developmentofnordic32systemmodeland ...1395253/fulltext01.pdf ·...

Vorgelegt an der Universität StuttgartInstitut für Energieübertragung und

Hochspannungstechnik

Development of Nordic 32 system model andperformance analysis based on real operation

statistics

Weiterentwicklung des Nordic 32 Netzmodells und Leistungsanalysen anhand realerBetriebsstatistikenDurchgeführt an der

Kungliga Tekniska högskolan (KTH), School of Electrical Engineering and ComputerScience (EECS), Teknikringen 33-III, SE-114 28 Stockholm, Sweden

Forschungsarbeit

von

Sharon Müller

3370517

Beginn der Arbeit:

Ende der Arbeit:

Betreuer (KTH):

Betreuer (IEH):

Prüfer:

01.05.2019

28.10.2019

Stefan Stankovic, M.Sc.

Ouafa Laribi, M.Sc.

Prof. Dr.-Ing. Krzysztof Rudion

i

Erklärung

Ich, Sharon Müller, versichere, dass ich diese Forschungsarbeit selbstständig durchge-führt und verfasst habe, abgesehen von den Anregungen, die mir von Seiten meinesBetreuers, Herrn Stefan Stankovic, gegeben worden sind und, dass ich keine anderen alsdie angegebenen Quellen und Hilfsmittel benutzt habe.

Stockholm 24.10.2019

Ort Datum Unterschrift

ii

Abstract/Kurzfassung

Abstract

In this project the existing Nordic 32 test system was analysed in DIgSilent PowerFactoryand approached to the actual Swedish transmission grid. Focus was the reallocation ofthe load and generation. On one hand, the installed capacity was nearly quadrupled, onthe other hand the geographic location of the plants was considered. Therefore, thefour most important generation types, hydro-, nuclear-, wind and thermal power areincluded into the model. Furthermore, the four electricity areas SE1 - SE4 were adoptedinto the test system and the transnational connection modelled as well.The modified test system allows simulations based on real operation statistics. In thisproject, the complete year 2018 was simulated in an hourly resolution. The stable gridoperation within the given voltage limits were secured by static and dynamic reactivesuppliers. A validation of the active power flows shows the coincidence of the simulationresults and the real operation data of 2018. Hence, the resultant grid model representsthe Swedish transmission grid more accurate and offers plenty of different study cases.Furthermore, it gives the yearly voltage profile for each bus and helps to identify weakand strong regions in the Swedish transmission grid.

Kurzfassung

Im Rahmen dieser Forschungsarbeit wurde das bestehende Nordic 32 Netzmodell inDigSilent PowerFactory analysiert und an das aktuelle schwedische Übertragungsnetzangepasst. Der Fokus lag dabei auf der Erzeugungs- und Lastverteilung. Zum einen wurdedie installierte Erzeugungsleistung nahezu vervierfacht, zum anderen die geografischenStandorte der Anlagen berücksichtigt. Dafür flossen die vier wichtigsten Erzeugungsarten,Wasser-, Atom-, Wind-, und konventionelle Wärmekraft in das Netzmodell ein. DesWeiteren wurde das Testsystem an die vier Marktbereiche SE1 - SE4 angepasst und dieVerbindungen in Nachbarländer modelliert.Mit Hilfe des modifizierten Netzmodells lassen sich reale Marktstatistiken einlesen undsimulieren. In diesem Projekt wurde das gesamte Jahr 2018 simuliert und mit Hilfevon statischen und dynamischen Blindleistungsquellen der Netzbetrieb innerhalb dererlaubten Spannungsgrenzen sichergestellt. Eine Validierung der Wirkleistungsflüssezeigt die Übereinstimmung zwischen Modell und Wirklichkeit. Das erhaltene Netzmodellrepräsentiert das schwedische Übertragungsnetz somit deutlich genauer und liefert einegroße Anzahl an unterschiedlichen Berechnungsfällen. Außerdem können die jährlichenSpannungsprofile für jeden Netzknoten angezeigt werden und somit starke und schwacheNetzregionen identifiziert werden.

Contents

Abstract ii

List of Figures v

List of Tables vii

List of Abbreviations ix

1. Introduction 11.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Aim of the Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3. Structure of the Report . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Nordic Test System 32.1. Overview Nordic 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2. Comparison Nordic 32 - Transmission Grid . . . . . . . . . . . . . . . 32.3. Modifications of the Nordic 32 . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1. Swedish Energy System . . . . . . . . . . . . . . . . . . . . . 82.3.2. Development of Modified Nordic 32 . . . . . . . . . . . . . . . 14

2.4. Validation of Obtained Model . . . . . . . . . . . . . . . . . . . . . . 172.4.1. Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.2. Quasi-Dynamic Simulation . . . . . . . . . . . . . . . . . . . . 19

3. Reinforcement 213.1. Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . 213.2. Active Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3. Reactive Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4. Discussion 294.1. Active Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2. Voltage Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2.1. Strong Bus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2.2. Weak Bus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2.3. Special Circumstances . . . . . . . . . . . . . . . . . . . . . . 34

5. Conclusion 37

iv Contents

6. Future Work 396.1. Operation Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 396.2. Grid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.2.1. Slack Generator . . . . . . . . . . . . . . . . . . . . . . . . . 406.2.2. Reactive Power Supply . . . . . . . . . . . . . . . . . . . . . . 40

Bibliography 41

A. Appendix 45A.1. Nord Pool Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 45A.2. Sinlge Line Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

List of Figures

2.1. Nordic 32 - Single line diagram . . . . . . . . . . . . . . . . . . . . . 42.2. Swedish transmission grid vs. Nordic 32 400 kV backbone . . . . . . . 62.3. Geographical approach of the Nordic 32 . . . . . . . . . . . . . . . . . 72.4. Location of the wind farms in Sweden . . . . . . . . . . . . . . . . . . 102.5. Annual load duration line in Sweden . . . . . . . . . . . . . . . . . . . 11

3.1. Overloaded lines and transformer . . . . . . . . . . . . . . . . . . . . 233.2. Capability curve of a synchronous generator . . . . . . . . . . . . . . . 253.3. Reactive power supply of a synchronous condenser . . . . . . . . . . . 27

4.1. Yearly active power flow between the areas . . . . . . . . . . . . . . . 304.2. Active power flow SE3>SE4 for two weeks . . . . . . . . . . . . . . . 314.3. Active power of the slack generator . . . . . . . . . . . . . . . . . . . 324.4. Balance of electricity production and consumption . . . . . . . . . . . 324.5. Simulated voltage profile of a strong bus . . . . . . . . . . . . . . . . 334.6. Simulated voltage profile of a weak bus . . . . . . . . . . . . . . . . . 344.7. Simulated voltage profile under special conditions . . . . . . . . . . . . 35

A.1. Single line diagram of the modified test system . . . . . . . . . . . . . 46

List of Tables

2.1. Installed load and generation Nordic 32 . . . . . . . . . . . . . . . . . 52.2. Active power transfer between the areas . . . . . . . . . . . . . . . . 82.3. Installed generation capacity in Sweden . . . . . . . . . . . . . . . . . 92.4. Rivers with installed hydro power . . . . . . . . . . . . . . . . . . . . 92.5. Percentage division of the total load into the areas . . . . . . . . . . . 122.6. Yearly electricity consumption per district . . . . . . . . . . . . . . . . 132.7. Installed capacity per generator split into production type . . . . . . . 162.8. Buses in the modified test system . . . . . . . . . . . . . . . . . . . . 18

3.1. List of overloaded components . . . . . . . . . . . . . . . . . . . . . . 223.2. List of inductors/capacitors . . . . . . . . . . . . . . . . . . . . . . . 263.3. List of synchronous condenser . . . . . . . . . . . . . . . . . . . . . . 26

4.1. Power lines between the areas . . . . . . . . . . . . . . . . . . . . . . 30

A.1. Used operation statistics from Nord Pool AS . . . . . . . . . . . . . . 45

List of Abbreviations

CHP combined heat and powerFACTS Flexible AC Transmission SystemSC synchronous condenserSG synchronous generator

1. Introduction

1.1. Background

The transition of the energy systems from using conventional fossil and nuclear basedenergy sources to using more environmentally friendly solutions leads to new challengesin the grid operation. The historical rather conservative planned transmission anddistribution grids operate nowadays under more stressed conditions. The networkoperating equipment reaches its limits and the risk of unacceptable operating statesincreases. Therefore, a deep understanding of the transmission grid including unsafescenarios such us high volatile feed-in, contingencies of power plants and grid equipmentor load concentration in rural areas is necessary to ensure a secure grid operation.With a adequate test system arbitrary study cases can be simulated in a fast and secureway and the respective conclusions can be drawn. However, to get valid results, it isimportant that the used model represents the actual grid as good as possible. Dependingon the aim and studies, a valid trade-off between accuracy and complexity must befound.For power system stability studies of the Swedish transmission grid, nowadays the Nordic32 test system plays an important role. It was proposed by [1] in 1995 for the simulationof long term phenomena. However, it has been used for dynamic studies such asshort-term voltage stability, power system restoration, system protection and small-signalstability studies as well [2]. Different examples for the wide use of the Nordic 32 can befound among others in [3–7].

1.2. Aim of the Project

The purpose of this project is the development of the Nordic 32 test system to obtaina better representation of the Swedish transmission grid. In a first step, the original,fictitious grid model is analysed and compared to the actual Swedish power supplysystem. Significant differences between the test system and the transmission grid canbe identified and the model changed accordingly. Focus of this work is on the amountand location of electricity production and consumption, taking into account the mostimportant Swedish energy sources. Furthermore a more detailed specification of the gridmodel is implemented. Nevertheless, the general structure of the Nordic 32, regardingvoltage levels, models for the network equipment and characteristics of the power linesare kept as implemented in [2]. The new grid model allows the running of simulationsbased on historical, public available operation statistics.

