Wind Power and Its Impact on the Moldovan Electrical System

UPTEC-ES12011

Examensarbete 30 hp April 2012

Wind Power and Its Impact on the Moldovan Electrical System

Joel Eriksson

Simon Gozdz Englund

Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

Postadress:

Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Abstract

Wind Power and Its Impact on the Moldovan Electrical System

Joel Eriksson & Simon Gozdz Englund

The master thesis project has been executed with the cooperation of Borlänge Energi, with the aim of reducing the high electric energy dependency which Moldova has on Ukraine, Transnistria and Russia.

The project examines what reduction that would be possible by wind power installations on the existing electrical grid of Moldova. The installations should not surpass the capacity of the transmission lines or the voltage levels according to regulation. The southern regions of Moldova proved to have the best wind conditions and the locations of Besarabeasca, Zarnesti, Leovo, Ciadyr and Cimislia in the

southern region were chosen for wind power installations.

For the analysis a model over the Moldovan electrical system is constructed. Each of the five chosen locations is modelled with a generator symbolizing the wind power installation. The power flow software PSS/E is used to construct the model. To examine possible wind power installations different scenarios are created. The scenarios are executed with the southern regions 110 kV system as a focus area. All scenarios are analysed with a contingency analysis, where transmission lines in the focus region are tripped. The contingency analysis and the scenarios are automated using the programming language Python.

An economic analysis shows payback periods for wind power investments in Moldova, the analysis also shows the sensitivity of the electricity price and discount rates.

The project concludes that wind power installations are possible with the Moldovan electric grid as it looks today. The installations would result in reducing the high dependency of imported electrical energy.

Sponsor: ÅForsk Sida

ISSN: 1650-8300, UPTEC ES** ***

Examinator: Kjell Pernestål Ämnesgranskare: Mikael Bergkvist Handledare: Ronny Arnberg

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I Förord (in Swedish)

Bakgrunden till detta spännande examensarbete är att författarna på egen hand sökte en utmaning vad gäller uppbyggnad och utformning av framtida elektriska kraftnät. Deras frågeställning var vad händer i ett kraftnät vid en massiv utbyggnad av t.ex. vindkraft, karakteriserad av stora variationer i effekt? Frågeställningen är höggradigt intressant i länder med lite tillgång på vattenkraft och ur perspektivet av utfasning av fossila bränslen. Ur den synvinkeln var det svenska kraftnätet mindre intressant. Efter kontakter med Ronny Arnberg, Borlänge Energi, kom projektet att fokusera på elförsörjningen i Moldavien vars kraftnät blev modell för studien. Målet är inte att lösa Moldaviens energiförsörjningsproblem.

De ambitioner som författarna hade inledningsvis har sedan modererats på ett förtjänstfullt sätt av ämnesgranskaren Mikael Bergkvist att bättre passa tillgänglighet, tid och resurser. Ronny Arnberg har bistått med mängder med kontakter i Moldavien som öppnat dörrar för författarna. Resultatet på författarnas initiala fråga har kanske inte blivit besvarad men väl gett stora insikter i de utmaningar som väntar.

2012-03-16 Kjell Pernestål Examinator Unv.lekt.

Uppsala Universitet

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II Acknowledgments

This Master Thesis Project has been financed by a MFS scholarship and a ÅForsk scholarship without which the project could not have been executed.

Technical support was provided by the Technical University of Moldova, Anatolie Boscneanu Main Specialist at the National Agency for Energy Regulation and Lise Toll Project Developer at E.ON Climate & Renewables. Technical support was also provided along with and guidance in times of need throughout the project by our supervisors at Uppsala University; Mikael Bergkvist and Kjell Pernestål.

Special thanks should be directed to Professor Arion Valentin and PhD student Victor Gropa at the Technical University of Moldova who took us in with the true spirit of the Moldovan people; with helping hands wanting nothing in return. Thank you

This project could not have been written without the help of Borläng energi and its enthusiast Ronny Arnberg who provided contacts and a workplace in Moldova.

We would also like to take the chance to express our gratitude for the opportunity to experience Moldova and its truly great people, out of which we now call many friends and whom we will never forget.

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III Populärvetenskaplig beskrivning (in Swedish)

Moldavien är ett av de fattigare länderna i Europa. Det finns ett starkt engagemang och en stor vilja för sammarbeten med västländer för att lämna fattigdomen och närma sig Västeuropa. Ett viktigt steg i detta är att bli av med det starka energiberoende gentemot Ukraina och Ryssland som finns idag. Moldaviens interna politiska situation är svår. En del av Moldavien, Transnistrien, existerar idag som en autonom republik och har en långdragen konflikt bakom sig som ännu inte är löst.

Transnistrien och situationen där är viktig ur en energisituation då den största kraftanläggningen i hela regionen ligger där.

Moldavien importerar idag mellan 94 och 98 % av sin totala energikonsumtion där de stora importprodukterna är naturgas från Ryssland och el från Ukraina och Transnistrien. Av sin elkonsumtion har Moldavien idag endast möjlighet att producera ca 26 % nationellt, resten importeras från Ukraina och Transnistrien.

I examensarbetet utreds möjligheterna att minska detta starka beroende genom att öka intern elproduktion genom vindkraft. Fokus ligger på elnätet, alltså hur mycket vindkraft som kan installeras till dagens existerande elnät utan att elledningarna blir överbelastade eller att spänningar i elnätet ökar eller sjunker utanför gällande gränsvärden.

Vindpotentialen har undersökts via tidigare studier och den visar på att potentialen är störst i den södra delen av Moldavien. Dessa vindkraftskarteringar är utförda utifrån vindmätningar på meterologiska stationer, ofta på 10 till 12 meters höjd. Genom simuleringsprogram har man sedan kunnat uppskatta vindhastigheter för olika områden och höjd.

Fem platser med bra vindpotential valdes ut för vidare studier över hur mycket vindkraft som kan installeras ur nätets perspektiv. Dessa platser i närheten av städerna; Besarabeasca, Zarnesti, Leovo, Ciadyr och Cimislia ligger alla i södra delen av Moldavien. Den begränsade faktorn för hur mycket vindkraft som kan byggas är elnätet.

För att undersöka effekterna från vindkraftsinstallationerna på elnätet var det nödvändigt att bygga upp en modell i datorprogrammet PSS/E, designat för att beräkna effektflöden i elnät. Datorn kan sedan utföra de komplexa beräkningar som krävs för att räkna ut effekter och spänningar i systemet.

