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IN

DEGREE PROJECT ENERGY AND ENVIRONMENT, SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2017

On the impact of wind power on

CO2 emissions in a power system

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Abstract

This master thesis is carried out at KTH Royal Institute of Technology in Stockholm the spring 2017. The project analyses the impact of wind power in a power system. A fictitious power system, created from the Nordic32 test system, is used for the analysis. The power sources in the test system are hydro power, nuclear power, CHP and wind power, resembling Swedish conditions. The power production planning in the system is solved as a mixed integer linear programming problem in GAMS with

hourly resolution. From the result of the planning problem calculations of CO2

emissions are carried out with Monte Carlo simulations. Different cases with differ-ent amounts of wind power installed in the test system are studied via a stochastic Markov model. The load model in the test system consists of hourly time series data for a specific day. Furthermore, challenges with wind power as a continuously varying power source are studied. These challenges are balance between production and consumption in the power system, excess of power etc.

The results show that increasing the wind power production results in a decrease

in CO2 emissions. This can be seen from the different simulations in the project.

However, the results show that increasing the wind power production means that the system becomes more sensitive to keep the power balance. Moreover, the discharge capacity and the efficiency of the hydro power plants are important factors in the test system.

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Sammanfattning

Detta examensarbete på masternivå är utfört vid Kungliga Tekniska högskolan våren 2017. Projektet analyserar påverkan av vindkraft i ett elkraftsystem. Ett fiktivt kraftsystem, skapat från testsystemet Nordic32, används för att utföra analysen. Kraftkällorna i systemet är vattenkraft, kärnkraft, kraftvärmeverk och vindkraft, liknande svenska förhållanden. Produktionsplaneringen i systemet är löst med blan-dad heltals- och linjärprogrammering i GAMS med timvis tidsupplösning. Från

re-sultatet av planeringsproblemet beräknas systemets CO2-utsläpp med Monte Carlo

simuleringar. Olika fall studeras med olika andel vindkraft installerad i testsys-temet via en stokastisk Markovmodell. Lastmodellen i testsystestsys-temet består av timvis tidsseriedata för en utvald dag. Vidare studeras utmaningar med vindkraften som en kontinuerligt varierande kraftproduktionskälla. Dessa utmaningar är balans mellan produktion och konsumtion i kraftsystemet, överskott av effekt etc.

Resultaten visar att ökad andel vindkraftproduktion resulterar i minskade CO2

-utsläpp. Detta kan ses från de olika simuleringarna i projektet. Emellertid visar resultaten att ökande andel vindkraftproduktion också innebär att systemet blir mer känsligt för att kunna upprätthålla effektbalansen. Dessutom är slukförmågan och effektiviteten i vattenkraftverken viktiga faktorer i testsystemet.

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Acknowledgements

I would like to express my thanks to my supervisor Mikael Amelin at the Depart-ment of Electric Power and Energy Systems, KTH Royal Institute of Technology, for enabling this master thesis. I would also like to thank Elin Dahlborg and Joakim Lönnberg at the department of Power Technology Research and Development, Vat-tenfall, for useful advice on how to develop the power system model in this project. Furthermore, I would like to thank Lennart Söder at the Department of Electric Power and Energy Systems, KTH Royal Institute of Technology, for being my ex-aminer. Last, but not least, I would like to thank friends and family for their encouraging support throughout the progression of the project.

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Abbreviations

CHP Combined heat and power

EU European Union

GAMS General Algebraic Modeling System HAWT Horizontal axis wind turbine

IPCC Intergovernmental Panel on Climate Change

LCA Life cycle analysis

PV Photovoltaic

SE1 Swedish electricity area 1

SE2 Swedish electricity area 2

SE3 Swedish electricity area 3

SE4 Swedish electricity area 4

TSO Transmission system operator

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Contents

1 Introduction 1

1.1 Background . . . 1

1.2 Aims and objectives . . . 3

1.3 Method . . . 4

1.4 Thesis disposition . . . 4

2 Theory 6 2.1 The Swedish power system . . . 6

2.1.1 The power grid . . . 6

2.1.2 Power system quality . . . 7

2.2 The Nordic electricity market . . . 8

2.3 Power system planning . . . 9

2.3.1 Time perspectives for planning . . . 9

2.3.2 Short-term planning for hours and days . . . 9

2.4 Energy sources and CO2 emissions . . . 10

2.5 Wind power . . . 11

2.5.1 Principals of wind power . . . 11

2.5.2 Properties of wind power . . . 12

2.5.3 History of wind power . . . 13

2.5.4 Wind power in Sweden . . . 14

2.5.5 Development of wind power in Sweden . . . 16

2.6 Hydro power . . . 16

2.6.1 Principals of hydro power . . . 16

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2.6.5 Hydro power as regulation power in Sweden . . . 19

2.6.6 Development of hydro power in Sweden . . . 21

2.6.7 Hydro power modelling for short-term planning . . . 22

2.7 Other power sources in Sweden . . . 23

2.7.1 Nuclear power . . . 23

2.7.2 Combined Heat and Power . . . 24

2.7.3 Condensing power . . . 24

2.7.4 Photovoltaic generation . . . 24

3 Test system 26 3.1 Model . . . 26

3.1.1 Hydro power and the river model . . . 28

3.1.2 Wind power model . . . 31

3.1.3 CHP model . . . 33

3.1.4 Nuclear power model . . . 33

3.1.5 Load model . . . 34

3.1.6 Optimisation model . . . 35

3.1.7 Data . . . 41

4 Results 49 4.1 CO2 emissions for the low wind case . . . 49

4.2 CO2 emissions for the high wind case . . . 50

4.3 How different factors affect the test system . . . 51

4.3.1 Geographical distribution of the wind power production . . . . 51

4.3.2 Decreasing the reservoir sizes of the hydro power plants . . . . 52

4.3.3 Decreasing the discharge capacity in the hydro power plants . 52 4.3.4 Marginal production equivalents of the hydro power plants . . 55

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5 Concluding remarks 56

5.1 Conclusion . . . 56

5.2 Discussion . . . 56

5.2.1 Input data for the test system . . . 56

5.2.2 The mathematical model . . . 57

5.2.3 The results . . . 57

5.2.4 Limitations and assumptions in the model . . . 57

5.2.5 Relevance of the project . . . 58

5.3 Future research . . . 59

References 60

Appendices 64

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List of Figures

1 Flowchart of the method used for the test system in this master thesis. 5

2 The Swedish transmission grid 2016. . . 6

3 Supply and demand curve. . . 8

4 Technical construction of a HWAT wind turbine. . . 12

5 Wind power development in Sweden from 1982 to 2015. . . 14

6 The amount of wind power production that is economically profitable at a certain production cost in Sweden. . . 16

7 Technical construction of a typical hydro power plant. . . 17

8 The regulation reservoir content per electricity area in Sweden 2014. . 19

9 Test system with 19 nodes, the different power sources, transmission lines and electricity areas. . . 26

10 River model with four hydro power plants. . . 28

11 Efficiency curves for four hydro power plants. . . 30

12 Power production curves for the four hydro power plants in the test system. . . 30

13 The wind power production in the four Swedish electricity areas SE1, SE2, SE3 and SE4 during 2015–2016. . . 31

14 The ten wind power levels for the wind power plants installed in the Swedish electricity area SE1, corresponding to node 2. . . 32