2 Introduction

The second aim of the project is to ensure a stable and secure grid operation for eachhour of the year. To keep the voltage limits within the defined limits, reactive power isused. Therefore the yearly voltage profile of each node is examined and, if the limits areexceeded, the necessary reactive power devices installed.To verify the developed model, the year 2018 is simulated in an hourly resolution. Theresults are used to exemplary locate weak and strong buses in the transmission grid oridentify challenging operation condition.The development and simulation are made in DIgSilent PowerFactory Version 2019SP1.

1.3. Structure of the Report

In chapter 2 an overview over the original grid model and the differences between thetest system and the real Swedish transmission grid can be found. Furthermore, thereallocation of the loads and generators and a more detailed version of the grid modelare explained.With the modified test system, real operation statistics can be used for load flowsimulations. To ensure a stable and secure grid operation, further changes, such asreinforcements of lines and transformers or local reactive power supply, are made inchapter 3.Afterwards, the results of an quasi-dynamic simulation of the year 2018 will be discussedin chapter 4 and strong and weak buses in the grid model located.Lastly the project will be evaluated (chapter 5) and possible future work suggested(chapter 6).

2. Nordic Test System

The Nordic 32 test system was developed by the Cigre Task Force 38.02.08 in 1995. Itis a fictitious model, however with similar properties as the Swedish transmission gridand was created to illustrate the voltage collapse in Sweden in the year 1983 [1]. In [8]an adjustment of dynamic models and parameters of the original Nordic 32 model ismade, to achieve a more representative test system. In [2] the implementation of theNordic 32 test system in DIgSILENT PowerFactory is explained, the result is used as abasis in this work. The following section gives a short overview over the Nordic 32 testsystem, an detailed description can be found in [8].

2.1. Overview Nordic 32

The Nordic 32 test system is based on the Swedish transmission grid from 1995. It isdesigned to simulate large transfers of electric energy from the hydro power stationsin the North to the high load areas in the center and south of Sweden. Therefore, thesystem is divided in four areas:

• "North" with basically hydro generation and some load;• "Central" with much load and rather much thermal power generation;• "Southwest" with a few thermal units and some load;• "EQUIV" interconnection to neighbouring countries in the "North" having a

mixture of generation and load.The system consists of the 400 kV transmission grid (19 nodes) and some regionalsystems at 220 kV (2 nodes) and 130 kV (11 nodes). Figure 2.1 shows a single linediagram of the grid model. The installed capacity of generation and load in each area isgiven in Table 2.1. Each generator and load is connected to the grid using a step-upand a step-down transformer respectively. All generators are modelled as synchronousgenerators (SGs). Two different standard models are used: a salient pole machine modelfor the hydro power and a round rotor model for the thermal power [1].

2.2. Comparison Nordic 32 - Transmission Grid

As mentioned, the Nordic 32 test system is both fictitious and outdated. A briefcomparison with the actual Swedish transmission grid, shows various differences.

4 Nordic Test System

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Figure 2.1.: Single line diagram of the original Nordic 32 test system - exported fromDIgSilent PowerFactory [2]

2.2 Comparison Nordic 32 - Transmission Grid 5

Table 2.1.: Active power of the installed load and generation in the original Nordic 32system

Area Production in MW Consumption in MWNorth 4628.5 118.0Central 2850.0 6190.0South 1590.0 1390Equiv 2437.4 2300Total 11505.9 11060.0

To reduce the complexity of the grid model, large simplifications has been made at theexpense of the accuracy. In particular, nearby located substations and power lines werelumped together into one to decrease the number of simulated grid equipment. Therefore,the 400 kV backbone of the Nordic 32 test system consists of only 19 nodes. Figure 2.2shows the actual and planned transmission grid (last updated 09.01.2018), provided bythe Swedish transmission grid operator Svenska Kraftnät, and the geographical structureof the Nordic 32 400 kV grid, published by [1]. In accordance to the given geographicscale of the Nordic 32 grid and the location of the big generators in the south, whichrepresent the nuclear power plants, both maps can be merged. Figure 2.3 shows theposition of the original Nordic 32 inside of Sweden. Furthermore, later added power-linesare drawn dotted (cf. subsection 2.3.2) and the four electricity areas SE1 - SE4 (cf.subsection 2.3.1) are sketched into the map. It stands out that important transmissionlines, mainly in the south and west of Sweden, are not modeled in the original testsystem. Besides, the Nordic 32 model neglect the connection to neighbouring countries,only the connection between the "North" and Norway is modeled by an external grid.Another big difference between the Nordic 32 grid model and real system is the installedcapacity. As listed in Table 2.1 the active power generation in the original Nordic 32 is11 505.9 MW, including the area "Equiv" which represents an external grid. However,according to [11] the installed power capacity in Sweden was 38 851 MW on 1st ofJanuary 2018. In addition, the location of the generators and loads has changed. Forexample, the Nordic 32 system is modelled with a large thermal generator at bus 4063 inthe south-west of Sweden. It is highly probable that this generator represents the nuclearpower station Barsebäck, which was shut down 1999/2005 in the course of the formerplanned nuclear phase-out in Sweden. The missing generation was mainly replacedwith wind power. In 1995, the wind energy had no impact on the energy production,nowadays it stands for approximately 10% of the Swedish electricity mix [12].These discrepancies lead to another significant difference between the Nordic 32 gridmodel and the real transmission grid. Nordic 32 was created to simulate large powerflows from the north to central and southern Sweden. Table 2.2 shows a comparisonof the active power transfer between the areas simulated in the Nordic 32 and thereal operation statistics provided by [10]. According to [1] the Nordic 32 study caserepresents a high load scenario. To compare the simulation results and the statisticsunder equal conditions and to avoid extreme values, the average of the 100 hours withthe highest load in 2018 were used as operation statistics. Further, Table 2.2 shows


Figure 2.2.: Comparison of the actual Swedish transmission grid [9] and the 400 kVbackbone of the Nordic 32 test system [1]

2.2 Comparison Nordic 32 - Transmission Grid 7

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scaled down operation statistics. Since the installed capacity in the model reach only30 % of the actual installed capacity in Sweden, Table 2.2 shows the power flow scaleddown with the same factor as well. A comparison of the simulated load flows betweenthe Swedish electricity areas and the real data reveals fundamental disparity, particularlybetween SE3 and SE4.

Table 2.2.: Comparison of the active power transfer in the Nordic 32 and operationstatisticsActive power transfer Simulation Statistics

Direction Nordic 32 original scaled downSE1>SE2 in MW 2201,1 1486.1 440.1SE2>SE3 in MW 3378,9 6087.5 1802.8SE3>SE4 in MW -467 3768.3 1116

Thus, it is important to adjust the test system to the present characteristics to obtainvalid results.

2.3. Modifications of the Nordic 32

In section 2.2 it is demonstrated that the original Nordic 32 test system needs variousmodifications to deliver valid simulation results. In order to adapt the characteristicsof the Swedish transmission grid to the Nordic 32, a deeper analysis of the modernSwedish energy system is necessary. Afterwards, the results can be used to modify thegrid model accordingly.

2.3.1. Swedish Energy System

A peculiarity of the Swedish energy system is, that it is split up into the four differentgeographical areas SE1 - SE4 (c.f. Figure 2.3). Depending on the actual generationand load data, there can be different electricity prices in each area. Therefore thestatistics such as generation, consumption or power transfers are available for each areaindependently.For this reason, the following analysis of the Swedish energy system and the resultantgrid model takes into account these different areas. To get an adequate and actualsystem overview, both the installed generation capacity with its location as well as thereal operation statistics of 2018 will be examined.

Installed Capacity

The Swedish electricity production is highly dominated by hydro- and nuclear powerplants. They represent more than 80 % of the annual average Swedish electricity mix.

2.3 Modifications of the Nordic 32 9

The remaining part is covered by wind energy and thermal power plants, often basedon renewable fuels. Other power sources such as coal or Photovoltaic do not playany or they play only a vanishing role in the Swedish energy system. The impact ofPhotovoltaics to the yearly energy production ranges about 1%�. A composition of theinstalled capacity sorted by type and area is provided by [11]. The most actual data,listed in Table 2.3, are from 1st of January 2018. The hydro power plants are located

Table 2.3.: Installed active power capacity in Sweden sorted by areas and generationtype, 01.01.2018 [11]

Type SE1 SE2 SE3 SE4 SwedenP in MW P in MW P in MW P in MW P in MW

Hydro power 5315 8055 2582 349 16301Nuclear power 0 0 8586 0 8586Wind power 521 2378 2178 1614 6691Photovoltaic 4 11 159 80 254Thermal power 264 532 4016 2162 7004Total 6105 10978 17561 4207 38851

mainly in the northern and central parts of Sweden and can be found evidently near tobigger rivers or watercourses. The installed capacity per plant variate from <20 MW upto 871 MW. Table 2.4 lists the most important rivers in Sweden, regarding the installedcapacity of hydro power. A map with all hydro power plants with a rated power above

Table 2.4.: List of important rivers and its installed capacity of hydro power, sorted fromNorth to South [11]

River Pinst in MW AreaLule älv 4273.6 SE1

Skellefte älv 1008.6 SE1Ume älv 1746.9 SE1/SE2

Angermanälven/Faxälven 2640 SE2Idalsälven 2100.7 SE2Ljungan 603.6 SE2Ljusan 817.1 SE2Dalälven 1155.3 SE2Klarälven 387.3 SE3Göta älv 299.9 SE3Others 1268 SE1-4SUM 16 301

20 MW in Sweden can be found in [13].

Nowadays, there are eight operational nuclear reactors on three different plants. Ringhals(≈3950 MW) and Oskarshamn (1400 MW) are located in the South of Sweden, Forsmark


(a) Area SE1 (b) Area SE2

(c) Area SE3 (d) Area SE4

Figure 2.4.: Location of the wind farms in Sweden, divided by electricity area [15]

(≈3280 MW) near to the metropolitan area Stockholm [14]. The exact location of eachplant is shown in Figure 2.3. Based on a referendum from 1980, the nuclear phaseout was scheduled originally until 2010, however, these plans were abandoned again.Depending on the growth of the renewable energies, all nuclear power plants shall beshut down until 2045. The two oldest reactors in Sweden, Ringhals 1 + 2 are plannedto be decommissioned until 2020, which implies a power loss of approximately 1600 MW[14].

