Modelling the Nordic Hydro Power System with Spine Toolbox

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IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2021

Modelling the Nordic Hydro

Power System with Spine

Toolbox

ANGELICA WAERNLUND

KTH ROYAL INSTITUTE OF TECHNOLOGY

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Modelling the Nordic Hydro

Power System with Spine

Toolbox

ANGELICA WAERNLUND

Master in Electric Power Engineering Date: March 6, 2021

Supervisor: Manuel Marin Examiner: Mikael Amelin

School of Electrical Engineering and Computer Science

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iii

Abstract

In the Nordic power system, the largest balancing resource is hydro power. For future developments of the Nordic power system with more renewable and varying energy, such as wind power, the hydro power and its limitations must thus be taken into account. To be able to study this, a model with these limitations is needed. In earlier projects at KTH, a model of the Swedish hy-dro power system was built, but with the interconnected Nordic power system and the large amount of hydro power in Norway, the Norwegian hydro power system also needs to be considered.

In this project, a model of both the Swedish and Norwegian hydro power system is built. Most of the data of the Swedish hydro power system is reused from the earlier projects, while new data of the Norwegian hydro power system is collected. Also data of transmission capacities and power generation and consumption for all areas, both in Sweden and Norway, were needed. Most of the data could be found, or calculated from, the Norwegian Water Resources and Energy Directorate, Nord Pool and Svenska Kraftnät.

The new model built in this project includes 363 Norwegian and 256 Swedish hydro power plants, divided into four Swedish and five Norwegian electricity areas. The model is built in Spine Toolbox and is an expanded and remade model based on an earlier, smaller model of the Skellefte river, which maximised the profits of sold electricity. In this project the model is changed to instead minimise the spillage and explore the flexibility of the hydro power system. That is, its possibility to adjust its power generation to both variable levels of demand and other sources of power generation without being forced to spill water.

The results from the simulations were hourly values of water flow between hydro power plants, discharged water and spilled water, electricity flow from each hydro power plant and between electricity areas, and reservoir volumes in each reservoir. From this, the simulated production in Sweden, Norway and all their electricity areas could be compared to real data of energy production. This comparison showed that the total simulated production was very similar to real data when factoring out import and export. The spillage and reservoir volumes were also discussed.

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iv

Sammanfattning

I det nordiska kraftsystemet är vattenkraft den största resursen för att balansera variationer i elproduktion. För framtida ändringar och utbyggnader i kraftsy-stemet med mer förnybara och varierade energikällor, som vindkraft, måste vattenkraften och dess begränsningar tas hänsyn till. För att kunna studera det nordiska kraftsystemet behövs en modell som tar häsyn till dessa begränsning-ar. I tidigare projekt på KTH togs en modell av det svenska vattenkraftsyste-met fram, men med det sammankopplade nordiska kraftsystevattenkraftsyste-met och den stora mängden vattenkraft i Norge, måste även Norges vattenkraftsystem beaktas.

I detta projekt skapas en modell över det svenska och norska vattenkraft-systemet. Majoriteten av data för det svenska vattenkraftsystemet återanvänds från tidigare projekt, medan ny data för det norska vattenkraftsystemet samlas in. Även data över överföringskapaciteter och elproduktion och konsumtion för alla områden, både i Sverige och Norge, behövdes. Den nya modellen som byggs i detta projekt inkluderar 363 norska och 256 svenska vattenkraftverk, uppdelade i fyra elområden i Sverige, och fem i Norge. Modellen byggs i Spine Toolbox, och är en ombyggd och expanderad modell, baserad på en tidigare, mindre modell av Skellefteälven som maximerade inkomst från såld energi. I detta projekt ändras modellen till att istället minimera spillet och undersöka flexibiliteten i vattenkraftsystemet. Det vill säga, dess möjlighet att anpassa kraftproduktionen till både varierande efterfrågan och annan elproduktion, ut-an att tvingas spilla vatten.

Resultaten från simuleringarna bestod av timvärden för vattenflöde mel-lan vattenkraftverk, tappat och spillt vatten, flöde av el från varje kraftverk och mellan elområden, och magasinvolymer. Den simulerade elproduktionen i Sverige, Norge och i alla elområden kunde sedan jämföras med verklig data. Denna jämförelse visade att den totala simulerade produktionen var mycket lik den verkliga vattenkraftproduktionen med import och export exkluderat. Även spill och magasinvolymer diskuterades.

Ytterligare arbete kan ge en ännu bättre modell, exempelvis kan framtida arbete vara att lägga till export och import, implementera minimala magasin-volymer, och lägga in verklig data för lokalt inflöde av vatten, men överlag gav dock modellen lovande resultat.

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Chapter 1 Introduction

1.1 Background

Due to the climate changes seen today, renewable energy sources will have an increasingly important role in the future. Many of the renewable solutions that exist today will give a continuously varying energy generation, for example wind energy, where energy is only generated when the weather is favorable. The power system must thus have enough resources to balance the variations in production and consumption. Power cannot be stored in the power lines for when it is needed. Too large difference between production and consumption will lead to variations in the frequency, which in turn could lead to disturbances or that parts of the grid need to be disconnected.

In the Nordic power system, one of the largest sources of renewable en-ergy is hydro power, which also is the largest balancing resource. For future developments of the Nordic power system, with more renewable energy such as wind power, the hydro power and its limitations must be taken into account. These limitations include reservoir capacity, water delay times, environmental restrictions, etc. Even though hydro power is a good balancing resource, there is a limit of how much it can balance at a given time and place, which can affect the way in which the power system should be developed in the future.

In earlier studies at KTH [1], [2], a detailed model of the hydro power sys-tem in Sweden was developed, but in order to study the Nordic power syssys-tem, the Norwegian hydro power system is also important, since Norway has even more hydro power than Sweden.

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2 CHAPTER 1. INTRODUCTION

1.2 Earlier projects

In 2009, a model was made in the program GAMS of the hydro power system in northern Sweden. This model, explained in [1], included 154 hydro power plants, and had a combined capacity of 13.2 GW. This corresponded to about 80 percent of the total installed capacity of all hydro power in Sweden and made it possible to, on an hourly basis, investigate the interplay between hydro power, wind power, other power plants and different loads. The model was made with a focus on the technical details of the hydro power system, and took aspects like water delay time, court decisions and physical limitations into account. The electricity market and short-term planning were modelled with less details though. This model was then used in case studies to investigate the balancing power when the wind power was expanded to different capacities, up to 12 000 MW.

The conclusion of that report was that the existing hydro power in northern Sweden is fast enough and has sufficient installed capacity to balance large amounts of wind power. The challenge with such an expansion in wind power would, instead of balancing, be about what to do with all the excess energy.