15 The power consumption during the first week of year 2013 in Sweden in electricity area SE1. . . 34

16 Power consumption in the electricity area SE1, SE2, SE3 and SE4 of Sweden (left to right) during January 3, 2013. . . 35

17 Two plots of the total wind production during the planning period for 1000 scenarios and the corresponding CO2 emissions. . . 49 18 Same kind of plot as in Figure 17 but increased wind power production. 50 19 The total wind power generation in 1000 simulations, the

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20 The total wind power generation in 1000 simulations, the

correspond-ing CO2 emissions, with changed discharge in the four hydro power

plants. . . 54

List of Tables

1 Eight challenges for a power system with a large share of wind power

and photovoltaic generation. . . 1

2 Power production and installed power in Sweden 2015/2016. . . 10

3 Minimum, median and maximum gCO2eq/kWh from life-cycle-analyses

of research reports compiled by IPCC. . . 11

4 Wind energy and power production in different counties of Sweden,

included new production, in 2015. . . 15

5 The largest hydro power plants in Sweden in 2017 and its installed

capacity. . . 20

6 The largest rivers of Sweden in 2017, its installed hydro power

capac-ity and yearly production. . . 21

7 Tables of expected CO2 emissions for different wind power and load

levels in the test system. . . 51

8 Tables of the expected CO2 emissions for the original maximal

dis-charge capacity of each hydro power plant and the corresponding emissions when the discharge capacity is reduced. . . 55

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1

Introduction

1.1

Background

On the UN climate conference in December 2015 in Paris 195 countries gathered and reached a climate agreement, the so called Paris agreement. This climate agreement

is the first in history where all countries (excluding Syria and Nicaragua)1 commit

to reduce emissions from green house gases. The conclusion is to limit the global temperature increase to 2 degrees above preindustrial level. Therefore, a part of the

agreement is that the net carbon dioxide, CO2, emissions in the second half of this

century should be zero. [2] The reason for the agreement is the global concern of

CO2 emissions and the impact on the environment due to the greenhouse effect.

A possible way to reduce the CO2emissions is to implement renewable power sources

in the power system, such as wind power plants and photovoltaics. This brings chal-lenges to the power system since these power sources have a continuously varying power production which is different from the conventional power plants that the power system is designed for. In the report [3] eight challenges are presented for a system with a large share of wind power and photovoltaics. The challenges are discussed for the Nordic countries where there are relatively large volumes of regu-lation hydro power compared to the rest of Europe. The challenges are summarized in Table 1.

Table 1: Eight challenges for a power system with a large share of wind power and photovoltaic generation in situations with low load and a high share of fluctuating production and vice verse [3].

1. System inertia

When conventional power sources are replaced by renewable power sources, such as wind power and photovoltaics, the inertia of the power system will be reduced. The reason for this is that the renewable power sources do not use synchronous machines with this property. Inertia is needed for stability and control of the power system, i.e. handling disturbances.

2. Balance between production and consumption

An increased amount of wind power and photovoltaic generation lead to a continuously varying power production in the short time perspective of seconds and hours. This will increase the need for regulation power that can compensate for the production variations. With a larger share of renewable power sources less conventional power plants are usually active. This means that less power plants must share the responsibility for balancing the power system and keeping margins to cover the variations.

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3. Excess of power

If there is high production and at the same time low load the excess of power must be handled. This situation is sensitive if it also occurs in another part of the power system and power cannot be exported.

4. Transmission capacity

If large amount of renewable power from wind power plants should be transferred from the north of Sweden to the south, and at the same time the synchronous power generation is low, there must be sufficient of other reactive compensation to keep the voltage level and thus the transmission capacity in the transmission grid.

5. Availability of top load capacity

Sometimes, there will be situations with low power production and high consumption. Also in these situations there must sufficient capacity. 6. A larger need of flexibility in controllable production and

con-sumption

It is expected that the wind power production is going to have as large variations as the consumption has today. The consumption is varying reg-ularly and in a predictable way but the wind power production varies with a stochastic behavior due to the wind pattern. This is a challenge for the hydro power production planning, handling a pattern and volume that the plants are not designed for. Hydrological couplings and water ecology considerations limit the opportunities for a quick replanning of the hydro power regulation.

7. Adaptation of shared responsibility and market mechanisms The division of labor and the allocation of responsibilities between the dif-ferent actors of the power system with the aim to maintain the physical balance and the market mechanisms for this are designed to handle the current needs. This means that the current market model may not be suit-able and rather inefficient in the future. Therefore a change in the market model might be needed where the trading takes place closer to the operat-ing hour. An alternative to this option is that the system responsible player manages the balancing and that the procurement of regulation services is extended.

8. Yearly regulation

If a high share of photovoltaic power generation is used it will lead to further need of seasonal storage capacity since a large part of the production takes place during off-season for consumption.

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fulfill human needs. This concept is touched upon in this master thesis. Renewable energy sources, such as wind power, do not put the same stress on the nature as

conventional energy sources (such as coal and oil). The CO2 gases are stored in the

atmosphere and is left for coming generations. Therefore, the comparison of CO2

emissions caused by a power system with different amount of wind power installed, leading to more or less emissions, is an interesting example to better understand the concept of sustainable development.

In Sweden around half of the energy used is from renewable power sources. This includes hydro power, biomass fuel and wind power. The European Union (EU) has the goal that 20 percent of the energy consumption within the EU should be covered by renewable power sources and 10 percent of the consumption of fuels should be biofuels in 2020. Moreover, another goal is to achieve 20 percent energy efficiency by the same year. This means that Sweden’s part of the responsibility is to achieve both these goals on a level of 49 percent by 2020. This goal is already achieved, but other goals are still in focus. [5]

The so called electricity certificate system which is applied to the electricity market in Sweden aims to increase the amount of renewable power sources in a cost effective manner. The certificate system was first introduced in Sweden 2003. Since January 1st 2012 Sweden and Norway have a common electricity certificate system. There is a common goal to increase the power production of renewable power sources with 28.4 TWh from 2012 to 2020. The system creates incentives for the power producers to use renewable power sources in the production since they obtain a certificate for every produced megawatt hour (MWh) renewable power. The producers are then free to sell the certificates on the certificate market where the price is settled between buyers and sellers and therefore the certificates are an extra income for the producers. The expected buyers of the certificates are the power suppliers which must buy certificates in order to fulfill a quota obligation between sold electricity and the certificates. [6]

1.2

Aims and objectives

Because of the complexity of the power system (such as complex interrelations and many depending factors) there is a need to sort out the challenges of increasing the amount of wind power and present the conclusions in a clear manner.

The objective of this master thesis is to develop a model which can be used to illustrate and quantify the impact of wind power in power systems and its relation

to CO2 emissions. The model is demonstrated on a fictitious power system with

properties resembling Swedish conditions. Moreover, the model includes a hydro power model for short-term planning (hours). The impact of wind power is measured

in CO2 emissions. Finally, the model should be as realistic as possible but still

feasible. It should take into account; efficiency curves of power plants, continuously varying wind power production, frequency control etc.