In the last 20 years, the wind sector in Sweden shows an exponential growth. Since 1997,the installed wind capacity was increased from 127 MW to 7141 MW in the year 2018[15]. Besides, there are many projects in progress, such as the Markbygden Wind Farmin the north of Sweden with an additional rated power of 4000 MW [16]. Figure 2.4shows the dispersion of all wind farms in Sweden. However, the blue framed numbers ofwind farms provide only a limited information about the installed power, given the fact


that in particular in the south small wind turbines with an active power smaller than1 MW are installed. To get the dispersion of the wind power, a closer look on [15] and[17] is necessary.

Furthermore, conventional thermal power plants are used. The thermal plants are mainlyinstalled as combined heat and power (CHP) generators and operate heat-driven. Thetotal amount of 7004 MW splits into district heating CHP (3078 MW), industrial CHP(1451 MW), gas turbines (1562 MW) and condensation power (913 MW) [11].

Operation Statistics

The operation statistics can be found in different sources. Svenska Kraftnät providesthe production statistics, subdivided in the generation type. Nord Pool AS, one of thebiggest electricity exchange markets in Europe and authority for the energy trading inScandinavia, provides the market data in an hourly resolution. All operation statisticsare available for whole Sweden and separately for the four different areas. In this project,the following data were used:

• Cumulative electricity production [10],

• Cumulative electricity consumption [10],

• Power flow between the areas [10],

• Import/export at each coupling point [10],

• Electricity production per generation type [18].

More information about the use of operation statistics are explained in chapter 6. Anexact explanation of the used files can be found in the appendix A.1. In this section,these statistics are used to analyse the yearly electricity consumption, production andexport in Sweden.

Figure 2.5.: Annual load duration line Sweden, divided in electricity areas [10]


Consumption The maximum load in 2018 was 26 558 MW at 28.02.2018 08am, theminimum 8930 MW at 04.08.2018 at 05am. Figure 2.5 shows the annual load durationcurve of 2018. It stands out that the load in SE1 and SE2 is rather small comparedto the more populated south of Sweden with the areas SE3 and SE4. The main partof the electricity demand takes place in the area SE3. This is also confirmed by [17],where the yearly demand per district is published. The corresponding data are listedin Table 2.6. Unfortunately, the data is only available in a yearly resolution. However,as a simplification the load ratio per district can be assumed constant during the year.Figure 2.5 shows that the parts of each area remain more or less equal. Table 2.5 provesthat the percentage of each area at high, middle and low demand, each the average of100 values, have no bigger discrepancies.

Table 2.5.: Load ratio of each area at high, middle and low demand scenarios, averageover 100 values

Area Percentage of load22 430 MW 16 930 MW 10 305 MW

SE1 7% 7% 8%SE2 11% 12% 12%SE3 64% 63% 63%SE4 18% 18% 17%

Production The nuclear power plants operate as baseload plants. In 2018 theyreached a utilization ratio of nearly 90 %. On the contrary, the mostly heat driventhermal power plants only operate on 15 % of their installed capacity. The averagefull load hours per year of the renewable power sources hydro- and wind power is onlyapproximately 3800 and 2500. However, the wind and hydro power plants in the northof Sweden operate normally above the average work load. This leads, depending on theexternal conditions, to temporary high power flows from north to south.

Export/Import The Swedish transmission grid has fourteen coupling points with theneighbouring countries. In 2018, Sweden exported approximately 31 TWh electric energyand imported only 14 TWh which gives an export surplus of 17 TWh. Examining thedifferent areas, it stands out that the regions SE1, SE3 and SE4 export with ≈ 9.5 TWhnearly the same amount of electric energy. Only SE2 has a smaller value, which can beexplained with the high energy transfer between SE2 and SE3. Regarding the import, itis noticeable that the region SE3, which has by far the highest load also has the highestimport. Therefore, SE2 and SE3 are the regions, where the import nearly equals theexport.


Table 2.6.: Absolute and relative yearly electricity consumption per district [17]District Load in GWh % Area

Stockholms län 20342,00 15.6% SE3Uppsala län 3072,00 2.4% SE3

Södermanlands län 3198,00 2.5% SE3Östergötlands län 6452,00 4.9% SE3Jönköpings län 4490,00 3.4% SE3Kronobergs län 2508,00 1.9% SE4Kalmar län 3341,00 2.6% SE3/SE4Gotlands län 1023,00 0.8% SE3Blekinge län 1822,00 1.4% SE4Skåne län 12866,00 9.9% SE4

Hallands län 4475,00 3.4% SE3/SE4Västra Götalands län 19227,00 14.7% SE3

Värmlands län 5252,00 4.0% SE3Örebro län 4122,00 3.2% SE3

Västmanlands län 2755,00 2.1% SE3Dalarnas län 6906,00 5.3% SE3Gävleborgs län 5288,00 4.1% SE2

Västernorrlands län 9362,00 7.2% SE2Jämtlands län 1793,00 1.4% SE2

Västerbottens län 4271,00 3.3% SE2/SE1Norrbottens län 7896,00 6.1% SE1


2.3.2. Development of Modified Nordic 32

The information described in subsection 2.3.1 can be used to adapt the respectivecomponents of the Nordic 32 grid model such that it matches the real power systemmore closely. In this process, an acceptable balance between necessary simplifications andthe complexity of the grid model must be found. Thereby, the structure of the originalNordic 32 serves as a basis and shall be maintained. With as few adjustments as possible,the existing model will be approached to the real transmission grid characteristics.Therefore, four types of changes are made in the model:

• Adding new lines and buses,• Amount and location of generators,• Amount and location of loads,• Interconnection with neighbouring countries,

The obtained test system for DIgSilent PowerFactory is available as a .pfd file, the singleline diagram of the grid model can be found in Appendix A.

Power lines and nodes

The original Nordic 32 model is characterized by a loosely connection of the areaSouthwest [1]. This structure causes that the electricity area SE4 is represented only bythe node 4063. In order to particularize the southern part of the Swedish transmissiongrid, the node 4064 was added to the model. Furthermore, in the area SE3 the newnode 4060, located in the western part of Sweden, were created. It is connected to 4031in the north and 4061 in the south and the power lines represent the before missingtransmission corridor between Östersund and Göteborg. The additional nodes and powerlines can be found in the map of the Nordic grid, shown in Figure 2.3 as dotted lines.As the distances match more or less, the number and characteristics of the new powerlines, such as impedance etc., were copied as follows:

New line Used Characteristics4051 - 4064

4062 - 40634064 - 40634060 - 4061 (2x)4031 - 4060 (2x) 4031 - 4041

Generators

The biggest difference between the test system and the actual Swedish grid is thecumulative installed capacity of the generators. In order to improve the grid model, theactive power was increased to reach the real values listed in Table 2.3. In this processthe location of the existing power plants was considered.


As a simplification, the different generation types are lumped together into one SG.Thus, on each node maximum one generator is connected. Just like in the original model,the generators are connected to the grid with a step up transformer. The characteristicsof the SGs and the transformers were maintained, only the rated power was adjusted tothe actual Swedish energy system. Thereby, the rated power results from the sum of theactive hydro-, nuclear-, wind power and CHP divided by the former given power factor.Due to the small amount, the Photovoltaic and other power sources were neglected.Additionally to the existing generators, the SGs g32, g60, g61 and g64 were implementedand connected to the corresponding 400 kV bus with an step up transformer.One of the most difficult parts of redesigning the new grid model is the correct locationand amount of the generation. The position of the three nuclear power plants is givenexactly and can therefore be assigned to the equivalent node in the model without anybigger error. As Figure 2.3 shows, Ringhals corresponds to node 4062, Oskarshamn tonode 4051 and Forsmark to node 4047. Each bus already had a comparatively biggergenerator in the original Nordic 32 grid model.The allocation of hydro and wind power however is, due to the huge number ofproportionally small plants more difficult. The maps of [13] for the location of hydro-power and [15] for wind farms were used to locate the plants. Although an error is notavoidable. Often, the smaller power plants are integrated into the regional grid whichleads to a spread that cannot be simulated in a 34 bus system. A similar problem occurswith the thermal power plants. In [19] it is proposed to include all CHPs as one lumpedgenerator per region into the grid model. Due to the lack of documentation about thelocation of the thermal power plants, this simplification was made in this project as well.The thermal power is concentrated in one bus per area except for SE3, where a fewbigger plants can be found. The error is negligible, since the concerned plants do notplay a decisive role in the electrical power supply.Table 2.7 gives an overview of all SGs, their rated power and the respective part of theproduction type. As the generators g19 and g20 represent an external grid connection,they do not appear in Table 2.7, more information can be found in section 2.3.2.