Det räcker dock inte att endast se på systemet som det faktiskt ser ut, man måste också undersöka vad som skulle händer då en elledning i systemet kopplas bort i en så kallad n-1 analys. Att en lina kopplas bort kan bero på behov av underhåll eller rena fel som kan uppstå vid till exempel olyckor.

Platserna undersöktes i den färdiga modellen bland annat en och en men även i ett scenario där det på alla platser samtidigt installeras vindkraft. Vindkraftparkerna symboliseras i modellen som generatorer som genererar aktiv effekt.

Resultaten visar att den maximalt möjliga installerade effekten varierar mycket beroende på plats.

Cimislia visar sig ha möjlighet för 100 MW, innan överföringskapaciteten blir begränsande. De övriga platserna begränsas på grund av att spänningsnivåer stiger eller sjunker utanför riktlinjerna. Då installation sker på alla platser samtidigt finns det möjlighet att installera omkring 260 MW, även här är höga spänningar en begränsande faktor för ytterligare installation.

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Den reaktiva effekten i elnätet har en stark koppling till spänningsnivåer och därav upprepas scenariona då vindkraftparkerna även har möjlighet att producera eller konsumera reaktiv effekt. Då vindkraftparkerna på detta sätt har möjlighet att kompensera med reaktiv effekt hålls spänningen konstant på basspänningsnivån.

De nya resultaten visar att detta ger en möjlighet att öka vindkraftinstallationen per plats. De platser i tidigare scenariot som tidigt fick spänningsproblem begränsas nu, precis som Cimislia, endast av överföringskapaciteten. Installation vid Cimislia minskar dock något då reaktiv effekt även den ”tar upp plats” på elnätet. Maximal produktion är dock fortfarande störst i Cimislia med ca 100 MW. Då vindkraft installeras på alla platser samtidigt ges en ökning till 355 MW, alltså en tydlig ökning av möjlig vindkraftsinstallation.

För att räkna ut den totala minskningen av importerad el bör man ta hänsyn till att en vindkraftpark med installerad effekt med t.ex. 260 MW inte kommer leverera 260 MW hela tiden på grund av att vinden inte blåser hela tiden. För att ta hänsyn till detta används två olika utnyttjandefaktorer för vindkraftparkerna, 0,1 och 0,3 där 0,1 är en relativt låg utnyttjandefaktor och 0,3 är en relativt hög utnyttjandefaktor. Resultaten visar att vindkraftverk som endast levererar aktiv effekt kan minska elimporten med mellan 7 % till 20 % beroende på utnyttjandefaktorerna. Då vindkraftparken har möjligheten att konsumera reaktiv effekt kan elimporten minska med mellan 8 % till 25 %.

I rapporten utförs även en ekonomisk analys där återbetalningstiden för ett vindkraftsprojekt tas fram. Återbetalningstiden beräknas med nettonuvärdesmetoden och återbetalningstiden tas fram för några olika räntesatser. Återbetalningstiden för vindkraftsprojekten varierar från 3 år till att aldrig betala tillbaka sig vid de olika ekonomiska scenarierna.

Slutsatsen är att Moldaviens starka beroende av importerad elektricitet kraftigt kan minskas med en utbyggnad av vindkraft i södra delen av landet.

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IV Executive summary

The Moldovan electrical energy imports can be reduced by as much as 25 %. This reduction is possible by wind power installations at the suitable locations of Besarabeasca, Zarnesti, Leovo, Ciadyr and Cimislia.

Assuming a possible good wind resource with a capability factor of 0,3 wind power installations of 355 MW would reduce the electrical energy imports by 25 % according to the model created for the project. The model has not been verified with other models, which is of priority for future work.

For a total installation of 355 MW the installed power needs to be allocated as shown below:

 Besarabasca 56 MW

 Zarnesti 68 MW

 Leovo 68 MW

 Ciadyr 91 MW

 Cimislia 72 MW

The strongest site for wind power production, one site at a time, is Cimislia with a total installed power of 102 MW possible. With all sites together the maximum installed power is 260 MW without reactive power compensation and 355 MW with reactive power compensation.

Economic calculations include a sensitivity analysis with different the electricity price and discount rates. The economic analyses shows that the payback time vary from 3 years to never being paid back and conclusions are drawn that further investigations needs to be made.

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V List of Acronyms and Abbreviations

ANRE National Agency for Energy Regulation AVR Automatic Voltage Regulation

CDM Clean Development Mechanism CER Certified Emission Reduction credits CHP Combined Heat and Power

DSA Dynamic Security Assessment

EBRD European Banc of Reconstruction and Development

ENTSO-E European Network of Transmission System Operators for Electricity FACTS Flexible Alternating Current Transmission Systems

HAWT Horizontal Axis Wind Turbine HPP Hydro Power Plant

IPS Integrated Power System MAWS Mean Annual Wind Speed

MSSR Moldovan Soviet Socialist Republic PSS/E Power System Simulator for Engineering

p.u Per Unit

SNC Second National Communication SSA Static Security Assessment TUM Technical University of Moldova

UNFCCC United Nations Framework Commission of Climate Change VAWT Vertical Axis Wind Turbine

WAsP Wind Atlas Analysis and Application Program

Table of Contents

I Förord (in Swedish) ______________________________________________________ i II Acknowledgments _______________________________________________________ ii III Populärvetenskaplig beskrivning (in Swedish)________________________________ iii IV Executive summary ______________________________________________________ v V List of Acronyms and Abbreviations ________________________________________ vi Chapter 1 Introduction ____________________________________________________ 1

1.2 Borlänge Energi ___________________________________________________________ 1 1.3 Moldova – Background _____________________________________________________ 1 1.3.1 Grid History _____________________________________________________________________ 2 1.3.2 Energy _________________________________________________________________________ 2 1.3.3 Bio Energy Potential ______________________________________________________________ 3 1.3.4 Solar Energy Potential _____________________________________________________________ 3 1.3.5 Wind Energy Potential ____________________________________________________________ 4 1.1.1 Environmental Goals ______________________________________________________________ 4 1.4 Aim and Goals ____________________________________________________________ 5 Chapter 2 Background _____________________________________________________ 6

2.1 Grid – Theory ____________________________________________________________ 6 2.1.1 Active and Reactive Power _________________________________________________________ 6 2.1.2 Introduction to the Electrical Power System ___________________________________________ 8 2.1.3 Components in the Electrical Power System __________________________________________ 11 2.1.4 Per-Unit System _________________________________________________________________ 15 2.1.5 Equivalents in Electrical Power Systems ______________________________________________ 15 2.1.6 Static Modelling _________________________________________________________________ 16 2.2 Wind Power ____________________________________________________________ 19