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1.3

Method

The main model, called test system, which is developed in this master thesis is set up as a mixed integer linear programming problem. The planning problem is solved for a 24 hour planning period with hourly resolution. The General Algebraic Modeling System (GAMS), which is an optimisation software for modeling linear, nonlinear and mixed integer optimisation problems, is used to solve the planning problem [7]. In Figure 1 a flowchart of the complete model is shown. A load model and a wind model (seen on the top of the Figure) is read by GAMS. A Python script is used to connect all parts of the model. The Python script runs Monte Carlo simulations of the planning problem. The Monte Carlo simulations use random samples to estimate

the expected value of the CO2 emissions. MATLAB is used to compute expected

value and standard deviation of the CO2 emissions in the test system.

Two years of hourly wind data from January 2015 to December 2016 for all electricity areas in Sweden is used for the wind model. [8] One day of hourly load data for the electricity areas has been used from January 3rd 2013 for the load model. [9]

1.4

Thesis disposition

The report includes the sections listed below. • Section 1. Introduction

• Section 2. Theory • Section 3. Test system • Section 4. Results

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.csv Hourly load data from

Nord Pool is saved

.csv Two years of hourly wind

data from Nord Pool is saved

MATLAB The load data is rescaled

GAMS

The planning problem is solved using the load and the wind data

MATLAB 1000 wind scenarios are created from the matrices .csv

The rescaled load data is saved to fit GAMS

MATLAB Markov matrices are created from the wind

data

Python The result of the computed CO2 emissions is extracted from the GAMS result file

.csv All computations of CO2

emissions are saved

MATLAB Expected value of CO2 emissons, variance are

computed Python

The steps are repeated

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2

Theory

2.1

The Swedish power system

2.1.1 The power grid

Figure 2: The Swedish transmission grid 2016 [10]. In 2011 Sweden was divided in four electricity areas [11]:

• Swedish electricity area 1 (SE1) Luleå, the northenmost area,

• Swedish electricity area 2 (SE2) Sundsvall, south Norrland to the frontier against Dalarna,

• Swedish electricity area 3 (SE3) Stockholm, from Dalarna to below the nuclear power plants Ringhals and Oskarshamn,

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excess of power, mostly depending on the nature with rivers and the possibility to utilise hydro power to a large extent. In contrast, during parts of the year, there is deficit of power in the south of Sweden. Due to the limitations in the transmission grid the bottlenecks appear when large amount of power is transferred from the north to the south. The electricity price may vary in the different areas because of excess or deficit and the power is always transferred from the area with the lower price to the higher. Therefore, the different prices give information that it will give a higher income to increase the production capacity in the south of Sweden compared to the north. [11]

2.1.2 Power system quality

There are requirements on the power system to provide an adequate quality of power. To achieve this there must be an acceptable voltage level and the frequency must be stable.

In Sweden Svenska kraftnät is responsible for the frequency control as the transmis-sion system operator. The nominal frequency is 50 Hz, which is the same as in the rest of Europe. Due to rapid changes (subsecond) in the consumption or production the frequency may deviate from its nominal value. The acceptable deviation within normal limits is ±0.1 Hz. [12]

To control the frequency so called regulation power plants are used and in Sweden these power plants are mainly hydro power plants [11]. If there is a rapid change in the consumption or the production the rotors in the synchronous machines will compensate for that. For instance, if the consumption is greater than the production the rotors compensate the loss of power leading to a decrease in the rotational speed, i.e. rotational energy, and the frequency drops. As the frequency drops the regulation power plants act as primary control and start to produce more power and thereby stabilise the frequency. On the other hand, if the consumption is lower than the production the rotors in the synchronous machines absorb the excess power and start to rotate faster and the frequency increases. This frequency change is detected by the regulation power plants which decrease the production and the frequency will stabilise. In case of larger frequency deviations than within the nominal limits the secondary control is activated, i.e., additional regulation power plants. If the deviations are sufficiently large loads will be disconnected from the grid in order to keep safe operation of the power system. [12]

An acceptable voltage level means that the voltage should be kept stable. Reactive power and voltage are closely related and changes in the reactive power in parts of the system will result in increase or decrease of the voltage level. The system is stable if an increase in injected reactive power results in an increase in voltage level. If voltage instability occurs the time scale is a few seconds to tens of minutes. [13]

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2.2

The Nordic electricity market

In the early 1990s the Nordic countries deregulated their power markets and changed their individual markets to a common Nordic spot market called Nord Pool [14]. This means that the electricity price nowadays is determined by supply and demand. The reason to introduce a deregulated market is to achieve a more efficient market where exchange of power between countries is utilised. The most efficient power plants will be used leading to, for instance, a more economical and better environmental use of the power plants. [15]

The electricity price is determined at the Day-ahead market for the coming 24 hours on an hourly basis. At 12:00 CET there is a deadline for submitting bids. Producers submit bids on a certain amount of power and the lowest acceptable price. At the same time consumers submit bids on a certain amount of power and the maximum acceptable price they are willing to pay. When the bidding period has ended a supply and a demand curve are constructed. The electricity price is settled at the price cross between the two curves as shown in Figure 3. At this time it is determined how much power each producer will produce and consumer will consume, respectively. [16]

Figure 3: Supply and demand curve [16].

In reality producers cannot always fulfil their promises and consumers likewise. Therefore Nord Pool arranges an Intraday market, Elbas, where imbalances are regulated. At the Intraday market power can be sold and bought to meet the bids submitted to the Day-Ahead market. Up- and down-regulation bids are settled ac-cording the same market mechanism as described for the Day-ahead market. When power plants with unpredictable nature are added to the power system, such as wind power, the Intraday market becomes more important to regulate the offset between bids and produced volume. [17]

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2.3

Power system planning

2.3.1 Time perspectives for planning

The power system production must be planned in such a way that the resources are used in the best possible way. This means that technical and economical aspects must be taken into account. Furthermore, because of the environmental aspects that are of importance the resources should be used in a sustainable way which

means that emissions, such as CO2, are used to a limited extent. Different models

are used for the planning depending on the time perspective for which the planning considers [12];

1. Seconds and minutes. The most important factors are safety and tech-nology. The stability of the power system is planned in order to control the frequency and the voltage level. The system must fulfil the stability criterion’s of the power system.

2. Hours and days. The planning of these time periods is often referred to as short-term planning. The power system must still be planned to maintain the stability and frequency. But in this time period also economical aspects are of importance. The planning includes decisions for the power companies of how much power they will trade at the power exchange. The power companies plan the power plants to operate in merit order, which means that the most cost effective power plant is first used.

3. Weeks or months. Economical decisions become more important when the time perspective is weeks or months. The planning must consider how to use the available resources. The properties of the different power sources must be taken into account. The hydro power production must be planned to utilise the energy in the water in the best way.

4. One or more years. The long-term planning considers economical aspects of the investments in the power system. The technical limitations are few since it is possible to make new investments.

2.3.2 Short-term planning for hours and days

In this project short-term planning for a day during different seasons of the year is considered. The objective of the planning is to make decisions for the power producers on how to operate the power system for the coming day when the resources should be utilised as efficiently as possible. The plan describes how much each power plant should generate during each hour of the days and how much power should be purchased or sold at the power exchange. An efficient use of resources means that the profits should be maximised. Therefore, this kind of planning is solved as a mathematical optimisation problem.