Loads

Unlike the installed capacity of the generators, the energy consumption is a fluctuatingand time dependent parameter. Therefore the loads cannot be modelled with a constantrated power, instead a variant factor that considers the actual energy demand isnecessary.As pointed out in subsection 2.3.1, the consumption apportionment of the four areasremain nearly constant during the year. Thus, a valid compromise is to assign eachload with a constant percentage, which represents their part of the complete electricitydemand. These load ratios base on the data of Table 2.6. Table 2.8 shows all loadratios with its node areas. Each electricity area was analysed independently, ergo thesum of all load ratios is 400%. To implement a real study case, the active power can becalculated out of the product of the real demand data per area and the load ratio.


Table 2.7.: List of all generators in the modified Nordic 32 test systems with its ratedpower and the production type

Generator S cos(ϕ) Hydro Nuclear CHP WindMVA MW MW MW MW

g01 1352 0,95 1033 0 0 251g02 1491 0,95 952 0 264 201g03 916 0,95 870 0 0 0g04 843 0,95 403 0 0 399g05 899 0,95 403 0 0 452g06 284 0,9 103 0 0 152g07 216 0,9 129 0 0 65g08 1319 0,95 403 0 0 850g09 1589 0,95 1441 0 0 69g10 1073 0,95 1020 0 0 0g11 3952 0,95 3222 0 532 0g12 2798 0,95 2658 0 0 0g13 2984 0,95 492 0 1936 407g14 1390 0,9 305 0 815 131g15 4300 0,9 0 3822 0 0g16 1694 0,9 0 1438 0 87g17 5187 0,9 0 3326 1295 48g18 1566 0,9 279 0 0 1130g32 2798 0,95 967 0 0 678g60 2984 0,95 1082 0 0 934g61 899 0,95 473 0 0 353g64 2984 0,95 70 0 2162 484SUM 43518 - 16303 8586 7004 6691

2.4 Validation of Obtained Model 17

Coupling points

The transnational transmission grid connections are modelled in the most simple way.Each coupling point is modelled by a SG and a load, both directly connected to the400 kV grid. The loads represent the export of electric energy, the generators the import.Depending on the actual export status, the active power of the generator and the loadcan be modified, the reactive power remains constantly 0 Mvar. An exception form thepart "EQUIV" of the original grid model. It already represents an external grid connection.Therefore, it can be used, as the connection between SE1 and Norway/Finland. Theexport/import can be simulated by variations of the generator g20 and the resultantdisparity of load and generation in this part. In total, seven additional transnationalcoupling points were added to the grid, Table 2.8 gives an overview over the affectednodes and countries.

2.4. Validation of Obtained Model

To validate the improved grid model, long term simulation studies are necessary. Due tothe complexity of the Swedish transmission grid and the differing generation mix, it ishard to find intuitively the operation scenario which can cause challenging conditionssuch as stability problems. As the long term dynamics of voltage fluctuations arefrom interest, for the examination of the grid model a quasi dynamic simulation in atime-scales of hours is used [20].To ensure a variety of different, but realistic load and generation cases, the historicaloperation statistics for the electricity production and consumption in Sweden are used.The data of the year 2018 will be simulated in an hourly resolution to obtain 8760different study cases. The results can be used to prove the stable and safe grid operationinside the voltage limits and verify the power flow between the different electricityareas.

2.4.1. Input Data

As mentioned in subsection 2.3.1, the operation statistics were used from [10, 18]. Theconverged data of both sources for the year 2018 in an hourly resolution can be foundin the spreadsheet all_data_2018.xlsx. This data builds the base to extract the timeseries for the active power of each generator and load in the grid model.To simulate the generation as accurate as possible, the actual active power of each SG iscompounded by the four different generation types. The composition of each generator isdiscussed in subsection 2.3.2 and can be found in Table 2.7. Depending on the installedcapacity and the actual generation in the corresponding area, the variable active powerproduction of each generator can be calculated. Unfortunately, the generation data of[10] and [18] does not coincide. As the consumption and load flow data are used from[10], the generation data by type are scaled to match the data from [10] and create


Table 2.8.: List of all buses in the modified Nordic 32 test systems with its installedpower, load-ratio, voltage level and corresponding areaBus Area Voltage level Generator Load Export

kV % Country1011 SE1 130 g02 33 % -1012 SE1 130 g01 50 % -1013 SE1 130 - 17 % -1014 SE1 130 g03 - -1021 SE2 130 g04 - -1022 SE2 130 g05 21 % -1041 SE3 130 - 3 % -1042 SE3 130 g06 2 % -1043 SE3 130 - 1 % -1044 SE3 130 g07 3 % -1045 SE3 130 - 6 % -2031 SE2 220 - 4 % -2032 SE2 220 g08 5 % -4011 SE1 400 g09 - -4012 SE1 400 g10 - -4021 SE2 400 g11 - -4022 SE2 400 - - NO44031 SE2 400 g12 - NO34032 SE2 400 g32 69 % -4041 SE3 400 g13 5 % -4042 SE3 400 g14 5 % -4043 SE3 400 - 3 % -4044 SE3 400 - - -4045 SE3 400 - - -4046 SE3 400 - 9 % FI4047 SE3 400 g15 16 % -4051 SE3 400 g16 2 % -4060 SE3 400 g60 30 % NO14061 SE3 400 g61 8 % DK14062 SE3 400 g17 8 % -4063 SE4 400 g18 67 % DK24064 SE4 400 g64 33 % PL/LT4071 EQUV 400 g19 flexible -4072 EQUV 400 g20 flexible -

2.4 Validation of Obtained Model 19

valid study cases. Thus, the active power of each generator can be calculated as shownin Equation 2.1.

Pact,gen,sum = PNP,sum

Psvk,sum∗

∑Type

P inst,gen,type

P inst,area,type∗ Pact,area,type (2.1)

where:

Pact ,gen,sum = Cumulative active power of a given generator at a given timestampPsvk ,sum = Cumulative active power in the corresponding area [18]PNP,sum = Cumulative active power in the corresponding area [10]Pinst ,gen,type = Installed capacity of the corresponding generator and type [Table 2.7]Pinst ,area = Cumulative installed capacity of the corresponding type and areaPact ,area,type = Active power of corresponding type, area at a given timestamp

The calculation of the flexible active power for the loads is simpler. The value arisesout of the product of the load ratio, given in Table 2.8, and the consumption valuein the corresponding area. The values for the generators and loads that represent ainterconnection can be extracted directly from the database.The resultant time series for each component are stored in the spreadsheet Time_Series.csv.DIgSilent PowerFactory can import the the time series for 2018 in an automated mannerand assign it to the belonging component.

2.4.2. Quasi-Dynamic Simulation

With the Quasi-Dynamic Simulation tool, DIgSilent PowerFactory provides a powerfulway to simulate a large amount of different load flow analyses in a very efficient manner.The calculation is based on the Newton Raphson algorithm and describes the behaviourof the grid under steady-state non faulted conditions [20]. Interesting quantities for thevalidation of the grid model are the loading of transformers and lines, the voltages atthe nodes as well as the active power exchange between the four areas.A first simulation of the modified grid model using the calculated time series leadsto a large amount of errors. More than 600 hours of the year cannot be simulated,because the Newton-Raphson algorithm does not converge. This means, that a stablegrid operation with the resultant model is not ensured over the year. Furthermore manylines and transformers are overloaded, partially up to more than 200 %. Even though apartial overloading of these components can be tolerated, 200 % is not acceptable.These results are expectable, given that, depending on the study case, the generationand load was nearly quadrupled compared to the original test system. Additionally, thenew location of the generator and loads cause load flows on lines and couple transformerswhich they were not designed for. Besides, both active and reactive power transferbetween the voltage levels increases. The new modelling of the consumption and


production leads to new active power flows, the attempt of PowerFactory to hold thevoltage on a predefined target value to new reactive power flows. This leads to anoverloading of the coupling transformers. To ensure the stable and secure operation ofthe grid, further reinforcement measures must be taken.

3. Reinforcement

Improper grid operation states and network collapses can be caused by different phe-nomena. In this chapter, the voltage stability and possible measures to ensure a safegrid operation will be elaborated. Furthermore the according modifications made in thegrid model to prevent an exceeding of the voltage limits will be presented.

3.1. Theoretical Background

In contrast to the frequency, voltage stability is a local phenomena. It refers to the abilityof a power system to maintain steady voltages at all buses. In the European grid code,the allowed voltage range for the Nordic grid are defined [21]. The voltage should notfall below 0.9 p.u. or exceed 1.05 p.u. The transformation of the energy system gives amore important role to voltage stability problems. As commented earlier, new operationcircumstances lead to increasingly stressed conditions for the grid. Among others, thehigh active power transfer over long power lines, increased electricity consumption andthe resultant heavy load areas or the use of new technologies such as a growing use ofinduction machines or the increasing penetration of wind energy should be mentioned ascauses. Therefore it is essential to keep the voltage near the nominal value, in particularvoltage drops can lead to collapses and partial or complete blackouts [22–24].Independently of the sort of electric network (DC or AC), there is a maximum amountof power that can be transferred between two nodes. The maximum power depends,among others, on the impedance of the connection between theses buses. The exceedingof this power leads to a drop of the voltage and could cause a voltage collapse [22]. Forpower lines with a length up to circa 80 km, normally the thermal impacts determinethe maximal power transfer over the line. A too high loading can damage the powerline and cause its outage. For longer power lines, voltage (circa 80 km to 320 km) andstability (>320 km) problems are the limiting factors during the operation. To avoidvoltage collapses, countermeasure such as reactive power supply or serial compensationmust be taken [25].In an electric grid, various reactive power sources and possibilities exist to stabilisethe voltage. In general, an inductor decreases and an capacitor increases the voltage.Historically, the reactive power was mainly supplied by rotating machines such as SGs orsynchronous condensers (SCs) or static compensator with mechanic tap changer. Nowa-days Flexible AC Transmission System (FACTS), in particular Static Var Compensator(SVC) or Static Synchronous Compensator (STATCOM) play an important role. Theyare based on power electronics and have so the ability to regulate their reactive power

22 Reinforcement

supply faster than compensation devices with mechanic tap changers. In the futurepower systems, FACTS could compensate the lack of SGs. A detailed description ofdifferent reactive power sources and voltage stability can be found for example in [22–24,26].