2.2.1 Moldova´s Wind Resource ________________________________________________________ 22 2.2.2 Economy ______________________________________________________________________ 23 2.3 Method ________________________________________________________________ 24

2.3.1 PSS/E _________________________________________________________________________ 24 2.3.2 Building the Model ______________________________________________________________ 24 2.3.3 Scenarios ______________________________________________________________________ 29 2.3.4 Economy ______________________________________________________________________ 30

Chapter 3 Results ________________________________________________________ 32

3.1 Base Case_______________________________________________________________ 32 3.2 Scenario I _______________________________________________________________ 33 3.2.1 Scenario I, With Reactive Power Compensation _______________________________________ 33 3.3 Scenario II ______________________________________________________________ 34

3.3.1 Scenario II, With Reactive Power Compensation _______________________________________ 35

1.1 Reduction of Imported Electric Energy _______________________________________ 36 3.3.2 Scenario I ______________________________________________________________________ 36 3.3.3 Scenario II _____________________________________________________________________ 37 3.4 Economy _______________________________________________________________ 37 Chapter 4 Discussion _____________________________________________________ 40

4.1 Scenarios _______________________________________________________________ 40 4.1.1 Scenario I ______________________________________________________________________ 40 4.1.2 Scenario II _____________________________________________________________________ 41 4.1.3 Economy ______________________________________________________________________ 42

Chapter 5 Conclusion _____________________________________________________ 43 Chapter 6 Future Work ___________________________________________________ 44 Appendix A Map of the Moldovan electrical system ___________________________ A-1 Appendix B Map over the wind potential in Moldova _________________________ B-1 Appendix C Description of WAsP __________________________________________ C-1 Appendix D Line diagram and data over the equivalent 330 kV circuit ____________ D-1 Appendix E Transmission Line Data ________________________________________ E-1 Appendix F Line diagram and data over the complete model ___________________ F-1 Appendix G General Python Script – executing the contingency analysis __________ G-1 Appendix H Python Script – Scenario I ______________________________________ H-1 Appendix I Python Script – Scenario II, Monte Carlo Simulation____________________ I-1 Appendix J Base Case - Contingency Loading Report _____________________________ J-1 Appendix K Base Case – Line Diagram with Line Capacities _____________________ K-1 Appendix L Scenario I – Overload Report _____________________________________ L-1 Appendix M Scenario I Reactive Power Compensation – Overload Report_________ M-1 Appendix N Scenario II - Overload Report ___________________________________ N-2 Appendix O Scenario II Reactive Power Compensation – Overload Report _________ O-2 Appendix P Scenario II – Contingency Loading Report _________________________ P-1 Appendix Q Scenario II – Line Diagram for Line Capacities ______________________ Q-1 Appendix R Scenario II All Generators – Results ______________________________ R-1 Appendix S The Contingency and Automation Process in PSS/E _________________ S-1 Appendix T Sub, Mon and Con files for the contingency analysis ________________ T-1 Appendix U Division of the Work Between the Authors ________________________ U-1

Table of Figures and Tables

Figure 1.1 Regional gropes of ENTSO-E and the IPS electrical systems [8] 2 Figure 2.1 The total power aka. the apparent power, active power and reactive power [18] 7 Figure 2.2 Real power and reactive power plotted against the load angle and voltage [20] 8

Figure 2.3 Structure of an electrical power system [20] 9

Figure 2.4 Showing the basic schematics of an on-load tap changer [20] 12

Figure 2.5 Transmission line equivalent 13

Figure 2.6 The magnetic field H between two conductors 14

Figure 2.7 Electric field E between two conductors 14

Figure 2.8 Busses connected in star and delta with line impedance Z [20] 16

Figure 2.9 An equivalent circuit of a short transmission line 17

Figure 2.10 An equivalent circuit of a medium transmission line 18

Figure 2.11 Schematic scheme over a contingency plan [23] 19

Figure 2.12 A typical arrangement for a HAWT [20] 20

Figure 2.13 A typical Cp/λ curve for a wind turbine [20] 20

Figure 2.14 Turbine power as a function of the wind speed [20] 21 Figure 2.15 An investment and payback curve for a nonspecific project [25] 23

Figure 2.16 One line diagram over the PSS/E model 25

Figure 2.17 Load and generation in Moldova, rectangles represent generation and circles loads 28 Figure 2.18 The algorithm for the contingency analysis where generator G is increased 30 Figure 3.1 The dispersion of voltage levels for the base case contingency analysis 32 Figure 3.2 A histogram of the dispersion of voltage levels with a contingency analysis 34 Figure 3.3 A histogram of the dispersion of voltages levels with a contingency analysis 35

Figure 3.4 Payback time with a capability factor of 0,3 37

Figure 3.5 Payback time with a capability factor of 0,1 38

Figure 3.6 Payback time including CER:s with a capability factor of 0,3 38 Figure 3.7 Payback time including CER:s with a capability factor of 0,1 39

Figure A-1 Map over the Moldovan electrical system [31] A-1

Figure B-1 Wind Potential in Moldova at the height of 70 meters [14] B-1 Figure D-1 Line diagram from PSS/E for the equivalent circuit over the Moldovan electrical system D-1 Figure F-1 Line diagram for the equivalent circuit over the Moldovan electrical system F-1

Figure K-1 One line diagram with line capacities K-1

Figure Q-1 One line diagram with line capacities Q-1

Figure R-1 Shows the iterations with all generators in scenario I. R-1 Figure R-2 Histogram over the maximum generation without reactive power compensation R-2 Figure R-3 Results from the second iteration with a narrow interval for each generator R-2 Figure R-4 F Histogram over the maximum generation with reactive power compensation R-2

Figure S-1 Shows the recorder function within PSS/E S-2

Figure T-1 Contingency file created for the contingency analysis T-1

Figure T-2 Monitor file created for the contingency analysis T-1

Figure T-3 Subsystem file created for the contingency analysis T-1

Table 1.1 Existing transmission lines in Moldova 3

Table 2.1 Load values for the active generation and consumption 28 Table 2.2 Model load values for the active generation and consumption 28

Table 3.1 Maximum generation before violation in the contingency report 33

Table 3.2 Maximum values regarding only line capacities 33

Table 3.3 Extended generation potential until line capacity is reached 33 Table 3.4 Possible generation capacity with reactive power compensation 33 Table 3.5 Maximum generation for each location giving maximum total generation for the region 34 Table 3.6 Maximum generation for each location giving maximum total generation for the region 35 Table 3.7 Imported electrical energy reduction due to wind power installations 36 Table 3.8 Imported electrical energy reduction with reactive power compensation 36 Table 3.9 Imported electrical energy reduction due to wind power installations 37 Table D-1 Bus data for equivalent circuit over the Moldovan electrical system D-2 Table D-2 Plant data for equivalent circuit over the Moldovan electrical system D-2 Table D-3 Machine data for equivalent circuit over the Moldovan electrical system D-2 Table D-4 Load data for equivalent circuit over the Moldovan electrical system D-2 Table D-5 Branch data for equivalent circuit over the Moldovan electrical system D-2

