 2000 2500 3000

Pro

babi

lity

#10-3

0

0.2

0.4

0.6

0.8

1

1.2


Figure 5.4: PDFs of the modeled wind energy production during 2012 forSweden using the 2015 profiles and the 2040 profiles.

the average market price better. For Denmark this result is also expected but

for another reason since the geographical distribution is almost unchanged. That

reason is the higher capacity factors for the wind power production which increases

the FLH and gives a less variable power output. Norway benefits from the increase

in capacity factors in the 2040 series as well, which is clear from the from the

increase in value factors. Even if the some regions in Norway got a lower capacity

factor most of the regions increased their capacity factor.

In Sweden however, the wind value factors barely change when the 2040 series are

used. This was not expected since the turbines gets more efficient for low wind

speeds which should be beneficial for the profitability of the wind production.

What could be an explanation is that assuming perfect distribution means that

the new wind sites that are added to the 2015 series are typically worse for wind

power production than the wind sites currently in use. For SE4 however, the wind

value factors increase quite a lot. A possible explanation is that since there is


already an almost perfect distribution in the 2015 model the only difference is the

improved power curve and the effect of adding more grid points with less beneficial

wind conditions is not present. The same goes for Denmark and especially DK2

which shows the largest increase in value factors. What is odd is that the value

factors for DK1 does not increase at all but actually decreases with a small number

for years 2045-2050. An explanation to why DK1 and DK2 get a big difference

could be due to the fact that the export for DK2 is saturated at certain times

when simulating with the 2015 profiles. The 2015 and 2040 profiles are scaled to

produce the same amount of energy in both simulations, but as seen in Figure 5.1

the maximum production is much lower, which would decrease export pressure on

the interconnectors when the 2040 profiles are used.

Chapter 6

The Finished Wind Profiles

6.1 Summary

This project was about modeling the future wind power production for the Nordic

countries by creating two sets of wind energy production series to be used in

simulations up until year 2040.

First the EMPS model and the ERA-Interim meteorological model was studied

which were the two important external models in this project. These two models

were described in Chapter 3 which was also the first objective in the project.

One set of wind series was created for the current situation, the so called 2015

series, which was the second objective. The 2015 wind series were created based

on the geographical location of the wind parks, the wind parks’ current installed

capacity and historical wind speed data from the meteorological model ERA-

Interim. The wind series performed well, particularly for Sweden and Denmark

which are the countries with the largest wind power capacity. The most difficult

country to model was Norway, which is represented in the results. The Norwegian

landscape has a lot of mountains and a long shoreline to the sea which mainly

impacts the meteorological model data which is the input data to this model. An

important reason for wanting to create new wind series was to try and capture

the correlation between the Nordic countries and the continent. These wind series

were verified against historical production data as described in Chapter 4 which

fulfilled the third objective.

63

Chapter 6. The Finished Wind Profiles 64

The fourth objective was to create second set of wind series to represent the

installed wind power system in the year 2040. To be able to do this the future wind

technology had to be incorporated into the model which was done by changing

the power curve and assuming a higher capacity factor for the installed wind

turbines. The second assumption that had to be made was to estimate the future

geographical wind capacity distribution. The assumption was that geographical

distribution would increase and finally a perfect distribution of wind capacity was

assumed.

The differences between the two wind series were evaluated and finally two EMPS

simulations were performed where one only used the first set of wind series and

the second simulation used a mixture of the first set and the second set by scaling

from the first set to the second from 2015 to 2040. The outcome turned out to give

higher wind value factors for when using the mixture of the first and second set of

wind series. Meaning that there is a need to take technological development and

future geographical distribution of the wind turbines into account. The EMPS

simulation was the fifth and final objective for this thesis.

6.2 General Conclusions

From the results in Chapter 4 it is clear that the model has high correlation to

historical data. It also gives low errors for most countries, where it seem to capture

the Swedish wind power production best and Norway is the hardest country to

model. We can also see that the PDFs between the model data and the historical

data match well for most regions. Here Finland has the largest mismatch in the

PDF which might be due to a small wind turbine fleet in the country where regional

effects at the wind park sites can have a large impact on the total production of

the whole Finland.

The perfect distribution test provided some results that made the future series use

all the grid points within a country for the year 2040. Whether or not this is the

accurate way to do it is not possible tell but it seemed that it would be a reasonable

way to do it when looking at the trend in geographical expansion in wind power

installations. In Sweden for example, the PDFs did not change and the errors only

increased a little when assuming perfect distribution. This was interpreted as once

wind power capacity is distributed over almost all regions in a country, without


using all the grid points, one can model it as a perfect geographical distribution

of wind capacity without almost any difference in the result.