Since then, the model has been expanded to include all hydro power plants with a capacity of more than 10 MW in northern Sweden, and 5 MW in the rest of Sweden. The updated model thus includes 256 hydro power plants, with an installed capacity of 15 640 MW. The actual number of hydro power plants in Sweden was around 1 800 at the time, with a capacity of 16 200 MW. This means that 96.5 percent of the hydro power capacity in Sweden, at the time of the work, was considered in the model [2].

1.3 Objectives

To study the Nordic power system, a model of the Swedish and Norwegian hydro power system is needed. This model also has to take into account the limitations of the hydro power system, such as reservoir capacity, water delay times, etc. To make such a model, data from the Norwegian hydro power system is needed in addition to the existing data of the Swedish hydro power system, used in earlier projects. The data used for the hydro power system in this project should be public data. In the cases where public data can not be found, approximations and assumptions may be needed.

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CHAPTER 1. INTRODUCTION 3

able to give an indication of how the hydro power system operates in different scenarios.

This master thesis project has two main objectives. The first objective is to collect enough public data from the Norwegian hydro power system to be able to make a model of the Norwegian hydro power system similar to the existing model of the Swedish hydro power system. The second objective is to build a model of the Swedish and Norwegian hydro power systems in the simulation tool Spine Opt [3], which is an open-source energy modelling toolbox. This project also has a secondary objective, which is to provide feedback to the Spine development team about the user friendliness, missing features, etc.

1.4 Contribution

The outcome of this project is a model of the Swedish and Norwegian hydro power system. This model will hopefully be able to give an indication of how the system works today in different situations and could help with future de-velopments in the power system, to know how much energy the hydro power is able to produce in different scenarios, and how much spillage there will be. Another outcome of this project is the feedback to the Spine development team throughout this project.

1.5 Overview of the report

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Chapter 2 The power system

In this chapter the basics of the power system is explained. The main focus is the hydro power system; how it works, what the situation is today, and the limitations that need to be taken into account. This chapter also briefly go through basic theory and calculations useful for hydro power modelling. For more theory and calculations, see [4].

Electric energy has an important part in society today, and most people are dependant on it, in most things done during normal everyday life. Because of the dependence on electric energy, it is important to have a power system that is reliable and well-balanced in terms of production and consumption.

The last decades, more and more focus has been put on renewable energy, due to the awareness of climate change and CO2 emissions. The Swedish government has decided on a goal which states that in 2040, 100 percent of the energy in Sweden should come from renewable resources [5]. In 2008, 44.7 percent of the total energy supply in Sweden came from renewable energy sources, and in 2018, 10 years later, that number had increased to 54.6 percent [6]. This represents the energy from different sources based on heat content, except for those that generate pure electricity. This increase can be seen in more detail in figure 2.1.

A problem with most renewable energy sources is that they are difficult to predict or regulate. The power generation of wind power is continuously varying due to variations in wind speed, and photovoltaics only produce elec-tricity when there is enough sunlight. This means that when the wind speed is low, on cloudy days or after sunset, those sources of energy may not produce enough energy. There can be large variations and the power produced can be difficult to predict. This makes it more difficult to only rely on renewable

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CHAPTER 2. THE POWER SYSTEM 5 1990 1995 2000 2005 2010 2015 Year 0 10 20 30 40 50 60

Percentage of total energy use

Use of renewable energy sources

Figure 2.1: Share of renewable energy sources in Sweden from 1990 to 2018. [6]

ergy. However, hydro power is one of the renewable energy sources where it is possible to regulate the energy production, by saving water when there is low energy demand, and using the water to produce energy, when the demand is high.

Another problem with renewable energy sources is that they are highly dependant on the geographical conditions being favorable, for example wind power is most effective in places with high, relatively constant, wind speeds, and hydro power is dependant on rivers, preferably with a high head. Because of this, more hydro power is produced in, for example, northern Sweden than in southern Sweden. This makes the transmission between electricity areas and countries even more important. Both Sweden’s and Norway’s electricity market is divided geographically into multiple electricity areas. In Sweden there are four electricity areas, and in Norway there are five.

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6 CHAPTER 2. THE POWER SYSTEM

2.1 Wind power

Wind power is the energy that increases the most in Sweden right now [8]. From a production of 457 GWh wind power in the year 2000, to 3 502 GWh 2010 and 19 847 GWh last year, 2019. [9]

The goal for year 2020 is to have a production of 30 TWh wind power per year [10]. During 2019, 19.5 TWh were produced, with an estimation that the existing turbines at the end of 2019 could produce 24.7 TWh during a whole year with normal wind conditions. The total installed capacity was then almost 9 000 MW. The planned capacity at the end of 2020 is 10 883 MW, with an estimation that the existing turbines at the end of the year could produce 30.9 TWh during a whole year with normal wind conditions. [11]

Wind power is difficult to control, since the power produced depends on the wind. Thus, an energy source that is easy and fast to control is needed to balance the power produced and consumed. One of the best alternatives for this is hydro power.

2.2 Hydro power

Potential and kinetic energy from flowing water has been used for a very long time. As far back as 2000 years ago, people have been using flowing water to automate different tasks, like grinding wheat or corn using water wheels, or pounding grain with trip hammers. The first modern water turbine was developed in 1849 by a British-American engineer, and the first hydroelec-tric project was to power a single lamp in England, in 1878. Only four years later, in 1882, the first hydro power plant to serve a system of costumers was opened in Wisconsin, with a power output of 12.5 kW. After that, the number of hydroelectric power plants increased quickly, and a decade later there were already hundreds of hydro power plants around the world [12]. The largest hydro power plant today is the Three Gorges Dam in China, with an installed capacity of 22 500 MW. [13]

Hydro power uses the difference in potential energy in the water levels above and below the turbine. When water is discharged from the upper water level to the lower, the potential energy in the water is transformed to kinetic energy. The discharged water then flows through a turbine, connected to a generator, which converts the kinetic energy to electric energy. [4]

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CHAPTER 2. THE POWER SYSTEM 7

power is needed. There are also hydro power plants without reservoirs, which are called run-of-river power plants. These have a fairly consistent water flow, but can only store a little to no water.