3.2. Active Power Flow

Figure 3.1 shows the overloaded power lines in the 400 kV voltage level in red. In general,three overloaded sections can be located. The large active power transfer from northto central Sweden and neighbouring countries causes overloaded lines in the areas SE1and SE2 and the connection to the equivalent grid as well. In the area SE3, it standsout that the remodelled load centre in the district Stockholm causes overloaded lines.Furthermore, the power lines in the former rather loosely connect south west of Swedenis overloaded. The more detailed model of loads in SE4 and nearby generation (c.f.chapter 4) leads to new power flows from SE3 to SE4.Additionally, some coupling transformers between the voltage levels are overloaded. Therespective buses are marked in blue (130 kV) and green (220 kV).

Table 3.1.: List of overloaded transformers and linesLines TransformersL1011-1013 Tr1012-4012L1012-1014 Tr1022-4022L4011-4021 Tr11-1011L4011-4022 Tr12-1012L4011-4071 Tr13-1013L4012-4022 Tr2031-4031L4012-4071 Tr22-1022L4021-4032 Tr47-4047L4021-4042L4022-4031L4031-4032L4031-4060L4051-4064L4062-4063L4061-4062L4046-4047L4043-4046

To avoid the overloading of the power lines and transformers, the affected componentswere reinforced. In case of the lines, a parallel system which shares the same characteris-tics as the existing power lines were included. In case of the transformers, the apparentpower of each transformer were increased to its maximum apparent power during the

3.2 Active Power Flow 23

Figure 3.1.: Overloaded lines and transformers of the Nordic 32 after the first quasi-dynamic simulation

24 Reinforcement

year.

Table 3.1 lists all reinforced components in the grid model.

3.3. Reactive Power Supply

In this project, three different kinds of local reactive power sources are used:

• Synchronous generators (flexible),

• Synchronous condensers (flexible),

• Inductor/Capacitors (constant)

While the SGs are already included in the grid model (c.f. Table 2.7), the SCs and theshunt elements have to be modelled additionally. The decision of what kind of reactivepower device is needed, depends on the yearly voltage profile of the corresponding bus.If the voltage remains more or less constant, but out of the limits, a static shunt elementcan be installed. If the voltage exceeds and go below the limits during the year, a flexiblereactive power supplier is necessary. After the implantation of all reactive power devices,a new quasi-dynamic simulation can be run which leads to a new yearly voltage profile.In an iterative process, the devices can be adapted according to the results to obtainthe best solution for the grid model.

Synchronous Generator

The operation of each SG depends of its predefined capability curve. In this project, theSGs are represented by two different standard models, one for a salient-pole machine(originally for the hydro power plants) and another for round-rotor machine (originallyfor thermal power plants). The respective capability curve was adopted from the originalgrid model. Figure 3.2 shows the capability curve for the salient pole machine. A detailedexplanation of the development of the capability curves and the modelling of the SG canbe found in [8]. As the SGs in the modified grid model represent a composition of hydro-,nuclear-, wind power and CHP and each generation type has different reactive powercharacteristics, a falsification must be accepted. Possible solutions and improvementsare discussed in chapter 6.

All SGs provide reactive power within their limits. During the simulation, the valuesfor the active power and the target voltage are given, the reactive power supply adjustitself regarding the local, study-case-dependent needs of the grid. If the SG reaches itslimits, normally paired with a high active power generation, it might happen that thevoltage cannot be kept in its limits. Therefore, additional elements must be installed inthe grid.

3.3 Reactive Power Supply 25

Figure 3.2.: Example for a capability curve of a salient pole synchronous generator

Shunt Elements

In this project static shunt elements, namely inductors and capacitors, are used. As asimplification and in contrast to reality they are connected directly to the correspondingbus and have a fixed value during the operation. This means, for all study cases, thereactive power supply is kept constant, to special conditions in the grid operation cannotbe reacted. Table 3.2 gives an overview of all installed inductors and capacitors in thegrid. It stands out, that the reactive power supply differs from 35 Mvar to 1290 Mvar.It represent the absolute value of reactive power needed at the corresponding bus tokeep the voltage in its limits. As the bus normally is connected to a substation andlower voltage levels, the reactive power could also be provided by the distribution grid.However, the value of the connected shunt element gives a good reference of the amountand kind of needed reactive power at each bus. Possible better solutions such as dynamiccompensator’s are discussed in chapter 6.

Synchronous condenser

Static reactive power sources without tap changer can only be used if the bus voltageremains more or less constant. If however the voltage exceeds and fall below the voltagelimits during the year, the reactive power supply must be adapted to the operationconditions. One possibility are SCs. As it is a expensive and rather rare solution, in thisgrid as few as possible SCs were installed. Figure 3.3 shows the reactive power supplyof the SC installed at bus 4047. During the year both, inductive and capacitive reactivepower is needed to stabilize the voltage. Therefore, a static shunt element cannot beused at this bus. While the blue dots are below the limits of the SC, the voltage can be

26 Reinforcement

Table 3.2.: List of all shunt elements with its reactive power and the corresponding bus

Name Bus Voltage Qcap QindkV Mvar Mvar

1022-Cap 1022 130 0 10001041-Cap 1041 130 80 01043-Cap 1043 130 50 01045-Cap 1045 130 400 04012-Ind 4012 400 0 3004041-Cap 4041 400 0 7504051-Cap 4051 400 0 7004071-Ind 4071 400 0 200

Shunt-4072 4072 400 0 1290Shunt-4044 4044 400 0 300Shunt-4021 4021 400 0 1200Shunt-4031 4031 400 0 1200Shunt-4011 4011 400 0 400Shunt-2031 2031 220 0 65Shunt-1021 1021 130 0 22Shunt-1014 1014 130 0 80Shunt-1013 1013 130 0 70Shunt-1012 1012 130 0 115Shunt-1011 1011 130 0 35Shunt-4042 4042 400 0 550Shunt-4047 4047 400 0 500Shunt-4045 4045 400 0 300Shunt-2032 2032 220 0 400Shunt-4064 4064 400 0 1000Shunt-4062 4062 400 0 600Shunt-4061 4061 400 0 500Shunt-4060 4060 400 0 600Shunt-4032 4032 400 0 600

Table 3.3.: List of all synchronous condenser with its reactive power and the correspond-ing bus

Name Bus Voltage S Qmax,cap Qmax,indkV MVA Mvar Mvar

4071-CS 4071 400 1500 1055,55 968,164047-CS 4047 400 1800 1266,66 1161,7924045-CS 4045 400 750 527,775 484,08

3.3 Reactive Power Supply 27

0 1000 2000 3000 4000 5000 6000 7000 8000 9000-1500

-1000

-500

0

500

1000

1500

Figure 3.3.: Reactive power supply of the CS-4047 during the year

kept on its target value. However it stands out, that in particular in the summer months,the SC reaches its limits. As it cannot be provided the needed amount of inductivereactive power, the bus voltage increases in this moments up to an still valid maximumvalue of 1.03 p.u.

4. Discussion

The main aim of the project was the adaptation of the original Nordic 32 test system tomatch more closely to the real Swedish transmission system. To validate the results, astable and secure operation must be ensured and the active power flows between theareas should correspond to the real conditions. If these conditions are accomplished goodenough, the new test system can be used to find weak and strong buses or challengingcircumstances for the grid operation.