From Chapter 5 it was concluded from the results that the 2040 series change

the PDF especially for Finland and Denmark, while Sweden and Norway kept the

same PDF shape. If Finland would expand its wind power geographically the PDF

would have a very similar shape to Sweden’s PDF. The system got more efficient

meaning that the same annual wind energy production was achieved with lower

installed capacity as could be seen most clearly in Figure 5.1.

The wind value factors of all countries increased with the exception of DK1 and

SE2. The largest increase was in DK2 and Finland, where Finland most probably

benefited from increased geographical distribution and Denmark from an increased

capacity factor.

6.3 Future Studies

The experience from this project has shown that there are some things that could

be further investigated or improved. One thing that could be done is to inter-

polate the grid point data so that there are wind speeds available at any specific

geographical point instead of having to locate the grid point to the closest grid

point, which could be up to 57 km away in case of the ERA-Interim grid resolution.

Another improvement that could be tested is to adjust the cut-in wind speed so

that the model better captures the minimum production as discussed in Chapter

4.

What might be of most interest to look further into is some sort of filtering method

of grid points. That grid points with a mean wind speed lower than a specific value

are filtered out. Which value should it be for Sweden and which value should it be

for Norway. Given that each country has different wind conditions this value will

most likely change. The value would represent the limit of mean wind speeds at

which investors would not find it profitable to install wind turbines in that area

but instead choose a site with higher wind speeds.

It would also make sense to investigate what capacity factor to use for each country,

or even region within a country. Since the different wind conditions will lead to

installation of wind turbines with different specifications that are optimized for


that site. This changes the power curve and the capacity factor. Perhaps some

relationship between the Weibull distribution of the wind and the installed power

curve could be found which could make the future wind series more accurate.

Bibliography

[1] Svensk Energi. Elaret 2014. page 33. URL http://www.svenskenergi.

se/Global/Statistik/El%C3%A5ret/El%C3%A5ret%202014_slututg%C3%

A5va.pdf.

[2] Svensk Vindenergi. Historic hourly wind energy production, 2015.

URL http://www.vindkraftsbranschen.se/start/vindkraft/

fragor-och-svar-om-vindkraft/.

[3] VTT. Wind energy statistics in Finland. URL http://www.

vttresearch.com/services/low-carbon-energy/wind-energy/

wind-energy-statistics-in-finland.

[4] EWEA. Wind energy scenarios for 2030. page 15. URL www.ewea.org/

publications/reports/wind-energy-scenarios-for-2030/.

[5] Jon Olauson and Mikael Bergkvist. Modelling the Swedish wind power pro-

duction using MERRA reanalysis data. Renewable Energy, 76:717–725, 2015.

[6] Wind Energy Foundation. History of wind energy. URL http:

//windenergyfoundation.org/about-wind-energy/history/. Accessed:

2016-01-04.

[7] Vestas. Vestas v90-3.0 mw, . URL https://www.vestas.com/en/products_

and_services/turbines/v90-3_0_mw#!facts. Accessed: 2016-01-04.

[8] WindPower Program. Wind turbine power ouput variation with

steady wind speed. URL http://www.wind-power-program.com/turbine_

characteristics.htm. Accessed: 2016-01-04.

[9] KTH Stockholm Jan Grandell. Time series analysis. URL http://www.math.

kth.se/matstat/gru/sf2943/ts.pdf. Lecture notes, Accessed: 2016-01-10.

67

http://www.svenskenergi.se/Global/Statistik/El%C3%A5ret/El%C3%A5ret%202014_slututg%C3%A5va.pdf



http://www.vindkraftsbranschen.se/start/vindkraft/fragor-och-svar-om-vindkraft/

http://www.vindkraftsbranschen.se/start/vindkraft/fragor-och-svar-om-vindkraft/

http://www.vttresearch.com/services/low-carbon-energy/wind-energy/wind-energy-statistics-in-finland



www.ewea.org/publications/reports/wind-energy-scenarios-for-2030/

www.ewea.org/publications/reports/wind-energy-scenarios-for-2030/

http://windenergyfoundation.org/about-wind-energy/history/

http://windenergyfoundation.org/about-wind-energy/history/

https://www.vestas.com/en/products_and_services/turbines/v90-3_0_mw#!facts

https://www.vestas.com/en/products_and_services/turbines/v90-3_0_mw#!facts

http://www.wind-power-program.com/turbine_characteristics.htm

http://www.wind-power-program.com/turbine_characteristics.htm

http://www.math.kth.se/matstat/gru/sf2943/ts.pdf

http://www.math.kth.se/matstat/gru/sf2943/ts.pdf

Bibliography 68

[10] Nord Pool Spot. Bidding areas in the nordic countries. URL http://www.

nordpoolspot.com/How-does-it-work/Bidding-areas/. Accessed: 2016-

01-04.