Hydro power has the highest energy efficiency rates, produces almost no emissions or pollutants, and also has a very low production cost. The life span of hydro power is also the longest of all power generation technologies. [14]

Even though there are a lot of advantages with hydro power, there are also disadvantages. Even though the production cost is low, the initial cost to build a hydro power plant is high. One of the largest disadvantages is the impact on the local environment and wildlife. The water flow in a river with a hydro power plant can vary a lot, which can either cause the river downstream to almost dry out, or flood the area around the hydro power plant. The fish living in the river is also highly affected by hydro power plants, and many hydro power plants have separate passages for fish migration to lower the risk of fish getting hurt by the turbines. Overall, many of the hydro power plants have regulations to reduce the impact on the environment. This can for example be minimum and maximum limits on how much water that can be discharged or spilled during a specific time. The local environment thus has an impact on the placement of the hydro power plant, along with other physical limitations such as high enough water flow, head, and proximity to the electrical power grid. [15]

Since the beginning of the twenty-first century, there has been a renewed increase in development of hydro power. This is partially due to an increase in demand for affordable, reliable and sustainable electricity sources, especially in developing countries. From the year 2000 until 2017, the installed capacity of hydro power in the world increased by as much as 65 percent, or nearly 500 GW. [12]

Sweden and Norway are two of the countries producing and using the most hydro power. One third of all hydro power in Europe is located in Sweden and Norway. [16]

2.2.1 The Swedish hydro power system

Hydro power has been used in Sweden for hundreds of years and is one of the reasons why Sweden has such a reliable energy system. With 16 200 MW installed capacity and around 2 000 hydro power plants, almost half of the electric energy used in Sweden comes from hydro power. Most of this energy, around 80 percent, is produced in the northern parts of Sweden. [16]

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general have low head, but large water flows.

The largest hydro power plant is called Harsprånget and is located in the Lule river. It has an installed capacity of almost 1000 MW and produces around 2 TWh/year. In Sweden, around 68 TWh hydro power is produced every year [17].

2.2.2 The Norwegian hydro power system

In Norway, over 90 percent of the produced energy comes from hydro power. There are over 1 600 hydro power plants, and more than 1 000 hydro power storage reservoirs. With a total reservoir capacity of more than 86.5 TWh, the reservoirs can store up to 70 percent of the annual electricity consumption in Norway. [18]

With a yearly production of, on average, 135.6 TWh, Norway produces al-most twice as much hydro power compared to Sweden. The installed capacity of hydro power in Norway is also around twice as large as in Sweden, with 32 671 MW in January 2020 [19]. In general, the hydro power plants in Norway have a higher head than in Sweden.

2.2.3 Theory and Equations

When calculating hydro power, a unit that is commonly used is hour equiva-lents (HE). Hour equivaequiva-lents represents a water flow of 1 m3/s during 1 hour, and can represent both a volume or a flow of water, depending on the context. Discharge, spillage and reservoir contents are often measured in HE. [4]

Some of the variables and parameters often used in hydro power calcula-tions, and their units, can be seen in table 2.1.

The functions that are commonly used when calculating hydro power are often approximated and expressed as linear or piece wise functions to make it possible to include them in an LP (linear programming) model. An example of this is the power generation H, which is a function of the discharge Q. The quota between the power generation and the discharge is the production equivalent, γ.

γ(Q) = H(Q)

Q (2.1)

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CHAPTER 2. THE POWER SYSTEM 9

Table 2.1: Variables and parameters used in hydro power calculations

Hi,t Power generation in power plant i during hour t [MW]

Mi,t Contents of reservoir i at the end of hour t [HE]

Qi,t Discharge through power plant i during hour t [HE] Si,t Spillage past power plant i during hour t [HE]

Vi,t Local inflow to reservoir i during hour t [HE]

κi The set of indices for power plants directly upstream of

power plant i

τj,i Water delay time between power plant j and the closest

downstream power plant i [h]

γi Production equivalent in power plant i [MWh/HE]

µi,j Marginal production equivalent for segment j in power plant i [MWh/HE]

µ = dH(Q)

dQ (2.2)

Both the production equivalent and the marginal production equivalent is measured in MWh/HE. When creating a piece wise linear model of the power generation, the power generation and discharge functions is often divided into segments. The power production expressed in segments can be seen in equa-tion 2.3, where the segments are represented by j, and the number of segments in power plant i is expressed by ni.

Hi,t = ni

X

j=1

µi,jQi,j,t (2.3)

When using this linear programming method, µ have to be decreasing with the segment j.

When modelling the hydro power system, it is also important to take the hydrological balance into account. This is a physical necessity, that the change in water in a reservoir over time is the same as the difference between water inflow and outflow. This balance equation can be written as in equation 2.4.

new reservoir contents = old reservoir contents

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The water inflow to a reservoir consists of discharged and spilled water from the upstream hydro power plant, along with the local inflow of water. Equation 2.4 can also be written as a mathematical equation, as seen in equa-tion 2.5.

Mi,t = Mi,t−1− Qi,t − Si,t +

X j∈κi Qj,t−τj,i + X j∈κi Sj,t−τj,i + Vi,t (2.5)

If the delay time τj,i between two hydro power plants j and i is assumed

to be constant throughout the year, with a delay time of hj hours and mj

min-utes, the discharge can be expressed as equation 2.6. The spillage can also be expressed in a similar way.

Qj,t−τj,i =

mj

60Qj,t−hj−1+

60 − mj

60 Qj,t−hj (2.6)

Other physical limitations that need to be taken into account could also be minimum and maximum discharge and reservoir content. These limitations can be formulated as mathematical expression, as seen in equation 2.7.

Q_i ≤ Qi,t ≤ Qi

M_i ≤ Mi,t ≤ Mi

(2.7)

In equation 2.7 Qi and Mi represents the minimum water discharge and

reservoir volume, and Qi and Mi represents the maximum water discharge

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Chapter 3 Norway Data collection

This chapter explains how the data from the Norwegian hydro power system is obtained. It goes through what values were found and which are approxi-mations, and how those approximations are made.

To build a model of the system, a lot of parameters are needed. Most of the data from the Swedish hydro power system were assumed to be the same as in the earlier project from 2012 [2], and thus reused in this project.

Because of the large amount of hydro power plants in Norway, not all of them are considered in the model that was created in this project. Since Nor-way has more than 1 600 hydro power plants, and more than 300 have a capac-ity of 10 MW or higher, the main focus of this project has been the larger hydro power plants. That is, those with more than 10 MW of installed capacity. A compilation of all the existing hydro power plants in Norway can be seen in table 3.1, with installed capacities and average yearly productions for different size categories.

Table 3.1: The hydro power system in Norway [19] Category Quantity Capacity [MW] Average prod.

[TWh/year] <1 MW 574 186 0.8 1-10 MW 737 2 633 10.3 10-100 MW 257 9 582 42.3 >100 MW 83 20 270 82.4 Total 1 651 32 671 135.8

In this project, a total of 363 Norwegian hydro power plants were included,

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12 CHAPTER 3. NORWAY DATA COLLECTION

with a total installed capacity of 30 093.18 MW, 92.1 percent of the total in-stalled capacity in Norway, and a total average yearly production of 125.64 TWh, 95.5 percent of the total average yearly production in Norway. Most of the real data used were from the year 2019, or average values.

3.1 Parameters

The parameters needed to build the model, for each of the included power plants, can be seen in table 3.2, along with the sources and methods used.

Table 3.2: Parameters needed to model the hydro power plants.