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2.4

Energy sources and CO

2

emissions

The electricity production in Sweden constitutes of a mixture of different power sources, where hydro power and nuclear power are the most utilised power sources and used as base power in the power production. In Table 2 the total power pro-duction and installed power during the winter 2015/2016 is shown. It should be noticed that wind power is the power source which has been most expanded in recent years. [11]

Table 2: Power production and installed power in Sweden 2015/2016 [11].

Power source Yearly production Installed power

(energy) winter

[TWh/year] 2015/2016 [MW]

Hydro power 50-80 16 155

Nuclear power 50-70 9706

Wind power approx. 15 6038

CHP 13-18 5013

Condensing power 0.5-0.9 3360

Photovoltaic approx. 0.1 103

Total 40 375

The Intergovernmental Panel on Climate Change (IPCC) has compiled different life-cycle-analyses (LCA) of research reports and computed minimum, median and

max-imum life cycle CO2 emissions. These are estimated values. The different sources of

emissions are divided into three categories: 1. direct emissions, 2. emissions from the fuel production and delivery, and 3. remaining lifecycle emissions connected to infrastructure of the energy system including the power plants. More details can be found in [18]. Table 3 shows the emissions from different electricity power pro-duction sources. The lowest emissions are from onshore wind power followed by emissions from offshore wind power and nuclear power. The most emitting power sources are coal and gas. [19]

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Table 3: Minimum, median and maximum gCO2eq/kWh from life-cycle-analyses of research reports compiled by IPCC [19].

Power source Minimum Median Maximum

gCO2eq/kWh gCO2eq/kWh gCO2eq/kWh

Coal 740 820 910 Gas 410 490 650 Biomass - dedicated 130 230 420 Hydro power 1.0 24 2200 Nuclear 3.7 12 110 Photovoltaics - rooftop 26 41 60 Photovoltaics - utility 18 48 180 Wind onshore 7.0 11 56 Wind offshore 8.0 12 35

2.5

Wind power

2.5.1 Principals of wind power

A wind power turbine converts the power in the wind into electricity. Thus, the wind turbines are used as electricity generators and are a renewable energy source since the energy originates from the sun. The most common design of wind power turbines today is the horizontal axis wind turbine (HAWT). [20]

In Figure 4 the different parts of a HAWT turbine is shown. The blades 1 are shaped such that a lower pressure is created on the top of the blades when the wind hits them. This creates a force on the blades which start to rotate. The blades are connected to a hub 2 (behind the cover in the Figure) which is connected to a shaft 3. The shaft rotates slowly and therefore a gearbox 4 is used to increase the rotation speed of a high speed shaft 5. If the wind is strong the protection brakes 6 will decrease the speed of the high speed shaft and thus the blades. The electricity generation is performed in the generator 7 which is connected to the high speed shaft. When the electricity generation is ongoing heat is emitted and the cooling fan 8 is used to cool the generator which otherwise would have been overheated. The last component marked in the figure is a wind sensor 9 which is connected to a control system and is used to change the angle of the blades and allows the turbine to face the wind. [21]

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Figure 4: Technical construction of a HWAT wind turbine [21].

2.5.2 Properties of wind power

Wind power plants have limited controllability and are dependent on the wind. This affects the short-term planning as well as the seasonal planning. Below some important properties of wind power are listed which are mentioned in [22], [13] and [3].

1. The wind power turbines do not provide synchronising power since they do not use synchronous machines.

2. The wind forecasts are stochastic and this must be regarded in power system planning. In general deviations from the forecasts have effect between hours but in a shorter time perspective the deviations are smaller. This means that the actual production can differ quite a lot from the planned production. 3. The continuously varying production means that regulation power must be

used to a larger extent to compensate for the production variations.

4. Wind turbines can cause power quality problems leading to harmonics and voltage flicker.

5. Congestion problems on transmission lines can be reduced by installed wind farms. Installed wind farms can also reduce transmission losses if they are installed close to heavy consumption areas.

6. Wind farms can provide voltage support depending on design (seconds to minutes). If reactive power support is built in connection to the wind turbine it can also provide the system with this support.

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9. If conventional power plants are replaced by wind power extra reserve power is needed.

The mentioned properties impact the system and mainly depend on the following factors; the share of wind power in the system, the generation mix in the power system and the grid size. The impact is usually split in short-term effects (1,2,3,4,6) and long-term (3,5,7,8,9) effects. Moreover, another dimension is to split the impact in local (2,4,5,6) and global (1,3,7,8,9) effects.

2.5.3 History of wind power

Wind power has been utilised by humans since a long time in history. The first means to use wind power were windmills and there are references already back to the 1st century describing windmills. Compared to the modern wind power plants windmills convert the power in the wind into mechanical power. The next reference of windmills is from 9th century Persia. This is the first windmill used which has been confirmed by archaeological findings and had a vertical axis rotor. In Europe windmills showed up in the 12th century in England. Those windmills had a different design with a horizontal axis rotor and were used for many mechanical tasks such as pumping water, grinding grain, sawing wood and powering tools. These types of windmills were used as a primary energy source in Europe up to the Industrial Revolution starting in the middle of the 18th century. At that time coal started to replace windmills since it had many advantages which the windmills did not possess. One of the major advantages with coal was that it could be used whenever it was desired. By the 18th century windmills had been developed significantly and included a number of features which were later used in some electricity-generating wind turbines. [20]

During the late 19th century wind power was first used to generate electricity. The first attempt was to use a windmill rotor connected to a generator. The turbines were small and were used until 1930s in the United States when the electrical grid was expanded and replaced them. At the same time, in Denmark larger wind turbines were constructed in the range 20-35 kW and later 30-60 kW. Denmark has since then been one of the leading nations in wind power. [20]

The re-emergence of wind power is considered to have started in the late 1960s since people were concerned about environmental issues. It was during the Oil Crises in the mid-1970s that governments increased funding for alternative energy sources, including wind power. In the late 1970s there were large development of wind power in California due to investment tax credits. However, this encouraged investments rather than efficient production leading to poorly developed wind power plants. The installed capacity was about 1500 MW. After the credits were withdrawn the California wind rush collapsed. The main development was moved to Europe and in the beginning of the 21th started to grow substantially. Nowadays wind power is a large share of the power production in many countries. [20]

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Figure 5: Wind power development in Sweden from 1982 to 2015 [23].

2.5.4 Wind power in Sweden

The development of wind power is shown in Figure 5. It can be seen from the Figure that the development of installed power and electricity production have in-creased significantly the ten years between 2004-2015. A pilot project was set up and subsidies were given for large-scale wind power constructions between 2003-2007. Moreover, the parliament of Sweden has put forward a planning framework of development of 30 TWh until 2020. The planning framework makes sure that municipalities plan for this amount but it leaves no guarantees that this amount will be installed. In the planning framework 20 TWh is onshore wind power and 10 TWh is offshore wind power. [23]

In Table 4 it can be seen that the total wind energy in 2015 was 16.3 TWh and the installed power (registered) was 5840 MW. Most of the power plants are onshore and the new construction is large-scale onshore wind power. When new construction is planned it is preferred to distribute the power plants geographically evenly. The reason for this is to reduce the dependence of wind conditions in only one or a few areas. [23]

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Table 4: Wind energy and power production in different counties of Sweden, included new production, in 2015 [23].