4.1. Active Power Flow

The Swedish transmission grid is characterized by long power lines and large powertransfers. The northern districts in the electricity areas SE1 and SE2 have an area of about240 500 km2 which is nearly 60 % of Sweden. Nevertheless, only approximately 11 % ofthe Swedish population live in this area. In particular the district Norbotten (≈ SE1) is,with a population density of 2.58 pers.

km2 extremely spare populated (district Stockholm:359.3 pers.

km2 ) [27]. However, in these two areas circa 44 % of the installed power is located.This leads to huge power flows from the north to the south. Furthermore, the areaSE1 exports nearly always electric energy to the neighbouring countries Norway andFinland. The high demand in the area SE3 is, apart of the three base-load driven nuclearpower plants and the other generation, covered by the imports from SE2. Since thenuclear power plants Ringhals and Oskarshamn are located in the south of area SE3,they also energize the highly populated but rather little energized (mostly wind and heatdriven CHP) area SE4. Therefore, power flows up to 5 MW from SE3 to SE4 can bemeasured.Figure 4.1 compares the real operation statistics with the simulation results for theyear 2018. The orange graph shows the real market data provided by [10] in an hourlyresolution. The blue bars illustrate the results of the quasi-dynamic simulation of thegrid model. Thereby, the power transfer arises from the loading of the power lineswhich connect the different areas. The corresponding lines can be found in Table 4.1.Furthermore, the borders between the four areas are marked in the map of the Swedishtransmission grid (Figure 2.3) or in the single line diagram of the power factory gridmodel (Figure A.1). The equivalent grid "EQUIV" represents the summed export/importdata from SE1 to Norway and Finland.Disregarding the first three months of SE1, it stands out that, the general power exchangecharacteristics are reproduced. Particularly the power flow SE2>SE3 and SE3>SE4 donot have any major error. A zoom-in of the power transfer between SE3 and SE4 shows

30 Discussion

Figure 4.1.: Comparison of the simulated active power flow and the real operationstatistics for 2018 in an hourly resolution

Table 4.1.: List of power lines in the grid model that connect the four areasEQUIV>SE1 SE1>SE2 SE2>SE3 SE3>Se44071>4011 4011>4021 4021>4042 4051>40644071>4012 4011>4022 4032>4042 4062>4063

4032>40444031>40414031>4060

4.1 Active Power Flow 31

that the simulation results follow the real market data, peaks and valleys are reproducedrather good. (Figure 4.2) illustrate exemplary the range of two weeks, from Monday,14.05.2018 00:00 to Sunday 27.05.2018 23:00.

3200 3250 3300 3350 3400 3450 3500-1000

0

1000

2000

3000

4000

5000

6000SimulationStatistics

Figure 4.2.: Comparison of the simulated active power flow and the real operationstatistics from SE3>SE4 for two weeks in an hourly resolution

However, the power flow from area SE1 to the equivalent grid and to SE2 showssignificant discrepancies. A deeper analysis of the equivalent grid, represented by onlytwo buses each of them connected to one generator and one load, can provide a possibleexplanation. One of the generators, g20, works as slack generator in the grid model,thus if necessary it balances the consumption and production in the grid. The targetvalue for its active power results from the sum of a permanent offset of 2000 MW andthe power transfer from or to Norway and Finland. Figure 4.3 compares the targetvalue of the active power generation (orange line) of the slack node with the actualvalue in the simulation (blue bars). As described, the grid model is simplified. Thereforethe system losses cannot be simulated exactly and smaller differences between the twographs are expected. However, it turns out that in the the first 2500 hours of theyear the simulated active power of the slack generator does not even approximatelycorresponds with the target value. It stands out that this time range correlates to thepower flow discrepancies visible in Figure 4.1. This leads to the conclusion that powerdifferences in the slack node lead to a false power transfer between the areas. As SE1 isthe only area connected directly to the equivalent grid, it is affected much more thanthe farther areas SE3 and SE4.

To find the reason for the discrepancies a further examination of the used operationstatistics is helpful. It becomes apparent that high differences are not related to a specialstudy case, but occur at both high and low demand. The composition of the electricitymix does not affect the error in the slack generator either. The lack of coherency leadsto doubts on the validity of the operation statistics. Figure 4.4 shows the balance ofgeneration and consumption for whole Sweden. Furthermore all imports and exportsfrom or to foreign countries are included. Therefore, each blue dot should show the

32 Discussion

0 1000 2000 3000 4000 5000 6000 7000 8000-2000

-1000

0

1000

2000

3000

4000

Figure 4.3.: Comparison of the target value and the actual simulated active power ofthe slack generator for 2018 in an hourly resolution

system losses in the specific hour. However, a lot of negative values are visible, whichwould mean a higher consumption than production, a technically impossible scenario.The orange line shows the corresponding delta between target and actual power of theslack generator. It is noticeable that both graphs have slightly the same trend anda higher error in the statistics leads to an higher error in the slack generator. If thestatistics are examined for each area, it stands out that the discrepancies in the areaSE1 are by far the highest.

As pointed out, the operation statistics are defective, therefore an error in the first 2500hours of the year 2018 might be an explanation for deviations in the simulation results.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000-4000

-3000

-2000

-1000

0

1000

2000

3000

Figure 4.4.: Differences between electricity production and consumption regarding exportand import and the corresponding active power error of the slack generator

4.2 Voltage Profile 33

4.2. Voltage Profile

Due to the measures presented in chapter 3 a stable and secure grid operation isguaranteed during each hour of the year. The voltages are kept within the limits of0.9 p.u. to 1.05 p.u. The simulation results can be found in the file data.mat or easilyreproduced with the DIgSilent PowerFactory grid model. In this section some buses willbe discussed to point out special characteristics of the Swedish transmission grid.

4.2.1. Strong Bus

Figure 4.5 shows the simulated voltages for each hour of the year 2018 on the bus 1014.It is located in the northern part of the grid, in the area SE1. The nominal bus voltage is130 kV. The bus is situated in a ring network. In addition to the two power lines, thereis only a generator and an inductor connected to the bus. It stands out that the voltage

0 1000 2000 3000 4000 5000 6000 7000 8000 90000.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

Figure 4.5.: Resultant yearly voltage profile of the bus 1014

remains nearly constant on an value of 1.04 p.u. The area SE1 is characterized by a highproduction, which leads to a high voltage. To remain the bus voltage below 1.05 p.u.,an inductive reactive power supply of 80 Mvar is necessary. The active power of theconnected generator differs comparatively little between 35 and 735 MW. Furthermore,the bus is rather good connected to the neighbouring buses in the grid, the loading ofthe power lines does not exceed 53 % during the year. These conditions lead to a stablevoltage on the bus, the delta between the highest and the lowest voltage values duringthe year is only 0.019 p.u.

4.2.2. Weak Bus

The bus 4063 is located in the south west of Sweden, in the area SE4. It forms partof the 400 kV backbone of the transmission grid and is connected to the bus 4062 in

34 Discussion

area SE3 and the bus 4064 in the area SE4. Furthermore, the connection to Denmark ismodelled by a load respective synchronous generator. Additionally a generator and loadwith fluctuating power values are connected.

0 1000 2000 3000 4000 5000 6000 7000 8000 90000.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

Figure 4.6.: Resultant yearly voltage profile of the bus 4063; coloured depending on thebalance of production and consumption on this bus

Figure 4.6 shows the bus voltage during the year. Each value is coloured, depending onthe power delta between production and consumption (regarding the import/export).It stands out, that the consumption is nearly always higher than the generation. Fur-thermore, there is a huge spread of active power, during the year the maximum andminimum value differ more than 4 GW. Figure 4.6 clearly shows that a high generationleads to a higher voltage, a high consumption to a voltage drop. The valid voltage rangeis utilised nearly completely, the lowest voltage is 0.92 p.u. This must be taken intoaccount if new network operation resources, especially large loads, want to be integratedon this bus. Depending on the influences, new measures must be taken to secure anstable grid operation.

4.2.3. Special Circumstances

Figure 4.7 shows the voltage of bus 2032 in the area SE2. The bus is located in the220 kV voltage level. It is connected to the 400 kV transmission grid as branch offconnection. Therefore, a difference between the generation and load will be balancedout over this power line. Figure 4.7 shows that the voltage on bus 2032 is nearly alwaysstable and about 1.04 p.u. Only on some hours in the year a significant voltage drop downto 0.96 p.u. is noticeable. A deeper analysis of these points shows a high generation,especially caused from a high penetration of wind power. The high generation causestwo effects regarding the voltage stability. Firstly, the generator reaches its limits andcannot provide the necessary reactive power to stabilize the voltage. Secondly, a highgeneration leads to a high active power transfer over the power line. In Figure 4.7 eachvoltage dot is coloured depending on the loading of the line. It stands out, that a high

4.2 Voltage Profile 35

0 1000 2000 3000 4000 5000 6000 7000 8000 90000.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

10

20

30

40

50

60

Figure 4.7.: Resultant yearly voltage profile of the bus 2032, coloured depending on theloading of the connected power line

loading causes a voltage drop. This phenomena can be explained with the PV-curve,where a high active power transfer conditions voltage stability problems [26]. Beforemore generation can be installed on this bus, further measures such as time-dependentcapacitive compensating or reinforcement of the power line must be taken.

5. Conclusion

With the obtained grid model significant differences between the original Nordic 32 testsystem and the Swedish transmission grid could be eliminated or reduced. In particular,the installed capacity of the electricity production was increased nearly four timescompared to the former value. Furthermore, the outdated location of the generators andloads were changed according to the actual situation. Thus, new developments suchas the continuous increasing penetration of wind power or the nuclear phase out areconsidered in the test system.The geographic outline of the project showed in Figure 2.2 gives each bus a location inSweden. Therefore, new generation or load can be integrated into the test system withoutdifficulties. Furthermore, Table 2.7 lists the generation mix of each bus. Individual plantscan be found easily which makes it possible to simulate contingencies or permanent shutdowns of specific power plants. All in all, future developments of the Swedish energysystem can be adopted in the test system whenever needed.The realized quasi-dynamic simulation is based on real operation statistics of a completeyear. Thereby, not only the data per area was used, but also the type of generation andexport/import were considered. The original Nordic 32 test system only simulated onespecial, fictitious study case, describing a high demand scenario. The new grid modeloffers 8760 different and realistic test scenarios instead. Depending on the analysis andthe wanted outcome, the adequate study case can be examined. Furthermore, newoperation statistics for example of the year 2019 can be included and simulated easily.The validation of the simulation results for the year 2018 shows that, with exceptions,the power flows in the grid model correlate with the real power transfer between theareas. Thus, the obtained model is a good representation of the Swedish transmissiongrid.Besides, a stable and secure grid operation is possible due to the reactive powersupply. The values of the shunt elements shows were high amounts of reactive powercompensation is needed and helps to find weak and strong buses in the grid. Furthermore,special circumstances for example a high generation paired with a low consumption canbe located and the grid reinforced accordingly.