Parameter Source Method

Installed capacity Found through [19]

-Production equivalent Calculated from [19] Section 3.2 Maximum reservoir volume Calculated from [20] Section 3.3 Reservoir volume at the start

Calculated from [21] Section 3.3 and end of the simulated week

Water flow at the start of

Calculated from [19] Section 3.4 the simulation

Local inflow of water Calculated from [19] Section 3.4 Downstream power plant,

Approximated from [19] Section 3.5 discharge and spillage

Flow time to downstream power

Approximated from [19] Section 3.5 plant, discharge and spillage

A lot of information was found through the website of NVE, Norwegian Water Resources and Energy Directorate [19]. For example, the installed ca-pacities and production equivalents of all hydro power plants, all reservoirs and to which hydro power plant they are connected. Average yearly productions and maps could also be found on this website, which were used for approxi-mations of values that were not found. Also, the total reservoir volume for all reservoirs in Norway, in percentages of the maximum volume, was found for all weeks of the year.

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CHAPTER 3. NORWAY DATA COLLECTION 13

Table 3.3: Parameters needed to model the electric power system.

Parameter Source

Electricity demand in all Found through [22] electricity areas

Electricity generation from Found through [23] other energy sources

Transmission capacities Found through [22] between areas

Total electricity generation Found through [22] and [23] in all areas

The electricity demand, or consumption, in all electricity areas, for every hour of the simulated weeks were needed, including the Swedish electricity areas. For the Swedish electricity areas, the electricity generation from other energy sources were also used. Also, the capacities in the transmission be-tween the different electricity areas were needed.

A lot of data of the power system could be found through Nord Pool [22]. There, the consumption in all electricity areas and the transmission capacities between areas were found, for every hour of the year. Also, production per hour in all areas in Norway was found from Nord Pool, but this was only used for comparing the results of the simulations with. The energy production per hour from different energy sources in Sweden was found through Svenska Kraftnät [23]. The production per hour in Sweden from other sources than hydro power, such as wind and thermal power, was added to the model. The production of hydro power was used to compare with the results. In Norway, data from different energy sources could not be found, thus all energy produced were assumed to be hydro power, since the hydro power stands for over 90 percent of the Norwegian power production.

3.2 Production equivalent

The production equivalents found through NVE [19] were in unit kwh/m3. To use them in the model, they had to be converted to unit MWh/HE. This calculation can be seen in equation 3.1.

γM W h/HE =

3600

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3.3 Reservoir volumes

Through NVE [20], a data file containing all reservoirs, their maximum vol-ume in GWh, and to which power plant they belonged to, was found. With the production equivalent of the power plants, in kWh/m3, or GWh/mill.m3, the maximum reservoir volume in mill.m3 could be found, and then recalculated to HE, as seen in equation 3.2,

Vmill.m3 = VGW h γ VHE = 106 3600Vmill.m3 (3.2)

where V represents the reservoir volume in different units, mentioned above, and γ is the production equivalent of the power plant to which the reser-voir belongs. Since the hydro power plants are not piece wise modelled in this project, the production equivalent γ is used.

Many of the hydro power plants had more than one reservoir. These reser-voirs were then approximated to be one large reservoir instead, as can be seen in figure 3.1.

(a) Real system (b) Approximation

Figure 3.1: All reservoirs belonging to the same hydro power plant were ap-proximated to one large reservoir.

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CHAPTER 3. NORWAY DATA COLLECTION 15

reservoirs in Norway, in percentage of the total maximum volume, could also be found on the website of NVE [21], and can be seen in figure 3.2. These per-centage values were used to scale all reservoir volumes for each week during the year, so that all reservoirs followed the same volume curve over the year. For example if, for a specific week, the total reservoir volume in Norway was at 70 percent, all individual reservoirs were set to be at 70 percent of their max-imum volume that week. For simplicity, the average values were used for all electricity areas, and in both Sweden and Norway, even though they could dif-fer a bit between areas, depending on geographical location, with for example differences in weather conditions and topography.

0 5 10 15 20 25 30 35 40 45 50 Week 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Percentage of maximum volume Highest

Lowest Average Year 2019

Figure 3.2: The total reservoir volume for all reservoirs in Norway over the year.[21]

3.4 Water flow

There is always water flowing in the rivers. Thus, when starting the simulation, there should already be water flowing between the hydro power plants. This is set to be the average water flow. Since no real data of this could be found, an approximation of this was made.

By taking the average energy production Paverage, in GWh per year, and

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calculation of the average water flow w can be seen in equation 3.3. w = 10

6_{· P} average

γ · 365 · 24 · 60 · 60 (3.3) To evaluate how much the calculated values differed from the real values, this calculation was also made for a few of the hydro power plants in Sweden, which already had values for the average water flow. The calculated values were then compared to the values already obtained in the earlier projects [1], [2]. The average difference between the calculated values and the real values were 9.3 percent, where the calculated values were, on average, 97.3 percent of the real values.

The local inflow, the extra added water between a hydro power plant and the upstream hydro power plant, was assumed to be the difference between the water flow through a hydro plant and the upstream hydro power plant. Since the inflow of water changes during the year, with more water in the spring or summer when the snow melts, the inflow was roughly scaled to follow the same curve as in the graphs presented in a report from NVE [24].

3.5 Flow time

It takes some time for the water to flow between two power plants. To find the downstream hydro power plants for all hydro power plants, the maps on NVE were used to see the locations. The rivers were then followed to see which hydro power plant was next downstream. Since no data of the flow time could be found, a method found in an earlier project [1] was used. By measuring distances along the rivers on maps, and assuming that the water flows at a speed of 4-5 m/s, such as in the earlier project when obtaining data from the Swedish hydro power system, approximations of the flow time between hydro power plants were obtained.

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Chapter 4 Spine model

This chapter will explain how the model was built in Spine toolbox, how it works and what the parameters used in Spine toolbox represent.

The Spine Toolbox is an open-source application containing software tools used to define, manage and execute models of energy systems. It makes it possible to, in a flexible and realistic way, model future energy systems, both detailed complex systems and larger scale systems [25]. During the autumn 2018, the source code and documentation was released to the public, but Spine Toolbox is still under development. Because of this, there are still features that are not yet implemented, and during this project there has been a continuous contact with the team working on developing Spine Toolbox to improve it and solve problems that have occurred.

The team working with Spine Toolbox has previously made a model of a smaller hydro power system of the Skellefte river in Sweden. This opti-mization model had the objective to maximize the revenues from selling the electricity produced by the hydro power system, thus discharging water when the electricity price was high [26]. The model of the Skellefte river was used as a starting point for this project, but instead of maximising profits, this new model minimises the spillage and explores the flexibility of the hydro power system. That is, its possibility to adjust its generation to variable levels of demand and other generation without being forced to spill water.