Table E-1 Data over transmission line types E-1

Table E-2 Impedance values for the lines in the 110 kV system E-1

Table E-3 Base impedance values E-1

Table E-4 Per Unit values for the lines in the 110 kV system E-1

Table F-1 Bus Data F-2

Table F-2 Branch Data F-2

Table F-3 Machine Data F-3

Table F-4 Plant Data F-3

Table F-5 Load Data F-3

Table F-6 Switched Shunt Data F-3

Table F-7 Three Winding Data F-3

Table F-8 Winding Data, MGRAS F-4

Table F-9 Winding Data, Vulcanesti F-4

Table F-10 Winding Data, Hancesti-Straseni F-4

Table F-11 Winding Data, Chisinau F-4

Table J-1 The busses with maximum and minimum voltage levels from the loading report J-8

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Chapter 1 Introduction

The introduction starts by giving a description of the company that the project has been executed in cooperation with. Thereafter follows a short background of Moldova with its electrical system, energy and renewable energy potential. The introduction ends with the aim and the goals of the project.

1.2 Borlänge Energi

AB Borlänge Energi is owned by the municipality of Borlänge. Borlänge Energi provides a wide range of services such as electricity, electricity grid, district heating, water, sewage, storm water and waste handling. In addition to these commitments Borlänge Energi also handles the municipality’s streets and parks [1].

Borlänge Energi has had international collaborations since the 1990^th, with a primary focus on the environment. In 1998 the local authorities in Borlänge and the Swedish embassy in Bucharest initiated a project to establish links between the Swedish and the Romanian municipalities. This led to collaboration between Borlänge and the Romanian city of Pietsi. In Pietsi Ronny Arnberg from Borlänge Energi and the mayor of Borlänge Nils Persson met with representatives from Chisinau city hall and from APA Canal, the water and wastewater company in Chisinau. This was the start for the cooperation between Borlänge Energi and Moldova with focus on the capital, Chisinau. [2].

The municipality of Chisinau has an interest in understanding “the Swedish way” of thinking. From the cooperation with the municipality of Borlänge they will try to study different ways of spreading information to the society, working with youth and sustainable development. From the start of the cooperation in the year 2009 several projects regarding the environment have been conducted [3].

With the cooperation as a base many master thesis projects have been written together with Borlänge Energi in Chisinau.

1.3 Moldova – Background

The Republic of Moldova is a small country situated in the south-eastern part of Europe with a total area of 33 800 m² and 3,6 million inhabitants. Bordering countries to the north, south and east is Ukraine and to the west Romania. The capital is Chisinau with a population of around 600 000 inhabitants, other important cities are Tiraspol (located in Transnistria, see below) and Baltsi. Around 41 % of the inhabitants live in cities. Moldova became an independent state 1991 with the dissolution of the Soviet Union [4]. With a GDP of 1500 US dollars per capita Moldova is the poorest country of Europe [5].

The population consists of different ethnical groups with the biggest being the Moldavians but there are also large groups of Ukrainians and Russians. The different ethnic groups have contributed to the violent history of the country. In connection with the dissolution of the Soviet Union an armed conflict broke out in the eastern part of Moldova called Transnistria. The majority of the population in Transnistria consists of Russians and Ukrainians who wanted to establish a breakaway republic of Transnistria. The breakaway republic never gained international recognition and the armed conflict ended in 1992. Negotiations between Moldova and Transnistria with help from Russia have ended in a greater sense of autonomy for Transnistria, to this date the conflict is not yet solved. [6]

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1.3.1 Grid History

Before the dissolution of the Soviet Union the electrical grid and power plants were laid out to jointly optimize the market in the south-western Soviet Union and the other countries in the region e.g.

Romania. With the fall of the Soviet Union these countries had to redesign their electrical systems.

Moldova and Ukraine stayed with the Eastern European system IPS (Interconnected Power Systems) together with Russia while Romania chose to connect with the Western European system ENTSO-E (European Network of Transmission System Operators for Electricity). ENTSO-E operates at the same frequency as IPS but the two systems do not operate synchronized with each other. [7]

Figure 1.1 Regional gropes of ENTSO-E and the IPS electrical systems [8]

The ENTSO-E is the joint European transmission system operator, in Figure 1.1; all marked zones except IPS are part of the ENTSO-E network and thus operate synchronously.

1.3.2 Energy

Moldova imports 94 % to 98 % [9] of its consumed energy from Russia, Ukraine and Transnistria. The country thus is very dependent on the eastern countries for energy supply. Striving to align itself with the western part of Europe the energy security is an important issue. The main possibility for improving the energy security is with new power supply within the country.

Today the electric power generation in Moldova and Transnistria consists of three CHP (Combined Heat and Power) plants, two HPP (Hydropower Plants); MGRAS, the biggest power plant in the region, fired with gas, and situated in Transnistria; and other minor power plants. The total capacity in Moldova, incl. Transnistria, is 3008 MW but around 2570 MW is generated by MGRAS and is thus not controlled by the Moldovan government. This means that Moldova only has around 438 MW of generation capacity. This is not enough to supply the demand of baseload in Moldova [10]. The total consumed electric energy in Moldova year 2010 was 4102 GWh out of which 1064 GWh was produced domestically and 3038 GWh was imported i.e. Moldova imported 74 % of all electrical energy consumed within the country. Due to the complex situation with Transnistria electrical energy imports have mainly come from Ukraine, but recently imports from Transnistria have increased and are now dominating. [11]

Moldova

3

The transmission grid in Moldova is interconnected with the neighbouring countries; six 330 kV overhead power lines to the Ukrainian power system, the connections to Romania consists of four 110 kV lines and one 400 kV line with which Moldova also gets connection with the Bulgarian power system see Appendix A. Because of the connections to the ENTSO-E system i.e. with a different synchronization than Moldova in Romania and Bulgaria, the transmission lines can only operate in island mode on the Moldavian side, or by using back to back frequency converters. [12]

The backbone in the Moldovan electrical system is the 330 kV line going from north to south, it is the main connection to both Transnistria and Ukraine. Well integrated together with the 330 kV system is the mesh of the 110 kV system which is spread out throughout Moldova. Table 1.1 shows the existing overhead line voltages and the total length of these. [13]