Counties Total [MW] New 2015 [MW] Production [TWh]

1. (1) Västra Götalands län 800 26 2.3 2. (2) Västerbottens län 652 79 1.8 3. (4) Jämtlands län 604 102 1.9 4. (13) Västernorrlands län 546 404 1.1 5. (3) Skåne län 522 10 1.5 6. (5) Hallands län 410 0 1.2 7. (6) Kalmar län 409 67 1.0 8. (8) Norrbottens län 354 36 0.9 9. (7) Gävleborgs län 323 –1 1.1 10. (9) Dalarnas län 271 3 0.9 11. (10) Jönköpings län 266 15 0.8 12. (11) Östergötlands län 171 –1 0.5 13. (12) Gotlands län 170 –2 0.5 14. (14) Värmlands län 109 0 0.3 15. (15) Blekinge län 79 0 0.2 16. (16) Örebro län 71 6 0.2 17. (17) Stockholms län 59 0 0.2 18. (18) Uppsala län 12 0 0.0 19. (19) Kronobergs län 8 0 0.0 20. (20) Södermanlands län 7 0 0.0 21. (21) Västmanlands län 0 0 0.0 Total 5840 744 16.3

In January 2017 reports indicate that the certificate prices have been reduced to one third of the prices the previous year and therefore new constructions have stagnated. There are several depending factors to why this has happened. It has been cheaper to build new power plants and the producers who built their power plants between 2006-2012 make a loss on each kilowatt hour due to low electricity prices and low certificate prices. Furthermore, it was a windy autumn 2016 and a warm winter which means that the demand for electricity certificates has decreased. However, decisions have been taken for several large projects which means that there is sufficient capacity planned to reach the goal on 28.4 TWh year 2020. [24]

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2.5.5 Development of wind power in Sweden

The development of wind power depends on technical issues in the power system and the market situation. An increased share of wind power means that more regulation power must be transferred over long distances in the country. Therefore, power lines may need to be reinforced and more reactive compensation must be implemented. [3] In the report [25] the cost of establishing new wind power is analysed. The conclusion is that an increase of the electricity price from 0.5 kr/kWh to 0.6 kr/kWh will make it profitable to expand the wind power production from 12 TWh to 140 TWh. See Figure 6. This means that there is great potential for wind power expansion.

Figure 6: The amount of wind power production that is economically profitable at a certain production cost in Sweden [25].

2.6

Hydro power

2.6.1 Principals of hydro power

Electric power is generated in a hydro power plant by utilising the difference in potential energy between an upper and a lower level of the water. The potential energy of the water at the upper level is converted to kinetic energy when the water is discharged to the lower water level. When the water flows from the upper level to the lower it passes a turbine, which drives a generator where the kinetic energy is transferred to electricity. Sometimes, there are several turbines in the same power plant which increase the efficiency. [26]

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Figure 7: Technical construction of a typical hydro power plant [28].

not have any reservoirs. When the control gate opens, the potential energy in the water is converted to kinetic energy. The intake 3 is the section of the reservoir immediately in front of the control gate where water is drawn into the penstock

4. Water travels through the penstock into the turbine 5 and thereby forcing the

blades in the turbine to spin. The most common type of hydro power turbines is Francis, but also Kaplan and Pelton are common. The spinning blades in the turbine turn a shaft that is connected to the generator. When the shaft spins electricity is produced in the generator 6. Electricity is transferred to a higher voltage level and fed into the transmission grid. Sometimes water is led into a spillway 7 besides the power plant and thereby the water level in the reservoir can be kept at desired levels. The head is the height difference between the water level at the intake and the water level at the end of the tailrace and influence the efficiency of the power plant. [27], [28]

2.6.2 Properties of hydro power

The importance of hydro power for the Swedish power system is explained in [11]. Hydro power have different roles in the power system and these are considered to become more important in the future. Below some important properties are listed: • Hydro power is a renewable power source and the emissions are one of the

lowest per kilowatt-hour according to an LCA.

• Hydro power is used to a large extent in the Swedish and Nordic power system. • Hydro power is a controllable power source which means that water can be stored in reservoirs and used later. This property can be utilised in power production planning. This applies to planning periods of seasons, weeks, days and even seconds. This ability to control the power plants is however restricted by reservoirs sizes and hydrological couplings between power plants.

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• Hydro power is used to control the frequency of the power system.

• Hydro power reduces the need of other controllable power sources, which today often are fossil fuels.

• Because of the properties of hydro power it is possible to increase the amount of other renewable power sources, such as wind power and photovoltaics. There-fore, it is possible to argue that hydro power can be seen as a “double renew-able” power source.

2.6.3 History of hydro power

The first use of hydro power is found in the ancient Greece and Rome around year 0 when the waterwheel was invented. Hydro power is used since then and in the 16th century it was an important energy source used for elevators, mining and milling in Europe, and in other places. During the 18th century the waterwheel was further developed and in the 1820s a complete theory of waterwheels was developed and a primitive form of speed control first originated. Later in the 19th century water turbines evolved. [29] In 1870 the first hydroelectric power plant was built in Cragside Rothbury England and was used for lighting a single bulb. The next step in the development was the first industrial hydroelectric power station of 12.5 kW in Fox river, USA, in 1882. [30] In modern times hydro power is used to a large extent since it has the greatest potential as renewable energy source. In [26] examples of different hydro power plants world wide in modern time are presented.

2.6.4 Hydro power in Sweden

There are around 2000 hydro power plants in Sweden. Out of the total amount a bit more than 200 are larger power plants with an installed power of 10 megawatt or more. The largest power plants in Sweden are summarized in Table 5. The largest utilised rivers in Sweden are summarized in Table 6. [31]

If the total amount of wind power is increased in the power system, the energy need in the hydro power plants will not be changed but there is a need for a larger power capacity to handle the fluctuation in wind power. Therefore, increasing the amount of wind power in the power system could lead to installation of several or larger turbines and generators with higher power capacity. [11]

Different factors affect the utilisation of the hydro power plants. There are differ-ences between different hydro power plants depending on its location. Near source flows and large reservoirs power plants have a running time of about 3000 hours per

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the same time since some reservoirs are preparing for the spring flood to come and others are already experiencing it. The phenomenon is displayed in Figure 8 where the reservoir contents in each electricity area of Sweden are displayed for year 2014. It should be noted that the levels vary from year to year depending on if it is a wet or dry year and other meteorological factors. Moreover, other factors that influence the hydro power production are outages, legal restrictions concerning water rights, limitations in the power grid and icing. [11]

Figure 8: The regulation reservoir content per electricity area in Sweden 2014 [11].