Since the original Spine model, that was used as starting point, maximises profits, penalty costs were introduced for parameters that should be minimised. Penalty costs were mainly introduced for spilling water, which means that the new model will try to avoid spilling water to keep the costs down. A higher penalty cost was also added for energy deficiency or excess, to make it possible to buy or sell energy if the model cannot otherwise find an optimal solution.

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18 CHAPTER 4. SPINE MODEL

Later on, another penalty cost was added for when the system had to little inflow of water, to avoid simulation problems during the time of year where there is a large local inflow of water. This was needed since the approximated local inflow was difficult to predict. The spillage penalty costs used in the simulation are the same for all hydro power plants, and the higher penalty costs are the same if there is energy deficiency or excess energy.

The objective is to minimise the cost of the system, in this case the penalty cost of water spillage and the penalty cost of producing a surplus or deficit of energy, subject to the hydrological balance and physical limitations, seen in equations 2.5 and 2.7. The objective function can be expressed as in equation 4.1. min T X t=1 (ρδ A X a=1 (δ_a,t+ + δ_a,t−) + I X i=1 ρiSi,t) (4.1)

T is the hours of the simulated week, A is the number of electricity areas, ans I is the number of hydro power plants in the system. ρδ represents the

penalty cost of producing a surplus or deficit of energy, where δa,t+ and δ − a,t

represents the positive amounts of electricity surplus and deficit in area a dur-ing hour t. ρi represents the penalty cost of spilled water from hydro power

plant i, where Si,tis the amount of the spillage from power plant i during hour

t.

This new model will contain most of the larger hydro power plants in Swe-den and Norway. The data for the Swedish hydro power plants is mainly from the earlier projects [1], [2], and the collection of data from the Norwegian hy-dro power system is explained in Chapter 3, where the approximations made are also explained. Of the around 2 000 hydro power plants in Sweden, 256 are included in the model, which corresponds to about 96.5 percent of the in-stalled capacity in Sweden. For Norway, 363 of the 1 651 hydro power plants are included, or 92.1 percent of the installed capacity. In table 4.1 a compi-lation of the data from the hydro power plants in Sweden and Norway can be seen.

4.1 Building the data store

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CHAPTER 4. SPINE MODEL 19

Number of

Capacity [MW] Average prod.

power plants [TWh/year]

Norway 363 30 093 125.6

Sweden 256 15 640 65.3

Total 619 45 733 191

Table 4.1: Data of the modelled hydro power system.

of the simulation is stored in the second data store, which is empty before the simulation.

Figure 4.1: The Data Stores and Tool in Spine Toolbox.

The input data store contains the power system information, in the form of objects and relationships between the objects, and input parameters. The objects and relationships used to build the system, together with the used pa-rameters, are explained below.

4.1.1 Objects

The objects used to build the model in Spine Toolbox can be seen in figure 4.2.

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Unit

In the Spine model, the hydro power plants are represented as units. Since they can have a cost and capacity, they are also used for setting a cost for spillage to make it possible to minimise the spillage, and for transmission capacities. To avoid problems when running the simulations, a unit called electricity_load was also added for each electricity area. These units could, for a high cost, produce extra energy or consume excess energy to avoid imbalances in the system.

Units were also used for the generation of wind and thermal power in Swe-den, with real hourly values added. These were, just like the electricity_loads, connected to the electricity areas.

Node

The upper and lower water levels of all hydro power plants are represented with nodes. Also, the electricity areas were represented as nodes.

The following parameters are used in this object:

• demand represents the local inflow of water to the node, or the energy consumption in the node. The demand should be a negative number when representing the inflow.

• has_state represents if the node has a storage. This is typically used for the upper nodes of the hydro power plants, which often have reservoirs which can store water. If the node has a storage, this parameter is set to T rue.

• node_state_cap is the maximum storage capacity. For example, the maximum volume of water that can be stored in the reservoir of a certain node, before excess water needs to be spilled.

• f ix_node_state represents the initial and final volume of the reservoir with a time series consisting of two values. The initial volume at the start of the simulated week and the final volume at the end of the simulated week.

Connection

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can also be used to represent the transmission between electricity areas, though in the model built in this project, units are used for the transmission. The reason for this was that the connection capacities were not working in Spine during the time of this project.

Commodity

The commodities represent the different energy types in the model. In this project there are two commodities; water and electricity. By creating a re-lationship between a node and a commodity, the energy type in the node is set.

Temporal_block

The parameter resolution defines the time resolution in the simulation. For this project the resolution is 1 hour.

Model

The model object defines the modelling parameters. The simulations were ex-ecuted a week at a time, for one week per month during the year. The duration of each simulated week was set in the model object.

• model_start sets the starting date and time of the simulation, for exam-ple, the first hour of a chosen week.

• model_end sets the end date and time of the simulation, for example, the last hour of the chosen week.

4.1.2 Relationships

Relationships describe how objects are connected to each other, and how they relate. Just like the objects, the relationships can also have parameters.

connection_from_node

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connection_node_node

connection_f low_delay is the time delay in a connection between two nodes. In this project that parameter is used to represent the time it takes for the water to flow from one hydro power plant to the next downstream.

node_commodity

This relationship sets what type of commodity that is present in the node. By creating a relationship between a node and, for example, the water commodity, it makes it so that there is water in the node, like the upper and lower nodes of a hydro power plant. In the model built in this project, the electricity nodes representing the areas have a relationship to the electricity commodity, and the upper and lower nodes in the hydro power plants are connected to the water commodity.

unit_from_node

The parameters used in the relationships between a node and a unit are the following:

• unit_capacity is the capacity of the hydro power plant. That is the max-imum amount of water that can flow through the unit.

• vom_cost is the cost of using the unit. This parameter is used in the relationships between the electricity load units, for the spillage units and for the later added extra water units. By adding a cost for these things, the simulation minimises the usage of these units, and only use them if necessary. Depending on how important it is that the system should minimise the usage of some unit, the costs could be higher or lower. If there, for example, are two spillage ways and one has a lower cost, the system will try to use the cheaper if possible. The vom_cost can also be negative, thus the system will try to use the unit as much as possible.

unit_node_node

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4.1.3 Overview of the Model in the Database

By using the object and relationships as explained, a model of the hydro power system can be built. In figure 4.3 it can be seen how a hydro power plant is built with objects and relationships, and how it is connected to a downstream power plant and the electricity area. The different objects can be seen in figure 4.2, and are explained in more detail, with their parameters, in section 4.1.1. The lines between the objects are the relationships, which are explained in more detail in section 4.1.2.

Figure 4.3: The hydro power plants Ritsem and Vietas modelled in Spine tool-box.

A typical hydro power plant consists of three nodes, two units, and two connections. In the example in figure 4.3, the first object in hydro power plant Ritsem is Ritsem_upper, a node which represents the upper water level of the hydro power plant, and also its reservoir. The discharged water then flows through the hydro power plant Ritsem_pwr_plant, represented by a unit, and onward to the lower water level of the hydro power plant, represented by the node Ritsem_lower. From the lower water level, the water flows toward the upper node of the next hydro power plant downstream, in this case Vietas, via a connection Ritsem_to_V ietas_disch. This connection represents the delay time, the time it takes for the water to flow between the two power plants.