Table 1.1 Existing transmission lines in Moldova

Voltage level [kV] Length of the overhead transmission lines [km]

400 214

330 532,4

110 5231,1

Total: 5977,5

1.3.3 Bio Energy Potential

Moldova has no experience of large scale applications of bio energy even though it’s an agricultural country. It has some experience in small scale applications in the rural area. Moldova’s biomass suitable for energy use comes from forestry, agriculture, food industry and waste from households, where agricultural waste has the biggest potential as an energy source. At present Moldova biomass is inefficiently used as many outdated and simple technologies are used to convert the biomass into energy e.g. domestic fires and stoves efficiency rating rarely exceeds 50 %. There is also a lot of biomass that today cannot be used because the lack of new, today already existing, technologies needed for the conversion of biomass into energy. [14]

The technical potential of biomass in Moldova is 5,4TWh, where 2,1TWh comes from agricultural waste, 1,2TWh comes from fuel wood, 1,3TWh comes from wood processing waste and 0,8TWh comes from biogas. The potential for bio fuels is another 0,6TWh, meaning that the total potential of bio energy in Moldova is 6TWh. [15]

Bio energy has the biggest energy potential in Moldova; both in theoretical values and in the potential to include it in today’s already existing social infrastructure and energy system development programs. [14]

1.3.4 Solar Energy Potential

There has been research about solar energy utilization in Moldova. The research where performed by the institute of Energy of the academy of Sciences of RSSM (Moldovan Soviet Socialist Republic) in the late 1950s. The research resulted in a greenhouse with solar installations and heat storage in the ground. Because of the low prices for fossil fuel and lack of politic incitements for renewable energy the project was terminated. In the 1980s the work for implementing solar installations where restarted. [14]

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Solar energy is received on the earth’s surface all the time, though the amount of energy received on the earth’s surface depends on several different factors. The most important factors are the suns brightness, duration and height above the horizon. In Moldova the theoretical duration of the sun, when it’s shining unimpeded, is 4445-4452 hours per year [14] but the real duration is 2100-2300 hours per year because of clouds concealing the sun. The amount of solar energy received on the surface of Moldova differs from 2300 kWh/ m² year in south to 2100 kWh/m² year in the north [14].

Other sources estimate the solar radiation in Chisinau to be 1300 kWh/m² year. [15]

The solar energy in Moldova is primarily used for heating water using solar panels, secondarily used to dry fruit, vegetables and medicinal plants and tertiary for converting solar energy into electricity via photovoltaic conversion.

1.3.5 Wind Energy Potential

Historically, the area that today is called the Republic of Moldova has been appreciated as favourable wind zone for wind energy development. Statistical data from 1901, before the development of steam engines and internal combustion engines, shows that a total of 6208 windmills were registered in the Moldova area and its surroundings. Some of these windmills were even used during the interwar period. During the 1950s even 350 windmills where built, exclusively to pump water for agricultural purposes. These where later replaced by cheaper and more easy to handle electrical systems. The electrification that occurred in Moldova during the 1950s as well as the low prices for electrical energy where factors that wind power could not compete with at the time. Today Moldova doesn’t have any wind power.

At present day Moldova has no wind power installed; however there are plans to install wind power plants in a near future. The south of Moldova is often mentioned as a preferable area to build wind power. The opinions of Moldova’s wind potential differ e.g. the organisation 3tier concluded MAWS (Mean Annual Wind Speed) of 4-6 m/s at the height of 80 m [15] while a feasibility study written by the UNDP Moldova concluded MAWS of 4,5-8,5 m/s at a height of 70 m [14]. Moldova’s technical potential for wind power is up to 1 GW installed power providing approximately 1,1TWh of electrical energy [15]. This correlates to a capability factor of 13 %, which is very low.

1.1.1 Environmental Goals

Renewable energy in Moldova would go in accordance with the goals set up in their SNC (Second National Communication) directed to the UNFCCC (United Nations Framework Commission of Climate Change). The national priorities to reach the goals of greenhouse gas reductions include wider use of CDM (Clean Development Mechanism) projects, implementing a more aggressive policy on transfer of the green technologies, intensifying the process of international cooperation. An analysis on the possibilities to construct a wind power plant in Moldova in regards of the wind potential and the stability of the electrical grid would facilitate and work for the Moldavian national goals. The SNC also identifies relevant policies for the energy sector where two out of five directly would be coherence with the intended study, “…assuring energy security of the country by improving the interconnection capacity with the neighbouring countries and construction of new local sources of power generation based of the most recent and advanced environment friendly technologies.”

and “…increasing the share of renewable sources of energy in the energy balance of the country”.

[16]

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1.4 Aim and Goals

Moldova has a high dependency of imported electrical energy from Ukraine and Transnistria. To rid this huge dependency Moldova could look to its national resources for domestic production. The national goals in Moldova are angled towards sustainable development with more renewable energy.

This project will investigate how much the dependency of electrical imports could be reduced by wind power installations in the Moldovan electrical system as it looks today.

The goals of the project:

 The project will conclude in how much wind power installations would be possible in Moldova considering limiting factors of the electrical system.

 The project will show how much the electrical imports can be reduced by wind power installations in Moldova.

 The project will also conclude in potential sites for wind power installation

 An economic analysis will show whether it would be profitable to construct wind power in Moldova

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Chapter 2 Background

The background describes the grid theory important for the project, a section with wind power potential and finally the method with the creation of the model. This is followed with the scenarios used to examine the model.

2.1 Grid – Theory

To understand transmission networks active and reactive power are important concepts described below, also described are definitions of terms and components in the electrical system. The section ends with a description of approximations needed for computerize model calculations.

2.1.1 Active and Reactive Power

Power is the rate of change of energy with respect to time [17]. It is the amount of energy being absorbed by a load during a time interval. Reactive power cannot be expressed in the same way, it cannot be seen as a constant flow of energy from one point to another, the reactive power is flowing back and forth in the system and when completing a cycle just as much energy that was flowing away has flowed back. The average reactive power in any system is always equal to zero. The reactive power is thus not measured by its average value, being zero, but by its amplitude, its maximum value. This gives a measurement of how much reactive power that is actually flowing through the system. [17]

In an RLC circuit, with inductance L and capacitance C, the voltage before and after the load will have a small angular difference described by the load angle , the current will be shifted from the voltage with the current angle . The difference between and is the power factor angle . With a purely inductive load the current lags the voltage by and in a purely capacitive load the current leads the voltage with . In the following equations the load angle is equal to zero.