2.6.5 Hydro power as regulation power in Sweden

Hydro power is used as regulation power over different time periods ranging from years to seconds. Water is stored in the reservoirs during spring, summer and autumn to be used during the winter. The consumption has its peak during the winter but at the same time the inflow is the lowest during this period of the year and therefore the stored water from the rest of the year is used. The difference in power consumption varies over the year where the peak consumption during the winter is double the amount of the consumption during the summer, 24 000 MW compared to 12 000 MW. The inflow changes a lot between different years and the variation is equivalent to a difference in production of 50-80 TWh. [11]

The largest hydro power reservoirs are located at the top of the rivers and can be used to regulate power fluctuations between seasons and years. The smaller reservoirs are located downstream and are used for regulation during shorter time periods (hours and days). There is a total volume in the reservoirs of 34 TWh and since the total hydro power production is about 65 TWh about 30 TWh must be used in a short time period in the smaller reservoirs. [11]

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in a power system at every moment leads to the need for regulation power which is also useful for time periods of seconds and which prevents frequency deviations in the power grid [32]. Because of the properties of hydro power plants these are suitable also for this purpose. In fact, hydro power is the only power source used for this purpose in Sweden. In other countries, for instance in Denmark and Finland, also thermal power is used as regulation power [11].

Due to water rights and other technical limitations there are limitations in the mini-mum and maximini-mum level in the reservoirs. Normally the reservoirs have a minimini-mum level of 10 percent and a maximum level of 85 percent. The water rights also give constraints to the amount of discharge of water. This can be either as a maximum amount of discharge or a limitation to the weekly or daily mean discharge. Further-more there can also be a limitation in the change of discharge between days. [32] Table 5: The largest hydro power plants in Sweden in 2017 and its installed capac-ity [31].

Power plant Installed power [MW]

Harsprånget 977 Stornorrfors 599.4 Porjus 480.6 Letsi 456 Meassure 446.1 Trängslet 330 Ligga 326.75 Vietas 306 Ritsem 304 Kilforsen 288 Porsi 274 Trollhättan 249 Krångede 248.4 Seitevare 225 Harrsele 223

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Table 6: The largest rivers of Sweden in 2017, its installed hydro power capacity and yearly production [31].

River Installed power [MW] Yearly production [TWh]

Dalälven 1100 4.3 Faxälven 817 3.7 Fjällsjöälven 560 2.0 Göta älv 326 1.6 Indalsälven 1832 9.0 Klarälven 351 1.3 Ljungan 479 2.0 Ljusnan 786 3.7 Luleälven 4358 14.7 Skellefteälven 1069 4.2 Umeälven 1804 7.6 Ångermanälven 1248 6.0 Motala Ström 153.4 0.5 Other rivers 1737 5.7 Total 16622 66.5

2.6.6 Development of hydro power in Sweden

The Swedish power system is capable to handle the share of wind power that is installed but an increased amount of wind power will need further regulation power [11]. Therefore, it is interesting to study the potential in increasing the power output of the regulation hydro power plants. There is not a straight forward con-nection between increased power production and increased regulation power. In most cases an increased amount of power output is closely related to an increased energy development. The reason for this non obvious connection is that the power producers are paid for the energy and not directly for the installed power capacity. It is mentioned in [11] that the technical potential in the Swedish hydro power is 95 TWh electric power as yearly production while the usage today is 65 TWh. This means that further 30 TWh can be utilised. However, the remaining four undeveloped rivers are protected and along with other protected water streams the real potential is 6 TWh by developing the present power plants and developed rivers. With this increase of energy the additional power output will be 1900 MW.

In [11] some measures for increasing the power capacity in the hydro power plants are discussed. One suggestion is to replace current turbines and generators or to

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increase the number of these in a power plant. Another suggestion is to increase the capacity of power plants upstream in the mountains since these plants have largest reservoirs both up and down stream. These power plants can also install pumps which return the water to the reservoirs when the power consumption is low in the system. This will increase the regulation power capacity to moderate increased share of wind power. Furthermore, redirection of water from undeveloped to developed rivers leads to increased water flow in the developed rivers and is therefore another suggestion. Finally, the last suggestion of technical improvements is to increase the storage capacity in suitable places to increase the flexibility to use the water. The same report [11] lists important prerequisites to develop hydro power. The analysis of the development of hydro power must be considered holistically which includes the whole river system. The goal should be to find possible solutions for modernisations, investments and reinvestments. The report also suggests reassessing environmental laws and to simplify and clarify regulatory approvals regarding hydro power. There also need to be a clear incentive to increase the power production. A possible solution is to include this in a new market model which rewards power and not only energy and also to lower the costs for grid connection and lower the taxes for the producers.

2.6.7 Hydro power modelling for short-term planning

It has been mentioned in section 2.5.2 that fluctuating power production increases the need for balancing power. Therefore, there is a value for hydro planning im-provements, since hydro power plants have the properties to support the short-term balancing in the power system. The most important aspects to consider in the models for short-term planning of hydro power in a system with uncertainties are:

• Day-ahead commitment, i.e. production bidding to the sport market. • Bidding strategy to the regulating market,

• Water inflow, • Future water value, • Time delay of the water.

There is need to address several of the mentioned uncertainties in order to have a more realistic production plan model. The multistage stochastic models are suitable for this purpose since these models consider information and decision flow in contrast to deterministic models. A multistage stochastic model uses partition of decision

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mentions that because of the uncertainties brought to the power system, when a large amount of wind power is added in the system, the planning has shifted. Ear-lier deterministic conventional models were used and now the focus is to develop multistage stochastic models to evaluate the impact of the uncertainties.

The first studied stochastic model in [22] is made by A. B. Philpott and others which have developed a hydroelectric unit commitment model subject to uncertain demand. The objective of the model is to determine which turbine unit to commit each half of the day. The next model in [22] by N. Gröwe-Kuska et. al. is for power management under uncertainty. The objective is to investigate weekly cost-optimal generation of electric power in a hydro-thermal generation system. The demand, prices for fuel and delivery contracts are uncertain. A third model in [22] is made by J. G. Gonzalez et. al. and it investigates the combined optimisation of a wind farm and pumped-storage facility where market prices and wind generation are uncertain. Furthermore, S. E. Fleten et. al. developed a model for short-term production planning for a price-taking hydro power producer where spot market prices and water inflow are stochastic.

In the course compendium [12] deterministic short term planning of linear program-ming models are discussed, where discharge and efficiency, hydrological couplings between hydro power plants and value of stored water are considered. This forms the basis for a master thesis work 2009 by Calle Englund and Andreas Fagerberg [32]. In this work a model is set up to study balancing of wind power with hydro power in the north of Sweden. The objective of the planning model is to maximise the electricity production during a studied week taking into account technical and legal restrictions. The deterministic model is refined to a stochastic model were scenarios for the wind power production are introduced.

2.7

Other power sources in Sweden

2.7.1 Nuclear power

In a nuclear power plant electrical power is generated from atomic nuclear fission that heats water. A synchronous generator is driven by a turbine and is used in the final stage of the power production [33]. Thus, nuclear power plants are designed in a way that fits the conventional power systems and therefore it is possible to control the power production and use developed methods to control the stability of the power system when these power plants are connected to the grid [13].

In section 2.4, Table 2, it can be seen that nuclear power and hydro power adds up to the largest share of the energy sources used for power production in Sweden. Out of the yearly power production around 40 % corresponds to nuclear power. Currently Sweden has three nuclear power plants (Forsmark, Oskarshamn and Ringhals) with nine operating reactors [34].