6. Future Work

As pointed out, the obtained grid model is a good representation of the Swedishtransmission system. It already offers a good basis for plenty of different studies of theNordic transmission system. However, it should be adapted to the special needs of eachstudy.As the specific changes always depend on the type and aim of the studies, in thischapter only general improvements of the test system will be specified a bit. It can bedifferentiated between the external input statistics and internal modifications of the gridmodel.

6.1. Operation Statistics

In section 2.4 the use and source of the different operation statistics which lead to thesimulated study cases is described. In this project, two different sources [10, 18] for thepower production were used with partially significant differences. To obtain valid studycases, the reliability of the statistics should be validated again, in particular the onesfrom [10]. As Nord Pool AS runs a electricity market, the published operation statisticsnot necessarily show the produced electric power, but the traded power. Hereby, it mustbe differentiated between the Day-Ahead-, the intraday market and the actual powerflow including grid losses.Besides, the production of wind power is published separately. In the validation processof the input data, it should be proven if these data are already a part of the totalpower production and if the wind power production is based on measured values or thepreviously traded power based on a wind forecast. A reflection about the Nord Pool ASstatistics regarding the wind power prognosis and data validity can be found in [28].Furthermore, the discrepancies in the operation statistics until the hour of year 2500(cf. section 4.1 and Figure 4.4) should be examined. As pointed out, an error in theoperation is highly probable. A possible explanation could be different calculation andpublishing conducts before and after approximately April 2018.To avoid the commented problems, it is highly recommended to obtain the operationstatistics from one source only, the Swedish transmission grid operator Svenska Kraftnät.Both, modified statistics of 2018 or completely new statistics of 2019 can be easilyincluded to the grid model as a time series using the formulas presented in section 2.4.A detailed list with the used operation statistics and further information to the datapublication can be found in section A.1

40 Future Work

6.2. Grid Model

In this section, two possible, general improvements of the grid model will be presented,the implementation of the slack generator and reactive power supply. Nevertheless thislist could be extended easily, for instance a more detailed version of the transmissiongrid or the modelling of lower voltage levels as well.

6.2.1. Slack Generator

The slack generator was taken from the original Nordic 32 test system. As described inchapter 4 it leads to errors in the active power transfer, affecting mostly the area SE1.Even with accurate operation statistics, the difference between actual and simulatedsystem losses, will lead to an error in the simulation. A possible solution can be theconnection to neighbouring countries. Instead of using an SG and a load, a moreaccurate and detailed model could improve the test system. If the system can bebalanced out by the seven connections to neighbouring countries, the individual impactof each connection will be less. Furthermore, all areas will be affected in a more or lessequal manner.

6.2.2. Reactive Power Supply

The reactive power compensation in the obtained model is regulated by both, the SGsand the additionally added devices. Until now, as a simplification, each generation type ismodelled as a salient-pole or round-rotor machine and provides reactive power accordingto its capability curve. To obtain a more realistic test system, each generation typeshould be modelled with an independent component. Especially wind turbines normallyuse other generators such as double feed induction machines or full scale converterinterfaced generators. These changes could lead to decreased reactive power provisioncapabilities, due to the decreased apparent power of the SG. However, a more detailedtest system offers the possibility for further simulations and analyses. For example, thebeneficial system behaviour of wind turbines or contingencies of nuclear power plantscould be examined.Furthermore, the additional reactive power compensation is modelled rather simpleand outdated. The inductors and capacitors (cf. chapter 3) are modelled as staticcomponents without any interaction with the grid, such as switchable reactive powersupply depending on the actual conditions. In further development of the test system,modern compensator’s such as FACTS should be used. A dynamic reactive power supplydepending on the local, volatile production and consumption scenarios could decreasethe need of reactive power elements in the grid and stabilize the voltage more effective.Furthermore, FACTS can be used to replace SC or SG and increase the options for newintegration of generation or load in the grid, even in weaker grid regions.

Bibliography

[1] CIGRE Task Force 38-02-08, “Long term dynamics phase ii: Final report”, 1995.[2] L. D. P. Ospina, A. F. Correa, and G. Lammert, “Implementation and validation

of the nordic test system in digsilent powerfactory”, in 2017 IEEE ManchesterPowerTech, IEEE, 18.06.2017 - 22.06.2017, pp. 1–6. doi: 10.1109/PTC.2017.7980933.

[3] C. D. Vournas and T. van Cutsem, “Local identification of voltage emergencysituations”, IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1239–1248,2008. doi: 10.1109/TPWRS.2008.926425.

[4] S. M. Shahrtash and H. Khoshkhoo, “Fast online dynamic voltage instabilityprediction and voltage stability classification”, IET Generation, Transmission &Distribution, vol. 8, no. 5, pp. 957–965, 2014. doi: 10.1049/iet-gtd.2013.0296.

[5] S. R. Islam, D. Sutanto, and K. M. Muttaqi, “Coordinated decentralized emergencyvoltage and reactive power control to prevent long-term voltage instability in apower system”, IEEE Transactions on Power Systems, vol. 30, no. 5, pp. 2591–2603, 2015. doi: 10.1109/TPWRS.2014.2369502.

[6] M. Jonsson and J. E. Daalder, “An adaptive scheme to prevent undesirable distanceprotection operation during voltage instability”, IEEE Transactions on PowerDelivery, vol. 18, no. 4, pp. 1174–1180, 2003. doi: 10.1109/TPWRD.2003.817501.

[7] M. R. S. Tirtashi, O. Samuelsson, and J. Svensson, “Long-term voltage collapseanalysis on a reduced order nordic system model”, in 49th International UniversitiesPower Engineering Conference (UPEC), 2014, Piscataway, NJ: IEEE, 2014, pp. 1–6. doi: 10.1109/UPEC.2014.6934733.

[8] IEEE PES-TR19, “Test systems for voltage stability analysis and security assess-ment”, 2015.

[9] The nordic/national grid, 2018. [Online]. Available: https://www.svk.se/en/national-grid/map/.

[10] Nord Pool AS, Historical market data. [Online]. Available: https://www.nordpoolgroup.com/historical-market-data/ (visited on 08/25/2019).

[11] Energi Företagen, Energiåret 2017, 2018. [Online]. Available: https : / /www .energiforetagen.se/statistik/energiaret/ (visited on 08/27/2019).

[12] Swedish Energy Agency, Energy in sweden - facts and figures 2019. [Online].Available: https : //www .energimyndigheten . se/en/news/2019/energy - in -sweden---facts-and-figures-2019-available-now/ (visited on 08/25/2019).

https://doi.org/10.1109/PTC.2017.7980933

https://doi.org/10.1109/PTC.2017.7980933

https://doi.org/10.1109/TPWRS.2008.926425

https://doi.org/10.1049/iet-gtd.2013.0296

https://doi.org/10.1109/TPWRS.2014.2369502

https://doi.org/10.1109/TPWRD.2003.817501

https://doi.org/10.1109/UPEC.2014.6934733

https://www.svk.se/en/national-grid/map/

https://www.svk.se/en/national-grid/map/

https://www.nordpoolgroup.com/historical-market-data/

https://www.nordpoolgroup.com/historical-market-data/

https://www.energiforetagen.se/statistik/energiaret/

https://www.energiforetagen.se/statistik/energiaret/

https://www.energimyndigheten.se/en/news/2019/energy-in-sweden---facts-and-figures-2019-available-now/

https://www.energimyndigheten.se/en/news/2019/energy-in-sweden---facts-and-figures-2019-available-now/

42 Bibliography

[13] Leif Kuhlins, Vattenkraften i sverige. [Online]. Available: https://vattenkraft.info/(visited on 08/25/2019).

[14] IAEA, Power reactor information system. [Online]. Available: https://pris.iaea.org /PRIS /CountryStatistics /CountryDetails . aspx ? current=SE (visited on08/25/2019).

[15] Michaël Pierrot, The wind power: Wind energy market intellegence. [Online].Available: https://www.thewindpower.net/country_maps_en_17_sweden.php(visited on 08/25/2019).

[16] A. Berglund, Markbygden. [Online]. Available: https://svevind.se/Markbygden(visited on 08/25/2019).

[17] Regionfakta, Elförbrukning i bostäder. [Online]. Available: http://www.regionfakta.com/jamtlands-lan/energi/elforbrukning-i-bostader/ (visited on 08/25/2019).

[18] Svenska kraftnät, Mimer. [Online]. Available: https://mimer.svk.se/ProductionConsumption/ProductionIndex (visited on 08/25/2019).

[19] Anton Thorslund, “Swedish transmission grid model based on open sources”,Masterthesis, Chalmers University of Technology, Gothenburg, 2017.

[20] DIgSILENT, “User manual”, 2019.[21] European Comission, “Comission regulation (eu) 2016/ 631: Establishing a network

code on requirements for grid connection of generators”, 14.04.2016.[22] J. Baillieul and T. Samad, Encyclopedia of systems and control, ser. Springer

reference. London: Springer, 2015.[23] V. Crastan, Elektrische Energieversorgung 3: Dynamik, Regelung und Stabilität,

Versorgungsqualität, Netzplanung, Betriebsplanung und -führung, Leit- und In-formationstechnik, FACTS, HGÜ, 2. Aufl. 2018. Berlin, Heidelberg: Springer BerlinHeidelberg, 2018.