Equation 1

Equation 2

With these expressions for voltage and current the instantaneous power can be expressed by:

Equation 3

This expression combined with trigonometric identities gives Equation 2.4.

Equation 2.4

Equation 2.4 consists of one real and one imaginary part; the real power is defined as the average value of the real part.

Equation 2.5

The average value of reactive part, as can be seen below in the Figure 2.1, is always zero; this is the definition of reactive power. Instead the reactive power is measured by its amplitude value, this gives us: [18]

Equation 2.6

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Figure 2.1 The total power aka. the apparent power, active power and reactive power [18]

P is expressed in Watts and Q in VAr (Volt Ampere reactive) both describing the same quantity but with different units to distinguish them. The power factor angle in the cosine term in Equation 2.5 and Equation 2.6 called the power factor. For inductive loads where the current lags the voltage the load consumes reactive power. With capacitive loads the current leads the voltage and the load creates reactive power. [17]

According to [19] the active and reactive power in a RLC four terminal electric circuit can be described by Equation 2.7 and Equation 2.8 if the resistance R is neglected and assuming that the load angle is small.

| || |

Equation 2.7

and

| |

| | | | Equation 2.8

Equation 2.7 describes the dependence the active power has on the differences between the phase voltages and the angle between these. The phase voltages in the power system may not differ much between busses and thus the active power is highly dependent on the load angle which is the angular difference between and . This gives us the characteristics that the active power is strongly dependent on the load. [20]

According to Equation 2.8 even a small change in voltage causes a large change in reactive power. If the reactive power is plotted against the voltage it corresponds to an inverted parabola, the dependency on the reactance gives us that the smaller the reactance the steeper will the parabola be, this means that with a low reactance small changes in voltages causes very large changes to the reactive power. The relationship can be seen in Figure 2.2 together with the sinusoidal characteristics of . [20]

Power

Time

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Figure 2.2 Real power and reactive power plotted against the load angle and voltage [20]

In the three phase system the power is increased by a factor of √ as seen in the equations below.

[17]

Equation 2.9

Equation 2.10

2.1.2 Introduction to the Electrical Power System

The modern society requires energy for use in the industry, agriculture, commerce, transportation, communications, domestic households etc. The total energy required during one year is called total annual energy demand. About 85 % [21] of the total energy demand in the world is today supplied by fossil fuels like coal, oil, and natural gas^. A large part of these fuels contribute to the electric energy production. Today the world is switching from these fossil fuels and more electrical energy is produced by renewable sources like wind power, solar power, hydro power, biogas, bio energy and geothermal energy. One of the major reasons for the increase in renewable energy is the global warming. In the future it’s likely that the share of the energy market taken by renewables will increase to high levels and play a more dominant role on the design of electrical power systems. [20]

2.1.2.1 Structure of the Electrical Power System

The electrical power system can be divided into three different parts; generation, transmission and distribution.

The transmission network is normally the network with the highest voltage, from 300 kV and above.

Transmission networks have the highest transferring capacities and are mostly built as meshed networks to increase the security of the system. To the transmission network only very large electrical energy consumers and producers are connected. The transmission network can also be used as connecting lines to other systems for example tying different countries together. [20]

The sub transmission network is a part of the transmission network. It consists of a high or medium voltage network, with the voltage levels ranging between 100 kV to 300 kV. Unlike the transmission network the sub transmission network is built as a radial network or a weakly coupled network. To the sub transmission network medium producers and consumers can be connected. [20]

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Figure 2.3 Structure of an electrical power system [20]

Distribution networks are networks with medium voltages, in the range of 1 kV to 100 kV. The distribution network is often radial built networks. To the distribution network small generation and medium sized customers are connected. Wind power plants are often connected to the distribution network. The classification of the different parts of the system is not a strict classification and can vary depending on who is classifying it. [20]

2.1.2.2 Reliability of Supply

One of the most important features of the electrical power system is that electrical energy cannot easily be stored in large quantities. At any instant in time the energy demand has to be met by the corresponding electricity generation. Fortunately the combined load pattern is pretty predictable whilst individual loads may vary quite much. This predictable system demand can thus quite easily be planned allowing scheduling the daily generation to be controlled in a predetermined manor. [17]

The electrical system is designed to operate within certain operational limits governed by grid codes.

These operational limits ensure that you avoid major interruption of supply that can lead to life- threatening situations for the normal consumer, and for the industrial consumer may pose severe technical and production problems and thus loss of income. This is why high reliability of supply is of fundamental importance for the electrical system. High reliability can be ensured by: [17]

 High quality of installed elements

 The provision of reserve generation

 Employing large interconnected power systems capable of supplying each consumer via Alternative routes

 A high level of system security [17]

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2.1.2.3 Stability and Security of the Power System

The stability of the power system is defined as the ability of the power system to regain equilibrium after being subjected to a change. The most common changes that affect the stability of the system are the variables described in the chapter on Active and Reactive Power i.e. the nodal voltage magnitudes, which affect the reactive power, and the nodal load angles, connected with the active power. This gives us the new terms of power angle stability, and voltage stability. [17]

The security of the power system refers to the ability of the power system to survive certain contingencies without affecting the quality of electrical supply to the customers. The stability of the power grid is part of the security but the concept of security is wider and also deals with other issues.

The assessment of the power system can be divided into the SSA (Static Security Assessment) and the DSA (Dynamic Security Assessment). The DSA deals with the stability and quality of electrical supply during a change in the system where as the SSA only considers before and after scenario and assumes that there was no breach in stability along the way. [17]

It is in the interest of the TSO to perform the SSA in order to first evaluate the pre contingency state i.e. determine available transfer capability of transmission links and identify network congestions.

Secondly to evaluate the post contingency states i.e. verify the bus voltages and power flow limits.

Being responsible for the grid security the TSO needs to find ways of controlling the system so that it does not break down. Having no direct control over the generating units the only way to affect power outputs or control settings of the power plants are the grid codes or commercial agreements.

[17]

As stated above the DSA deals with problems regarding the system stability and quality of electrical supply, the analysis in this report strictly deals with SSA and will thus not describe the problems regarding the dynamic simulations. A short description of some of the problems that occur follows in the next chapter. [17]

2.1.2.4 Quality of the Electrical Supply

It is not just important that there is a high reliability to the system, there also has to be a high quality of the electrical supply. Electrical energy of high quality is provided by:

 Regulated and defined voltage levels with low fluctuations

 A regulated and defined value of the frequency with low fluctuations

 Low harmonic content

 Low content of transients and flicker

To ensure the quality of the electrical supply two basic methods can be used. Firstly the proper uses of automatic voltage control i.e. shunt elements, tap transformers, frequency control methods and AVR (Automatic Voltage Regulation) within the generating units. Secondly by employing large interconnected systems because larger systems are naturally affected by load variations as well as other disturbances. To ensure the quality of electrical supply the TSO set codes that the grid should operate within. A common standard is that the frequency should not deviate from the base value with more than ± 0,1 Hz and the nodal voltages should stay within ± 10 % of its normal value. These regulations vary depending on voltage level but also depending of fault scenario. [17]

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2.1.3 Components in the Electrical Power System

The most important components of the electrical power system are generating units, transformers, shunt elements and transmission lines. These are described below.