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unit Ritsem_to_V ietas_spill_unit, which has a cost for water flowing through it, to the node Ritsem_to_V ietas_spill_node. This ensures that the model minimises the amount of spillage in the system. From there it also flows towards the downstream power plant, through the connection Ritsem_to_V ietas_spill which gives the water flow a time delay before it reaches the next power plant, Vietas.

Appart from these objects, there is also the node electricity_node_SE1. From the hydro power plant, the generated electricity flows to the electricity node, representing the electricity area to which the power plant belongs. All hydro power plants in one area are connected to the same node in the model, for example are both Ritsem and Vietas in the figure connected to the same electricity node representing area SE1.

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Chapter 5 Results and Discussion

This chapter will present the simulation results from the model built in Spine Toolbox. The results will be compared to real data, where real data could be obtained, and discussed to explain what the reason could be for differences between results and real data. For the results not compared to real data, dis-cussions will try to evaluate the reliability of the model.

5.1 Results over the year

The first results presented will show an overview over the whole year. 12 weeks were simulated, one week per month during the year 2019, to get a overview over how production, spillage and reservoir volumes changed over the year.

5.1.1 Production

Real data of the energy production was compared to the simulated production for 12 weeks of the year, one week per month. In figure 5.1 the simulated production and the real production in Sweden and in Norway can be seen.

The simulated production differs a bit from the real production. This was mainly thought to be because the import and export to other countries were not included in the model. The net exchange of Sweden and Norway, found at Nord Pools website [22], was added to the real data of the energy produced, to see how this affected the results. Thus, comparing the simulated to the real production minus the energy export and plus the import, since the model does not take import and export into account. The results from this can be seen in figure 5.2.

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CHAPTER 5. RESULTS AND DISCUSSION 27 0 10 20 30 40 50 Week 0 0.5 1 1.5 2 2.5 3 3.5 4 Production [TWh] Simulated SE Real SE Simulated NO Real NO

Figure 5.1: The hydro power produced in Sweden and Norway during 12 weeks of the year. Simulated result compared to real data.

0 10 20 30 40 50 Week 0 0.5 1 1.5 2 2.5 3 3.5 4 Production [TWh] Simulated SE

Real SE - export + import Simulated NO

Real NO - export + import

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28 CHAPTER 5. RESULTS AND DISCUSSION

When comparing the energy production without import and export, the curves have a more similar shape, though there are still differences between the simulated and the real data. One noticeable difference from figure 5.1 though, is that the simulated production, as seen in figure 5.2, in Sweden is now higher than the real production. The production in Norway is still lower in the simulation. In figure 5.3, when the whole hydro system is compared with the total hydro power production in Sweden and Norway together, it can be seen that the total simulated production for the whole connected hydro power system is very similar to the whole real system without export and import.

0 10 20 30 40 50 Week 0 1 2 3 4 5 6 Production [TWh] Simulated SE+NO Real SE+NO

Real SE+NO - export + import

Figure 5.3: The total hydro power produced in Sweden and Norway during 12 weeks of the year, compared to real production, with and without the imported and exported energy.

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CHAPTER 5. RESULTS AND DISCUSSION 29

Since export and import changes the energy balance in the system, it is rea-sonable that the simulated results differ from the real data, when the real data includes export and import. When removing the impact of these parameters from the real data, they should be much more similar, which the results also shows.

Even though the export and import seems to affect the result the most, there are also other aspects that can affect the results. A few examples could be data errors, in both collected data and calculated or assumed values, model discrepancies or deviations caused from the Spine software itself.

Another difference between the real and simulated production is where in the system the power is produced, the simulation divides the production different between Sweden and Norway than the real system. In the real system, there is no coordinated generation planning, all producers decide themselves how to schedule their units based on price, demand and weather forecasts. It might be interesting to add a low transmission cost to the model, in order to make it produce power closer to where it is needed, to see how much this would affect the results. Another thing that is clear from these results is that the import and export should be taken into account in the model, and maybe add other countries and electricity areas with energy production and consumption.

5.1.2 Spillage

Some water often needs to be spilled in a hydro power system, for example, due to environmental reasons, but unnecessary spillage is something that should be minimised. In the model built in this project, a penalty cost was added to minimise the water spillage.

The spillage was simulated for every hour during 12 weeks spread out over a year. Every week consists of 168 hours, and in figure 5.4 the total spillage in the system can be seen for every hour.

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30 CHAPTER 5. RESULTS AND DISCUSSION 0 20 40 60 80 100 120 140 160 Hour 0 1 2 3 4 5 6 7 Spillage [HE] 105 Week 3 Week 7 Week 12 Week 16 Week 20 Week 25 Week 29 Week 34 Week 38 Week 42 Week 46 Week 51

Figure 5.4: The hourly water spillage in Sweden and Norway during 12 weeks of the year.

from the previous week.

The main spillage is still during the last hour of the simulations though. This is probably due to the set reservoir volume value at the end of each week, based on real total reservoir volumes over the year, seen earlier in chapter 3, figure 3.2. If there, at the end of the week, is more water in the reservoir than the real data value, the reservoir will spill the excess water, even if the reservoir is not full. Ideally, the last hour reservoir level should be set as a minimum reservoir volume, and not a set volume. Minimum reservoir volumes were un-fortunately not yet implemented in Spine Toolbox at the time these simulations were made. This would be interesting to redo at a later stage when this feature is added, to avoid the unnecessary spillage.

Since this model finds an optimal solution, and the real world is not opti-mal, it is reasonable that the system could be able to spill less water. Approx-imations made of, for example, water inflow could also lead to a difference in reservoir volume at the end of the week.

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a logarithmic scale on the y-axis, it is clear that the spillage is largest during weeks 20 and 25. These are the weeks with the most local inflow of water due to the melting snow.

0 20 40 60 80 100 120 140 160 Hour 101 102 103 104 105 106 Spillage [HE] Week 3 Week 7 Week 12 Week 16 Week 20 Week 25 Week 29 Week 34 Week 38 Week 42 Week 46 Week 51

Figure 5.5: The hourly water spillage in Sweden and Norway during 12 weeks of the year in logarithmic scale.

5.1.3 Reservoir change

As stated earlier, the amount of water in the reservoirs change during the year, depending on, for example, energy demand or inflow of water. For the simu-lations that were made, the reservoir volumes at the start and the end of each week was set, as fixed values, based on real historical data, which can be seen in figure 3.2. The amount of water in the reservoirs were simulated for every hour of the 12 simulated weeks. Some weeks the amount of water increased during the week, and some weeks it decreased. The change in total amount of water in the reservoirs, in percentage of the starting reservoir volume, during all 168 hours of the simulated weeks can be seen in figure 5.6.