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Nuclear power and hydro power production have low CO2 emissions and therefore the total emissions from electricity production in Sweden are low compared to other countries. However, the use of nuclear power has been debated a long time due to the risky atomic fission process which needs comprehensive safety regulations. In 1980, because of the nuclear accident in Harrisburg USA, the Swedish government decided after a referendum to phase out nuclear power and aim for closing twelve power plants by 2010 if there were available energy sources to replace them. But in 2010 the parliament decided to change the policy and allow new construction only to replace decommissioned reactors at the same places as the existing power stations. Furthermore, in 2015 decisions were taken to close four older reactors by year 2020. [34]

2.7.2 Combined Heat and Power

Combined heat and power (CHP) is production of electricity and heat at the same time used in industries and district heating systems. Heat is released during the power production and used in the district heating systems and therefore the energy resource is utilised efficiently. In Sweden the CHP plants are fired with biomass fuel (8-10 TWh) and fossil fuels (3-6 TWh) and the efficiency is around 90 percent [11]. The CHP plants are not directly dependent of weather conditions but they are dependent on the heat demand which is weather dependent. Therefore these power plants are used as a supplement to the base power. When phasing out the nuclear power CHP can be used as a replacement but in order to fully utilise the capacity of these power plants there must be adequate district heating systems. [35]

2.7.3 Condensing power

Electricity production in condensing power plants is similar to the process in CHP plants but the heat released during the production is not used. Condensing power in Sweden constitutes of biomass fuel, fossil fuel thermal power plants, gas turbines and diesel generators [11]. Today, the fossil fuel power plants are used to a limited

extent and mostly during the winter in Sweden due to the high CO2 emissions during

electricity production. This is in contrast to the global usage were coal is the most common power source. [36]

2.7.4 Photovoltaic generation

Photovoltaic (PV) generation is a renewable power source free from CO2 emissions.

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con-PV panels give a low voltage (0.5V) and therefore they are connected in series in order to increase the voltage level and work properly for power production. However, the disadvantage of series connection is that if a single cell is partly or totally out of function, for instance when shaded, this reduces the capacity of the whole module. [38] The electricity production from PV panels in Sweden is largest between March and October [39].

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3

Test system

3.1

Model

In this master thesis a test system is developed. The purpose of the test system is to solve a planning problem for the power production during a day. Therefore, components that exist in a power system are introduced, such as different power sources, loads and transmission lines. The test system consists of 19 nodes and its structure is based on a reworked version of the Nordic32-test system. [40] However, the Nordic32-test system is not used for load flow calculations as it usually is. The test system is shown in Figure 9. All data for the test system can be found in section 3.1.7. 1 2 3 4 5 6 7 8 9 11 10 12 13 14 16 19 15 17 18 Wind CHP Nuclear Electricity area Hydro E1 E2 E3 E4 n Node Transmission line En

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by studying properties of real systems and translate these to the test system. An important property of the system is the introduction of similar power source as in Sweden. The reason for this is that one of the outcomes of this master thesis is to mimic the power sources available in the Nordic countries. This makes it possible to study hydro power as regulation power for the continuously varying wind power generation.

Moreover, the power mix is chosen with similar proportions as in Sweden. This results in a system which has resemblance with a real world system and is therefore interesting and worthwhile to study. As presented in section 2.4 the Swedish power mix consists of roughly 40% hydro, 40% nuclear, 10% wind and 10% CHP. Other power sources are disregarded in order to keep the test system simple while keeping the main properties of a real power system.

Another property of the test system is the load. The load ratios between the different electricity areas are chosen according to the load ratios present in the four Swedish electricity areas. Loads are located in all nodes in varying sizes. Within each area the load is then distributed unevenly to simulate the presence of cities and factories in certain nodes.

In the most northern electricity area E1, shown in Figure 9, hydro power is the dominating power source. A river model is created with four hydro power plants connected to each other. In the next electricity area E2 the only power source available is wind power plants. The wind model used is a stochastic model in order to simulate the fluctuating wind power production. In the largest electricity area E3 the two remaining power sources nuclear and CHP are present. Nuclear power is modeled as a constant power source supplying the system with a base power. CHP is another available conventional power source used to support the system under high load conditions.

In this test system many real world properties has not been included in order to obtain a simple system that is possible to study. Some of the properties not included are:

• No market model. Usually the electricity market determines which power sources are supplying the power. In this model the cost of each energy source is assumed to be constant and in production they are used in merit order. • No transmission losses. In real world systems transmission losses are important

and put limits on the capability to transfer power between different parts of the system. This is not taken into account in this model.

• No stability analysis. Introducing wind power in a system affects the stability and robustness of the system. A stability analysis would demand a consider-able extension of the work and is not included due to the time frame of this project.

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• No import or export. A power system is seldom isolated from the the rest of the world. But in some cases the link to outside systems is weak. To simplify and avoid assumptions about neighbouring systems this system has no import or export capabilities.

3.1.1 Hydro power and the river model

The river model consists of four hydro power plants as in Figure 10. The reservoir in the most northern power plant Ahlen is the largest followed by Fjället and the two remaining plants Forsen and Kärret have substantially smaller reservoirs. The fact that all hydro power plants are in electricity area E1 is similar to the situation in Sweden, where most of the hydro power plants are situated in electricity areas SE1 and SE2.

There is a lower boundary for the minimal content of the reservoir in Kärret but no such limits on the other reservoirs. The reservoirs are relatively full at the beginning of the planning period and a restriction is that the content at the end of the planning period should not exceed the start values and remain above certain minimal values. The installed capacity of the hydro power plants are comparable except that the power plant in Kärret is substantially smaller.

Ahlen

Forsen

Fjället

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Fjället have the largest capacity while the other two plants have smaller capacity. The plant in Kärret also has a minimal discharge limit. Moreover, to avoid rapid changes in the water flow, changes in the discharge is limited in each plant. Since the plants have limited discharge capacity and the reservoirs have limited size the power plants have the ability to spill water, i.e. to lead water past the generators without generating power. This spillage is however limited to a maximal level in each power plant and in Kärret also to a minimal level. As can also been seen in Figure 10 there is a local inflow to each reservoir.

The four power plants are based on power plants in the Lule river and these are located at certain distances from each other. This means that water released from an upstream power plant will flow to a downstream plant with a delay which can be substantial. This is modeled by assuming a fixed delay time between the power plants.

The relation between discharge, generated power and head is a non-linear function. This function is often determined by measurements. In this master thesis the impact of the head is not taken into account since it will often have a small effect on the generated power. [12]. The relation between generated power and discharge is presented in the form of efficiency curves.

In [41] examples are given of re-scaled efficiency curves from real hydro power plants. Four of these curves are chosen as a starting point for the efficiency curves in this master thesis. The relation between discharge Q and generated power H(Q) is constructed in the following way;

1. Measure points on the efficiency curves. These curves can be found in Fig-ure 11. The four curves are found in [41].

2. The curve in example 1 corresponds to Ahlen, example 2 corresponds to Fjället, example 3 corresponds to Forsen and example 4 corrsponds to Kärret.