2.1.3.1 Generating Units

Generating units are the elements in the electrical power system that produces electrical energy.

There are several different types of generators with different properties. Examples of different generators are the synchronous generator and induction generator. The generators are converting kinetic energy into electrical energy. Electrical energy is produced by a generator driven by a kinetic energy source, often a turbine or diesel engine. The turbine is equipped with a turbine governor which controls either the speed or the power output according to a pre-set power-frequency characteristic. The generated power is then fed to the electrical power system. [17]

Traditionally the electrical power system has been operated with relatively few large power plants connected to the transmission network. These large plants are usually either thermal or hydro based.

Concerns about global warming and sustainability have increased the interest for renewable generation like thermal power plants which uses bio fuels, wind power and solar. This requires major changes in the electrical power system as the generation will increasingly be based on large amount of small producers often with the generation situated close to the energy source. Renewable energy has lower energy density than non-renewable energy sources and therefore the renewable power plants tend to be smaller, around hundreds of kilowatts to a few megawatts. Plants of this small size are often connected to the distribution level of the power system, rather than the transmission level because of the lower costs for the connection. These plants are called distributed generation. [17]

Wind turbines are a typical example of distributed generation power source. Wind turbines often use induction generators with either fixed speed or doubly fed generators to convert the power in wind into electrical energy. It is important to know that the rotating magnetic field in the induction machine is produced by a magnetizing current, whether it is operating as a generator or a motor. The magnetizing current is always supplied from an outside power source, often from the electrical power system. This means that the induction machine always consumes reactive power and therefore always must be connected to a power system that can provide the induction machine with reactive power for it to function properly. The reactive power can either be provided directly from the electrical power system or via reactive power compensation units installed together with the wind turbine. [17]

2.1.3.2 Transformers

Transformers are needed to connect parts of the power system with different voltage levels.

Generator step-up transformers are used when connecting generators to the grid. Tap transformers are used when there is a need for voltage regulation. Transformers can also be used for reduction of voltage to suit the low voltages needed by the consumers. This is done with distribution transformers. Connection of different parts of the electrical network with different voltage levels is done with transmission transformers. [20]

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Transformers are built up by a magnetic core with windings wrapped around the core. For two winding transformer there are two sets of windings and with the three winding transformer there are three sets of windings. The three winding transformer can thus transform one voltage level into two different to suit several needs at once. The relation between the phasor voltage and the number of turns at each winding is shown in Equation 2.11. [17]

Equation 2.11

Thus the change in number of turns for the windings will affect the voltage levels proportionally.

Transformers that can control voltage levels by changing the number of turns of the windings are known as tap changing transformers. The tap changers can operate ether as off load or on load. The off-load tap changers have a regulation rate of generally ± 5 % of voltage levels. The off load tap changers are operated manually and change is normally made to accommodate the seasons. The on- load tap changers have a general operational range of maximum ± 20 % of voltage levels and change is controlled by a regulator and can thus respond directly to disturbances such as a load change. A basic principle of a tap changer is shown in Figure 2.4 where the selectors S1 and S2 can move between the windings to cause small changes to the voltage. [20]

Figure 2.4 Showing the basic schematics of an on-load tap changer [20]

2.1.3.3 Shunt Elements

Due to the fact that reactive power causes losses and uses the capacity in electrical lines the optimal operation is reached if reactive power is compensated for close to the point of consumption and not produced at the generation sources far from the consumption. One way to compensate for the reactive power is with shunt compensation i.e. by installation of capacitors or inductors close to the point of interest. Shunt compensation can also be used to stabilize voltage levels and thus strengthening the stability of the electrical power system. [20]

Transmission lines are generally consuming reactive power but if the load is very low the production of reactive power can exceed the consumption. This may lead to very high reactive power levels which in turn may lead to very high voltage levels due to the strong correlation between reactive power and voltages seen in Equation 2.8. Compensation for this effect is generally done for lines longer than 200 km by installation of shunt reactors. In a loaded line, shunt capacitors may be used to produce reactive power and compensate for voltage drops, more commonly series capacitors are connected in series with the conductors to compensate for the reactive power consumed by the line.

[20]

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Shunt compensation can also be supplied by a synchronous motor or generator running at no load called synchronous compensation. Being rather expensive switched shunt capacitor banks and reactors are often used in addition to the synchronous compensation at substations. Small such compensators, of several MVA, are often used on the tertiary winding of transmission transformers while larger compensation, of up to hundreds MVA, are connected to by individual step-up transformers to high-voltage substations. [20]

2.1.3.4 Transmission Lines

There are both overhead and underground transmission lines though the overhead transmission lines are the most common. An overhead transmission line consists of three main components, conductors, insulators and support structures. Transmission lines often also have shield wires placed above the conductor to protect it from lightning.

2.1.3.4.1 Important Parameters

The design of the transmission line determines these parameters e.g. conductor type, the space between conductors and the size determines the series impedance and shunt admittance where the series impedance affects the ohmic losses, line-voltage drops and the stability limits. The shunt admittance, which is primarily capacitive, affects the line charging currents. The line charging currents are the currents which increases reactive power in the power system. In light loaded power systems shunt reactors often are installed to absorb this reactive power and thus reducing over voltages. [17]

A transmission line can be described with the equivalent seen in Figure 2.5 where R is the resistance, L is the inductance, G is the conductance and C is the capacitance.