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32 CHAPTER 5. RESULTS AND DISCUSSION 0 20 40 60 80 100 120 140 160 Hour -6 -4 -2 0 2 4 6 8 10

Reservoir volume change [%]

Week 3 Week 7 Week 12 Week 16 Week 20 Week 25 Week 29 Week 34 Week 38 Week 42 Week 46 Week 51

Figure 5.6: The hourly change in water volumes in the reservoirs in Sweden and Norway during 12 weeks of the year.

every week, just like the earlier mentioned increase of spillage during the last hours of the simulations. The spillage is what makes it possible to decrease the water in the reservoirs without creating too much energy, which would instead have to be sold for an even higher cost than spillage. As mentioned earlier, it would be interesting to redo these simulations with a lower limit and not a fixed value of the water volume in the reservoirs at the end of the simulated weeks, to see how much water that could be saved instead of spilling it, and also to see how much the spillage would decrease.

5.2 Results from one week

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pro-CHAPTER 5. RESULTS AND DISCUSSION 33

duced power during one week in more detail, it can be seen how the energy production looks like on an hourly basis, instead of weekly. The hourly total production in the whole system can be seen in figure 5.7.

Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 0 5 10 15 20 25 30 35 40 Production [GWh] Simulated production Real production

Real production - export + import

Figure 5.7: The hourly total hydro power production in Sweden and Norway during week 7.

As mentioned earlier, the results from the simulation differ a bit from the real values. Since this is probably mostly due to the export and import of energy in the real system as stated earlier, the results were also compared to the the real data with export and import removed. As can be seen in the figure, the simulated results are very similar to the real data without export and imported energy.

5.2.1 Production in different electricity areas

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Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 0 50 100 150 200 250 300 Production [MWh] Simulated SE4 Real SE4

Figure 5.8: The hourly power production in electricity area SE4 during week 7.

A reason for this could be the export and import mentioned earlier. Elec-tricity area SE4 is also the area that has the most connections to other countries, which are not included in this model. As mentioned earlier in 5.1.1 though, the large difference between simulated and real production could be due to a combination of different aspects.

One of the electricity areas where the simulated production was instead most similar to the real production was area SE1. The hourly hydro power production in area SE1 can be seen in figure 5.8.

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Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Production [MWh] Simulated SE1 Real SE1

Figure 5.9: The hourly power production in electricity area SE1 during week 7.

5.2.2 Vietas and Vamma

To see in detail how the system works, the results from two specific hydro power plants were put together. Two hydro power plants were chosen, one in Norway and one in Sweden. They are both quite large and of similar size. They are not the first in a river, and not the last, but have hydro power plants both upstream and downstream in the river. The hydro power plant in Sweden is Vietas, located in electricity area SE1. The Vietas power plant can be seen as built in Spine Toolbox in chapter 4, figure 4.1. The hydro power plant in Norway is Vamma, located in electricity area NO1.

Production

Figure 5.10 shows the production of the two hydro power plants Vietas and Vamma. Each of these hydro power plants has quite sudden large changes in production, and often discharges either their maximum amount of water, or does not discharge any water at all.

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Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 0 50 100 150 200 250 300 350 Production [MWh] Vietas production Vamma production

Figure 5.10: The hourly power production in hydro power plants Vietas and Vamma during week 7.

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Reservoir change

In figure 5.11 the change in reservoir volume during the week can be seen, as a percentage of the maximum reservoir volumes.

Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 40 42 44 46 48 50 52 54 56 58 60 Reservoir volume [%]

Vietas reservoir volume Vamma reservoir volume

Figure 5.11: The hourly reservoir volume, in percentage of maximum volume, in hydro power plants Vietas and Vamma during week 7.

When comparing figures 5.11 and 5.10, it can easily be seen how they re-late. When a power plant discharges or spills water, the volume in the reservoir decreases, and when not discharging or spilling water the volume increases due to the inflow of water. How steep the increase in the graph is depends on how large the inflow and outflow of water is, compared to the maximum reservoir volume.

Spillage

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due to the fixed set volume of water at the end of the week, together with differences between the model and real life values from 2019.

5.2.3 Double wind power production

A scenario with double wind power production was also simulated, to see how the system would be affected. The wind power production was only doubled in Sweden, since data of the hourly wind power production in Norway could not be found, and because of the assumption that all power produced in Norway is hydro power. The rest of the system, data and values were the same as in the earlier simulations.

With a doubled production of Swedish wind power, the hydro power pro-duction in the system decreased, as can be seen in figure 5.12. This was ex-pected since an increase in wind power production decreases the demand for hydro power.

Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 0 5 10 15 20 25 30 35 Production [GWh] Standard production

Double wind power production

Figure 5.12: The total hydro power production in the system during week 7, with doubled wind power production in Sweden.

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power produced when there is more wind power in the system, more water can be saved, as long as the reservoirs does not become full. In that case the hydro power plants either has to discharge or spill water.

Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

Reservoir volume change [%]

Standard production

Figure 5.13: The total hourly change in reservoir volume during week 7, with standard and double wind power production.

When comparing the standard case, with a normal wind power production, to the case with doubled wind power in Sweden, it can be seen that the spillage increases, with several peaks during the week. This is shown in figure 5.14.

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Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 101 102 103 104 105 106 Spillage [HE] Standard production

Figure 5.14: The total hourly spillage in the system during week 7, with stan-dard and double wind power production. Logarithmic y-axis.

5.2.4 Resolution

To reduce the computation time of the simulations, the time resolution can be changed. For week 7, the simulation was run with a few different resolu-tions to see how this affected the results. In figure 5.15, the total hydro power production in the system can be seen, with a resolution of up to 12 hours.

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Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 2019 0 5 10 15 20 25 30 35 Production [GWh] 1h resolution (Standard) 2h resolution 4h resolution 8h resolution 12h resolution

Figure 5.15: The total hydro power production in the system during week 7, simulated with different time resolution.

5.3 High water flow

During the weeks with high inflow of water, issues were encountered with finding a solution to the model. This was found out to be, because of variations in local inflow to different parts of the system. The local inflow of water used in the model, based on average local inflow to the hydro power plants, is roughly scaled accordingly to the total average inflow over the year in Norway. In real life, the peak in local water inflow, mainly due to melting snow, occurs at a slightly different time depending on where the power plant is located. Also, the magnitude of the inflow can differ depending on geographical placement. In some areas, the peak could be higher, or more sudden, and in some areas, the peak might be a few weeks later or earlier.

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could buy extra water to satisfy the constraint of water in the reservoir at the end of the week.

The weeks where extra water was needed were weeks 20, 25 and 29. The amount of extra water needed and how many reservoirs that needed extra water can be seen in table 5.1.