[11] Joakim Widen. Correlations between large-scale solar and wind power in a

future scenario for Sweden. Sustainable Energy, IEEE Transactions on, 2(2):

177–184, 2011.

[12] Svenska Kraftnat. Historic hourly wind energy production. URL http://

www.svk.se/. Accessed: 2015-12-08.

[13] The EMPS model. SINTEF.

[14] Gerard L. Doorman. Hydro power scheduling. pages 78–132, 2010.

[15] DP Dee, SM Uppala, AJ Simmons, P Berrisford, P Poli, S Kobayashi, U An-

drae, MA Balmaseda, G Balsamo, P Bauer, et al. The ERA-Interim reanal-

ysis: configuration and performance of the data assimilation system. QJR

Meteorol. Soc, 137:553–597, 2011.

[16] MathWorks. Matlab, . URL http://mathworks.com/products/matlab/.

Accessed: 2015-11-26.

[17] MathWorks. Cubic spline data interpolation, . URL http://mathworks.

com/help/matlab/ref/spline.html. Accessed: 2015-11-26.

[18] NASA/Goddard Space Flight Center. Introduction to merra. URL http://

gmao.gsfc.nasa.gov/research/merra/intro.php. Accessed: 2016-01-08.

[19] Matthias Fripp and Ryan H Wiser. Effects of temporal wind patterns on the

value of wind-generated electricity in california and the northwest. Power

Systems, IEEE Transactions on, 23(2):477–485, 2008.

[20] Hans Stephenson. Valence of electric energy. Power Apparatus and Systems,

IEEE Transactions on, (1):248–253, 1973.

[21] Lion Hirth. The market value of variable renewables: The effect of solar wind

power variability on their relative price. Energy economics, 38:218–236, 2013.

[22] NVE. Wind park map. URL http://gis3.nve.no/link/?link=

vindkraftverk. Accessed: 2015-12-13.

http://www.nordpoolspot.com/How-does-it-work/Bidding-areas/

http://www.nordpoolspot.com/How-does-it-work/Bidding-areas/

http://www.svk.se/

http://www.svk.se/

http://mathworks.com/products/matlab/

http://mathworks.com/help/matlab/ref/spline.html

http://mathworks.com/help/matlab/ref/spline.html

http://gmao.gsfc.nasa.gov/research/merra/intro.php

http://gmao.gsfc.nasa.gov/research/merra/intro.php

http://gis3.nve.no/link/?link=vindkraftverk

http://gis3.nve.no/link/?link=vindkraftverk

Bibliography 69

[23] Y Wan, Erik Ela, and Kirsten Orwig. Development of an equivalent wind

plant power curve. In Proc. WindPower, pages 1–20, 2010.

[24] PDR Associates Energy Group. Locating wind turbines. URL http://www.

pdrassocs.com/wind.html. Accessed: 2016-01-08.

[25] TU Munich Jose A. Garrido. Renewable energy ph2160. Lecture notes.

[26] Global Wind Energy Council. Global wind energy outlook 2014. GWEC,

October, page 14, 2014.

[27] X&Y Partners. Cannibalization in renewable energies (part ii: Offshore, 2012.

URL http://thisisxy.com/sites/default/files/ficheiros_artigos/

xypartners_cannibalization_in_offshore.pdf. Accessed: 2016-01-08.

[28] IEA WIND. 2014 annual report. pages 94,108,156,172, 2015. URL http://

www.ieawind.org/annual_reports_PDF/2014/2014%20AR_smallfile.pdf.

[29] Vestas. Vestas v136, . URL https://www.vestas.com/en/products_and_

services/turbines/v136-_3_45_mw#!power-curve-and-aep. Accessed:

2015-12-30.

http://www.pdrassocs.com/wind.html

http://www.pdrassocs.com/wind.html

http://thisisxy.com/sites/default/files/ficheiros_artigos/xypartners_cannibalization_in_offshore.pdf

http://thisisxy.com/sites/default/files/ficheiros_artigos/xypartners_cannibalization_in_offshore.pdf

http://www.ieawind.org/annual_reports_PDF/2014/2014%20AR_smallfile.pdf

http://www.ieawind.org/annual_reports_PDF/2014/2014%20AR_smallfile.pdf

https://www.vestas.com/en/products_and_services/turbines/v136-_3_45_mw#!power-curve-and-aep

https://www.vestas.com/en/products_and_services/turbines/v136-_3_45_mw#!power-curve-and-aep

TRITA TRITA-EE 2016:034

ISSN 1653-5146

www.kth.se

Documents

Modeling the Future Wind Production in the Nordic Countries924504/FULLTEXT01.pdf · F or ar 2040 skapas en ny upps attning vindproduktionsserier d ar h ansyn tas till teknologisk