Figure 2.5 Transmission line equivalent

2.1.3.4.2 Resistance in Transmission Lines

The DC resistance in the conductors depends on the length, cross sectional area and the conductivity of the conductor. The conductivity also depends on the temperature. The DC resistance is described below:

Equation 2.12

where is the conductivity at temperature T, is the length of the conductor and A is the cross sectional area. The conductivity depends on the material and common materials for conductors are copper and aluminium. Temperature and current magnitude also affect the resistance in conductors with AC current. The resistance is frequency dependent due to the “skin effect” which is the phenomenon that the current distribution tends to be denser at the surface of the conductor. This

14

causes a conductor loss, the effect only occurs with AC currents. The higher the frequency the higher is the real power losses due to the “skin effect”. losses is always bigger than losses [17].

| | Equation 2.13

2.1.3.4.3 Conductance in Transmission Lines

The conductance can be modelled as the shunt admittance in overhead lines. The conductance occurs because of the leaking currents due to the corona effect, damaged insulators and dirt, salt and other contaminants. The corona effect occurs when the electrical field strength at the conductor surface causes the surrounding air to ionize and thereby conduct. The losses from the conductance are much lower than the ohmic losses in the conductor, and are thus normally neglected. [17]

2.1.3.4.4 Inductance in Transmission Lines

The inductance in conductors comes from the current flowing in the transmission line.

Figure 2.6 The magnetic field H between two conductors

The inductance depends on the magnetic field intensity H, the magnetic flux density B, the flux linkages , and inductance from flux linkages per ampere as can be seen in Figure 2.6. [17]

2.1.3.4.5 Capacitance in Transmission Lines

An electric field is created between two conductors because of the difference in potential between the conductors, represented by ΔV in Figure 2.7.

Figure 2.7 Electric field E between two conductors

The capacitance is defined by the charge divided by the voltage . The charge is dependent on the electrical field and the flux. In an ideal solid cylindrical conductor the flux and electrical field is equal to the area integral of the electric field strength and the electric flux density over the surface area of the conductor. [17]

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2.1.4 Per-Unit System

Working with electrical systems with different voltages the per-unit system is often introduced.

Basically it reduces the risk of making calculation error when going from one voltage level to another.

If values are expressed in per-unit there can be a direct comparison from one side of a transformer to another. The expression for calculating the per-unit value is shown in Equation 2.14.

Equation 2.14

The resistance and reactance base values are calculated using the base value of the impedance and the base values for the conductance and susceptance is calculated with the base value for the admittance . The connection between the two base values can be seen in Equation 2.15. [17]

Equation 2.15

2.1.5 Equivalents in Electrical Power Systems

Electrical systems are generally very large with a lot of components, modelling this as a complete system including all components is often an impossible task if even a desired one. One method of creating an equivalent of parts in an electrical system is called model reduction methods. This method consists first of physical reductions, where suitable models for the system are chosen depending on how influential the system elements are to a disturbance. A component far from a disturbance is not as affected by a disturbance and can thus be modelled more simply. Secondly there is topological reduction where busses can be reduced to limit the size of the equivalent network and number of components in it.

The topological reduction can be achieved by many techniques using matrix operation. The reduction can be done with Gauss-Rutishauser elimination, also called Ward equivalent, which use the admittance matrix as a starting point, se 2.1.6.1 for how to create the bus admittance matrix.

Reduction can also be done looking at one specific bus, a typical such reduction is reduction of a centre bus in a star bus system creating a delta connected bus system. Equation 2.16 is describes the new admittance derived from old admittances in the system, k here describing the centre bus in the star system. [20]

Equation 2.16

The directly connected busses i.e. its neighbours will be affected in such a way that the admittance needs to be changed between these busses. Busses in the system not directly connected to the bus being removed will not be affected by the removal. With the star – delta equivalent, a change of impedance needs to be regarded in lines AB, AC and BC. [20]

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Figure 2.8 Busses connected in star and delta with line impedance Z [20]

In the case with the star connected bus Equation 2.16 can be written as seen in Equation 2.17. When taking into consideration that the admittance is the inverse of the impedance the equation can be rewritten as seen in Equation 2.18. [20]

Equation 2.17

Equation 2.18

Considering a circuit which consists of only three busses connected in serial Equation 2.18 is simplified and is expressed by Equation 2.19.

Equation 2.19

2.1.6 Static Modelling 2.1.6.1 Bus Based Equations

For computing the power flow in an electrical system it is necessary to compute voltage magnitudes and phase angles at each bus in the system. The input data for these calculations are the voltage magnitudes V, the load angle δ, the net real power P and the reactive power Q. Two of these parameters are always input data at each bus in the system and two are calculated by the power flow program. The bus categorization is as follows: [17]

 Swing bus, also known as slack bus

o The electrical model can only contain one swing bus being the reference bus for other busses in the system. Input data are the voltage and the load angle, normally as 1 p.u. and 0 . The swing bus is not a real bus. It is only a way to help model the system and perform numerical calculations.

 Load bus

o Normally the most common bus in a power system where P and Q are input data and V and δ are calculated.

 Voltage controlled bus, also known as generator bus

o Normally the bus to which a generator is connected. P and V are input data and Q and δ are calculated. With this bus there are also some extra input data, one can here also decide for example which interval a generator can operate between i.e.

QMAX and QMIN. A bus to which a tap-changing transformer is connected to should also be designed this bus type.

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Computer programs calculating power flows in electrical system use the bus admittance matrix which forms Equation 2.20 together with the voltage and current. The bus admittance matrix is built up on the diagonal by the sum of admittances connected to the specific bus in question and all off diagonal elements are the negative sum of all admittances between the specific bus and other busses in the system. [17]

Equation 2.20

Equation 2.20 is combined of the bus admittance matrix Y, the column vector of the bus voltages V and the vector of current sources I. The system admittance and the bus connections can be input data for the computations which result in the bus admittance vector. With the bus admittance vector and the current at each bus the bus voltage can be determined. [17]

For one line these calculations can be made manually but for a system with many components this builds up to complex matrix calculations best suited for computer computation. There are many different programs for computing power flow problems e.g. PSS/E, PSCAD, Power World Simulator, Aristo, etc. The solution type used to solve can also vary but the most common is the Newton- Raphson method. [17]

Since power flow bus data consist of the real and reactive power for load busses, and real power and voltages for generator busses. Equation 2.20 has to be rewritten while using Newton-Raphson methods of solving matrix equations, but it is still the base for the calculations. [17]

2.1.6.2 Line Approximations

Transmission lines characteristics can be modelled for calculations and depend on the length of the transmission line. A short transmission line, while having a 50 Hz system, shorter than 100 km can be represented as Figure 2.9 i.e. only with series resistance and inductance. The subscript S and R stands for the sending end and receiving end voltage and current and is the length of the line.

Figure 2.9 An equivalent circuit of a short transmission line

For a medium length transmission line the admittance, Y, cannot be neglected, and is represented by the admittance making the equivalent circuit change to a Π-circuit with the admittance connected in parallel with half at each end of the circuit, as seen in Figure 2.10. It is the same equivalent seen in Figure 2.5 but here with the admittance divided between the sending and receiving end. Medium- length lines ranges from 100 to 300 km.