Week Amount of water [HE] Number of reservoirs

20 280 163.7 80

25 175 759.1 51

29 4 655.6 6

Total 460 578.4 137

Table 5.1: Extra water needed in the system during a week with high inflow of water.

Because of the difference in local inflow, and the approximation to scale inflow to all hydro power after the same average curve, there are also reser-voirs that receive too much water during these weeks. This leads to a higher amount of spillage for these hydro power plants. The spillage for all weeks, in a logarithmic scale, can be seen in figure 5.5. For a closer look at the three weeks with high water inflow, the spillage for these weeks can also be seen in figure 5.16.

These results show that the inflow of water, ideally should be scaled over the year accordingly to each hydro power plant, or at least accordingly to a smaller area. Scaling the inflow to all hydro power plants after the same aver-age inflow curve might not give a result that is good enough to be compared to reality. If all hydro power plants are scaled the same, some of them might get too much water during some weeks, and some might get to little water.

5.4 Electricity load

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CHAPTER 5. RESULTS AND DISCUSSION 43 0 20 40 60 80 100 120 140 160 Hour 102 103 104 105 106 Spillage [HE] Spillage week 20 Spillage week 25 Spillage week 29

Figure 5.16: The total spillage during weeks 20, 25 and 29. Logarithmic y-axis.

When looking at the amount of energy that flows to or from the electricity load, it is clear how much extra energy the system needs but is not able to produce, or how much extra energy the system overproduces and needs to sell or consume during a certain hour.

The results from the simulations show that for all the simulated weeks, the system managed to produce enough energy to satisfy the demand each hour. During one week though, the system produced too much energy. This week was week 25. During this week, a total of 8 105 MWh excess energy was produced, which needed to be sold or consumed in the electricity load. All of this extra energy was sold by one electricity area, SE3, to the load.

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5.5 Additional Discussion

Ideally, the model should have included a few more parameters, such as mini-mum and maximini-mum discharge and spillage, and a minimini-mum reservoir level at the end of the simulated weeks instead of a fixed value as in the simulations in this thesis. Also, transmission capacities, import and export to the other countries connected to Sweden and Norway, should be taken into account.

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Chapter 6 Conclusions

To summarise this report, the main purpose of this project was to build a model of the Swedish and Norwegian hydro power system in the program Spine. To build such a model, data from the Norwegian hydro power system was needed, along with the already existing data of the Swedish hydro power from earlier projects [1], [2]. This model should be detailed enough to give an indication of how the Swedish and Norwegian hydro power system works today, and how it is affected by future changes in the energy system.

The data collected for the Norwegian hydro power system were mainly obtained from NVE, a Norwegian Water Resources and Energy Directorate, and from Nord Pool, the Northern European power exchange. Specific data for each hydro power plant and reservoirs, along with maps were mainly found through NVE, while most data regarding the power system, such as production and consumption, or transmission capacities were found through Nord Pool.

Some data needed was more difficult to find, and thus assumptions and ap-proximations had to be made. For example, for hydro power plants with more than one reservoir, the reservoirs were assumed to act like one large reservoir instead of several smaller. The amount of water flowing between power plants at the start of the simulated week was assumed to always be the same average value, and the local inflow was roughly scaled in the same way for all hydro power plants regardless of geographical placement, over the year. The time it takes for the water to flow to a downstream power plant was approximated by measuring the distance between them, as in an earlier project. In Norway, all the produced energy was also assumed to be hydro power.

The model was then built in Spine Toolbox, based on an earlier smaller model of the Skellefte river in Sweden. The model was built as a data store, with objects, such as units, nodes and connections, and relationships between

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46 CHAPTER 6. CONCLUSIONS

them. Each object and relationship has different parameters, where data of the power system was added. The model built included 619 hydro power plants, 256 in Sweden and 363 in Norway. It included all of Sweden and Norway’s electricity areas, and transmissions between them, but not the electricity grid outside of Sweden and Norway, such as import and export to other countries. Simulations were executed in Spine, with an output consisting of unit flows, connection flows and node states for all hours of the simulated weeks. That is, the amount of energy flowing through each unit or connection, and the volumes in the reservoirs. The energy production both in Sweden and Norway, as well as in all electricity areas, was compared to historical data. From this, it could be seen that the main difference between the simulations and the real data was because of the import and export of energy, which was not included in the model. Another difference was where in the system the power was pro-duced. The simulated power produced in Sweden was higher than the real amount, and in Norway, the simulated power was instead lower than in the real data. This could be because the model does not take transmission costs or losses into account, and can just as well produce energy far away from where it is needed rather than close by. The smoothness of the production curves also differed a bit between real and simulated values, when looking at the hourly production during a week. For a real hydro power plant, the power production varies depending on the discharge, and is often modelled in linear segments with different production equivalents. In the model, the production equivalent is only one value, creating a linear relationship between discharge and power production. In real life, a smoother flow of water might also be preferred. For future improvements to the model, it might be a good idea to add at least one more production equivalent to create a segmented relationship between dis-charge and production. It might also be useful to add a cost for changing the discharge too suddenly, to create a smoother curve.

When looking at the results of the reservoir volumes during each week, it could be seen that, during most weeks, the volumes decrease a lot during the last hours. This is probably due to the fixed reservoir volumes set at the end of each week. For future improvements, this fixed value should instead be a minimum value. A minimum reservoir volume at the end of each week would also decrease the spillage. Most of the spillage occurs at the end of the week, just like the decrease in reservoir volumes.

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CHAPTER 6. CONCLUSIONS 47

life during some weeks, or less during other weeks. Because of this, it would be a good idea to scale the inflow differently depending on the placement of the power plants. Ideally these values should come from real data and not approximations, since it could be difficult to get a good enough approximation. The effect of the model resolution was also investigated. Week 7 was sim-ulated using time resolutions from 1 hour to 12 hours. For the simulations with up to 8 hour resolution, the results gave similar production curves and results, but with a 12 hour resolution the curves differed more, probably due to the variation in demand over the day. The 12 hour was too low to account for these variations, and thus not suitably to use in simulations over a week.

6.1 Future work

As mentioned earlier, there are ways that the model can be improved. Here, a few suggestions for future work are presented.

• Add import and export to and from Norway and Sweden. From the results and comparison to real data, it has been found that the export and import makes quite a large difference in how similar the model is to real life.

• The hydro power system in other interconnected countries, for example Finland, could be added to the model. Even though they do not produce as much hydro power as Sweden and Norway, it could still be interesting to see how an even larger system with more countries work.

• Try to simulate a more realistic operation, with electricity cost minimi-sation instead of minimiminimi-sation of spillage.

• Changing the fixed reservoir volumes at the end of the simulation to a minimum value, to make it possible for the system to save excess water, decrease unnecessary spillage and make the system more similar to the real system.