3. Rescale the x values of each plot to match the maximal discharge in the hydro power plants in the test model.

4. Multiplying all y-values with Q.

5. Re-scale the y values to determine H(Q) by making the maximal value equal to the installed power in each hydro power plant. This results in the dotted curves in Figure 12.

6. Linearise each re-scaled curve into two segments of a piece-wise linear model with decreasing slopes. The segments are displayed in Figure 12.

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Example 1 Example 2 2 4 6 8 10 85 90 95 100 Discharge [m3/s] E ffi cienc y [%] 2 4 6 8 10 85 90 95 100 Discharge [m3/s] E ffi cienc y [%] Example 3 Example 4 2 4 6 8 10 85 90 95 100 Discharge [m3/s] E ffi cienc y [%] 2 4 6 8 10 85 90 95 100 Discharge [m3/s] E ffi cienc y [%]

Figure 11: Efficiency curves for four hydro power plants.

Ahlen Fjället 150 300 450 600 0 100 200 300 400 Discharge [m3/s] Po wer [MW] 40 80 120 160 0 60 120 180 240 Discharge [m3/s] Po wer [MW] Forsen Kärret 250 500 750 1000 0 75 150 225 300 Discharge [m3/s] Po wer [MW] 200 400 600 800 0 10 20 30 40 Discharge [m3/s] Po wer [MW]

Figure 12: Power production curves for the four hydro power plants in the test system.

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3.1.2 Wind power model

In Figure 9 wind power plants are installed in eight different nodes in the test system. In this project two situations for the wind power production are considered. The first case, also called “low wind”, includes wind power production in nodes 2, 7, 18 and 19. The generated power amounts to approximately 10% of the total power production in the test system. The second case, also called “high wind”, adds wind power plants in nodes 3, 6, 9 and 17. The new plants will have exactly the same power production as the plants in node 2, 7, 19 and 18, respectively, resulting in a doubling of the total wind production in each electricity area compared to the low wind case.

As wind power production is highly fluctuating a stochastic model is developed for this project. From the Nord Pool webpage [8] two years of hourly wind power production in the four Swedish electricity areas are collected. In Figure 13 the historic wind power production is plotted. The statistics from Nord Pool is used to develop the wind power model.

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0

500 1000 1500

2000 2015 and 2016 wind generation is area SE1

Hours Power [MWh/h] 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 500 1000 1500

2000 2015 and 2016 wind generation is area SE2

Hours Power [MWh/h] 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 500 1000 1500

2000 2015 and 2016 wind generation is area SE3

Hours Power [MWh/h] 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 500 1000 1500

2000 2015 and 2016 wind generation is area SE4

Hours

Power [MWh/h]

Figure 13: The wind power production in the four Swedish electricity areas SE1, SE2, SE3 and SE4 during 2015–2016.

The model is constructed by first rescaling the historic wind power production in each of the electricity areas SE1, SE2, SE and SE4 so that the maximal wind pro-duction corresponds to the maximal installed capacity in nodes 2, 7, 18 and 19. The power output is then split into ten levels for each node. The different levels of SE1, corresponding to node 2, are illustrated as horizontal stripes in Figure 14.

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0 2000 4000 6000 8000 10000 12000 14000 16000 0 50 100 150 200 250 300 350 400 450 500

2015 and 2016 wind generation is area SE1

Hours

Power [MWh/h]

Figure 14: The ten wind power levels for the wind power plants installed in the Swedish electricity area SE1, corresponding to node 2.

It is assumed that the wind power production in each node only assumes one of the ten levels each hour. The power production jumps between these ten levels according to some probability. This means that only the power production in the current hour will influence the power production the next hour, i.e. the power production is assumed to be a Markov chain.

The probability pij of jumping from power level i in the current hour to power level j

in the next hour is calculated from the two years of statistics by

pij =

Number of transitions from power level i to j

Total number of transitions .

All these probabilities are collected in a transition matrix

P =        p1,1 p1,2 . . . p1,10 p1,1 p1,2 . . . p1,10 ... ... ... ... p10,1 p10,2 . . . p10,10       

one for each node. The transition matrices can be found in the data subsection 3.1.7.

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To generate a wind scenario the start power level `1 in hour 1 is randomly chosen

according to the probabilities pi, then for hour 2 the transitions probabilities p`1,j are

used to randomly choose the power level `2. The power level of hour 3 is then chosen

according to the transitions probabilities p`2,j and so on until the power level `24 of

the last hour is chosen.

3.1.3 CHP model

In node 10 and 17 in the test system CHP plants are installed which correspond to around 10% of the total installed power of the test system. These power plants are used under heavy load conditions to supply the system with power when other power sources are limited or there are transmission bottlenecks in the system. Each CHP plant has a minimal and maximal power setting when it is running. The increase and decrease in power output are also limited since the plants act slowly to changes, due to the physical processes involved in the power generation. Once a CHP plant is running or has been stopped there is often a fixed minimal amount of time the plant must be running or being offline. [12]

The cost C associated with running a CHP plant can in many cases be modeled as a linear function of the generation G,

C(G) = αG+ βGG, (1)

where βG is dependent on the fuel that is used. When a CHP plant is started och

stopped there is an associated cost, C+ and C, respectively. It is this cost function

that is used in the model.

A number of factors are not considered in this model, such as ramp up and ramp down time of the power production, banking costs, staff and maintenance costs etc. It is also assumed that there is demand for all heat produced. These limitations of the model is chosen to make the CHP model sufficiently simple. A reason for this is that the main focus of the project is on wind power in combination with hydro

power and the CO2 emissions in the system.

3.1.4 Nuclear power model

Nuclear is a base power in the test system and it produces a constant level of power of roughly 40% of the total installed power. Since it delivers a constant power output to the system it has a fixed price. This means that this power source will not affect the outcome of the planning problem regardless of the other factors.

The mechanism of generating power in a nuclear power plant is similar to the one in a CHP plant. This is a heavy handed way of modeling nuclear power which ignores all the factors present in the CHP model, but is motivated by the fact that the

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generation in a large nuclear power plant is seldom changed during a 24 hour time frame. [42]

3.1.5 Load model

The load in a typical power system has cyclic nature. Each weekday the power con-sumption is the lowest during the morning and the night and has two peaks during late morning and late afternoon. This pattern can also be seen during weekends but then the peaks are less prominent. An illustration of this behaviour can be seen in Figure 15.

Figure 15: The power consumption during the first week of year 2013 in Sweden in electricity area SE1.

To construct a load model for the test system the power consumption in Sweden on one particular day, January 3 2013, is chosen. This is a winter day when the consumption is high and has a typical behaviour as can be seen in Figure 16. The power consumption in each of the four electricity areas are rescaled by a con-stant factor to give a corresponding load in the four electricity areas of the model. Within each area the load is then distributed slightly unevenly to the different nodes to simulate larger and smaller power consumption nodes in the area. The exact pro-portions can be found in subsection 3.1.7.

Figure

Figure 1: Flowchart of the method used for the test system in this master thesis.
Figure 2: The Swedish transmission grid 2016 [10].
Figure 3: Supply and demand curve [16].
Table 2: Power production and installed power in Sweden 2015/2016 [11].
+7

References

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