[24] J. Hossain and H. R. Pota, Robust Control for Grid Voltage Stability: HighPenetration of Renewable Energy: Interfacing Conventional and Renewable PowerGeneration Resources, ser. Power Systems. Singapore: Springer Singapore, Imprint,and Springer, 2014.

[25] Prof. H. Lens, Vorlesung dynamik elektrischer verbundsysteme, 2018.[26] T. Cutsem and C. Vournas, Voltage Stability of Electric Power Systems, ser. Power

Electronics and Power Systems. Berlin: Springer US, 2008. doi: 10.1007/978-0-387-75536-6. [Online]. Available: http://gbv.eblib.com/patron/FullRecord.aspx?p=571861.

[27] Holger Frommert, Schweden karte bevölkerungsdichte und verwaltungsgliederung,19.08.2019. [Online]. Available: http://geo- ref .net/de/swe.htm (visited on08/27/2019).

https://vattenkraft.info/

https://pris.iaea.org/PRIS/CountryStatistics/CountryDetails.aspx?current=SE

https://pris.iaea.org/PRIS/CountryStatistics/CountryDetails.aspx?current=SE

https://www.thewindpower.net/country_maps_en_17_sweden.php

https://svevind.se/Markbygden

http://www.regionfakta.com/jamtlands-lan/energi/elforbrukning-i-bostader/

http://www.regionfakta.com/jamtlands-lan/energi/elforbrukning-i-bostader/

https://mimer.svk.se/ProductionConsumption/ProductionIndex

https://mimer.svk.se/ProductionConsumption/ProductionIndex

https://doi.org/10.1007/978-0-387-75536-6

https://doi.org/10.1007/978-0-387-75536-6

http://gbv.eblib.com/patron/FullRecord.aspx?p=571861

http://gbv.eblib.com/patron/FullRecord.aspx?p=571861

http://geo-ref.net/de/swe.htm

Bibliography 43

[28] L. Herre, T. Matusevičius, J. Olauson, and L. Söder, “Exploring wind powerprognosis data on nord pool: The case of sweden and denmark”, IET RenewablePower Generation, vol. 13, no. 5, pp. 690–702, 2019. doi: 10.1049/iet-rpg.2018.5086.

https://doi.org/10.1049/iet-rpg.2018.5086

https://doi.org/10.1049/iet-rpg.2018.5086

A. Appendix

A.1. Nord Pool Statistics

Table A.1.: List of used operation statistics from Nord Pool AS1

Statistics FileActive power generation production-se-areas_2018_hourly.xls

Active power loads consumption-se-areas_2018_hourly.xlsExport/Import elspot-flow-se_2018_hourly.xls

Power flow between areas elspot-flow-se_2018_hourly.xls

A.2. Sinlge Line Diagram

1All files were downloaded form https://www.nordpoolgroup.com/historical-market-data/, the date ofthe last actualisation is 01.01.2019

46 Appendix

DIgSILENT

CENTRAL

NORTH

EQUIV.

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

SG~

1

1

1

1

1

1

1

1

1

1

1

1 1

1

1

1

1

1

1

1

4

55

5

2

1

1

1

5

5

5

35

45

15

5

54

4

4

1010

0

5

5

1212

33

1-1

5

1

1

3

3

4

1

5

16

5

0

5

4 1

-1

5

15

0

5

0 0

4

0

4

0

554

55

3

4063-Cap

L40

22-4

031

a

Shunt-4047

pha

se s

hift

er(3

4)

l_ex

_P

L

g_ex

_P

L

Shunt-4042

Shunt-1011

Shunt-1012

Shunt-1013

Shunt-1014

Shunt-1021

Shunt-1042

Shunt-2031

Shunt-4011

Shunt-4031 Shunt-4032

Shunt-4060

phase shifter(30)Shunt-4061

Shunt-4062

Sh

unt-

40

64

phase shifter(10)

phase shifter(35)

phase shifter(33)

phase shifter(32)

phase shifter(31)

phase shifter(29)

phase shifter(28)

phase shifter(27)

phase shifter(26)

phase shifter(25)

phase shifter(24) phase shifter(23)

phase shifter(22)

phase shifter(21)phase shifter(20)

phase shifter(19)

phase shifter(18)phase shifter(17) phase shifter(16)

phase shifter(15) phase shifter(14)

phase shifter(13)

phase shifter(9)

phase shifter(8)

phase shifter(7)

phase shifter(6)phase shifter(5)

phase shifter(4)

phase shifter(3)

phase shifter(2)

phase shifter

Shunt-4072

Shunt-2032

L4043-4046a

L40

46

-40

47

a

L406

1-40

62a

L4

06

2-4

06

3c

L4051 - 4064a

L4031 -4060b

L4031-4032a

L402

2-40

31c

L40

21-4

042a

L40

21-4

032a

L4012-4071a

L4

012-

4022

a

L4011-4071a

L401

1-4

02

2a

L40

11-4

02

1a

L1012-1014c(1)

L1011-1013c

L40

71

-40

72

c

Shunt-4045

60

Tr4

1-4

041(

1)

64

Tr51-4051(1)

Tr4041-g13(2)

g64

Tr4

041

-g13

(1)

g60

4032(1)

Tr4

6-40

46(1

)

Shunt-4063

Shunt-4021

Shunt-4044

L4063 ..

L4051 - 4064

l_ex_NO1

g_ex_N..

L4060 -..

L4031 ..

L4060 - ..

L4031 ..

g_ex_FI(1)

l_ex_FI(1)

g_ex_DK2

l_ex_DK2

g_ex_DK

l_ex_DK

g_ex_NO3

l_ex_NO3

l_ex_NO4

g_ex_NO4

Tr4

061

-g17

(2)

g32

Tr4

061

-g17

(1)

g61

g13 (CS)

Tr4

04

1-g

13

63

Tr6

3-4

06

3

g18

Tr4

06

3-g

18

L406

2-40

63b

L406

2-40

63a

L4045-4062

L40

61-

4062

62

Tr6

2-4

062

g17

Tr4

06

1-g

17

L40

45-4

051

a

L404

5-40

51b

4051-Cap

51

Tr5

1-4

051

g16

Tr4

05

1-g

16

g15

Tr4

047

-g1

5

L4

046

-40

47

L404

3-40

47

47

Tr4

7-40

47

L404

4-4

045b

L404

4-40

45a

Tr1

045-

4045

b

Tr1

04

5-4

04

5a

L1042-1045

L1041-1045a

L1041-1045b

1045-Cap

05

Tr5

-104

5

1041-Cap

01

Tr1

-104

1

L104

1-10

43b

L104

1-10

43a

02

Tr2

-10

42

L1042-1044b

L1042-1044a

g06

Tr1

042

-g6

g14

Tr4

04

2-g

14

4046-Cap

46

Tr4

6-4

046

L4043-4046

4043-Cap

43

Tr4

3-4

043

L4043-4044

L40

42-4

043

Tr1

04

4-4

04

4b

Tr1

04

4-4

04

4a

1044-Cap

04

Tr4

-10

44

L1043-1044b

L1043-1044a

g07

Tr10

43-g

7

1043-Cap

03

Tr3

-104

3

61

Tr6

1-4

061

L40

41-4

061

L4042-4044

L4032-4044

L4041-4044

L402

1-40

42

42

Tr4

2-4

042

L403

2-4

04

2

41

Tr4

1-4

04

1

4041-Cap

L4031-4041b

L4031-4041a

L402

1-40

32

L4031-4032

g12

Tr4

03

1-g

12

L4

02

2-4

03

1b

Tr2031-4031

31

Tr3

1-20

31

L2031-2032b

L2031-2032a

32

Tr3

2-20

32

g08

Tr2

03

2-g

8

g04

Tr1

02

1-g

4

L1021-1022b

L1021-1022a

g05

Tr1

02

2-g

5

22

Tr2

2-10

22

1022-Cap

Tr1022-4022

L40

11-4

02

2

L4

01

2-4

022

L4

011

-402

1

g11

Tr4

02

1-g

11

4012-Ind

g10

Tr4

01

2-g

10

Tr1012-4012

12

Tr1

2-10

12

g01

Tr1

01

2-g

1

L1012-1014b

L1012-1014a

g03

Tr1

01

4-g

3

L1

013

-10

14a

L1

013

-10

14b

13

Tr1

3-1

01

3

g02

Tr1

013-

g2

L1011-1013b

L1011-1013a

11

Tr1

1-1

011

Tr1011-4011

L4

011

-401

2

L4012-4071

g09

Tr4

011

-g9

L4011-4071

g19

Tr4

071

-g1

9

4071-Ind

g2072

Tr4

072

-g20

Tr7

2-4

072

L407

1-40

72b

L407

1-4

07

2a

71

Tr7

1-4

071

4063

(1)/

406

4

4041(1)/4060

4063/4063

4062/4062

4051/4051

4047/40474045/4045

1045/10451041/1041

1042/1042

4046/40464043/4043

1044/1044

1043/1043

4061/4061

4044/4044

4042/4042

4041/4041

4032/40324031/40312031/20312032/2032

1021/1021 1022/1022 4022/4022

4021/4021

1012/1012

1014/1014

1013/10131011/1011

4012/4012

4011/4011

4072/4072

4071/4071

SE1

SE2

SE3

SE4

InactiveOut of CalculationDe-energised

Voltage Levels

9999 kV400 kV220 kV130 kV110 kV20 kV15 kV

Figure A.1.: Single Line Diagram of the modified test system, exported fromPowerFactory

developmentofnordic32systemmodeland ...1395253/fulltext01.pdf ·...

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