Wind Farms Influence on Stability in an area with High Concentration of Hydropower Plants

Wind Farms Influence on Stability in an area with High Concentration of Hydropower Plants

Staffan Engström

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

Staffan Engström

The number of large-scale wind farms integrated to the power system in Sweden is increasing. Two generator concepts that are widely used are Doubly-Fed Induction Generators (DFIG) and Full Power Converters (FPC). The study is of a quantitative character and the aim of the Master thesis is to compare DFIG-models with FPC-models integrated in an area with high concentration of hydropower. Then it is possible to examine how the dynamics in the power system change depending on the selection of technology (DFIG or FPC) when connecting a wind farm. The power system is simulated during a summer night, i.e., a low load is connected. The Master thesis covers stability analysis of the power system by using rotor angle stability that are split into small-signal stability and transient stability (time-domain simulations) and finally voltage stability to see how the hydropower generators react when varying the power production in the wind farm.

The Master thesis concludes that independently of wind turbine technique, integration of a wind farm has slight impact on the stability in the power system compared to a power system without a wind farm, even though the load is low. Further, an integration of a wind farms affects the reactive power production in neighbouring hydropower plants. Finally, when increasing the size of the wind farm the

neighbouring hydropower station consume less reactive power which can induce problem with the voltage stability.

Sponsor: Vattenfall Vattenkraft AB ISSN: 1650-8300, UPTEC ES11 026

Examinator: Kjell Pernestål, Uppsala University Ämnesgranskare: Urban Lundin, Uppsala University

Handledare: Jonas Persson and Peter Olsson, Vattenfall Research and Development AB

år enligt Vattenfall AB [2]. Då ny produktionskapacitet i form av vindkraft ska anslutas till det nordiska elsystemet är det intressant att undersöka om den påverkar redan befintlig vattenkraftproduktion. I norra Sverige planerar man att markant bygga ut vindkraft på flera olika platser där Markbygden (2101 MW) är ett av projekten och Statkraft SCA Vind AB (1140 MW) är ett annat. Då en stor del av vattenkraftproduktionen finns i norra Sverige är det intressant att undersöka om den nya vindkraften kommer att påverka den redan befintliga vattenkraften som är en viktig del i det nordiska elsystemet. Både hur rotorvinkeln och hur nätets stabilitet förändras kommer att undersökas då en vindkraftpark i storleksordningen 200 MW ansluts till stamnätet, där koncentration av vattenkraft är hög. Genom att jämföra svängningen för rotorvinkeln i vattenkraftverket, den aktiva och den reaktiva effekten som produceras/konsumeras från vattenkraftverket då nätet kortsluts är det möjligt att undersöka om det finns någon skillnad i svängningen beroende på var vindkraftparken kopplas in på nätet. Med hjälp av linjäranalys av systemet kan egenvärdena beräknas för systemet och systemets stabilitet kan sedan analyseras. Egenvärdet består av en realdel och en imaginärdel. För att ett system ska vara stabilt behöver realdelen för alla egenvärdena vara negativa.

Föregående studier har visat att vindkraft både har och inte har en påverkan på nätets stabilitet beroende på teknik. Modellerna som använts i tidigare studier har varit förenklade. Därför kommer en mer avancerad modell av nätet användas i denna studie för att undersöka om tidigare resultat stämmer.

Vid byggnation av vindkraft kan flera tekniker utnyttjas. I detta examensarbete kommer de två vanligaste teknikerna på dagens (2009) vindkraftmarknad att användas, nämligen Doubly-Fed Induction Generator (DFIG) och Full Power Converter (FPC). De två generatormodellerna kan drivas med ett variabelt varvtal vilket möjliggör att vindturbinen kan optimeras till flera olika vindhastigheter jämfört med ett vindkraftverk som har konstant varvtal.

DFIG kan generera effekt via rotor och stator ut till nätet. Statorn är kopplad direkt till det anslutande nätet. Mellan rotorn och nätet finns en omriktare då rotorn kan rotera med olika hastigheter och kommer därför inte generera el med samma frekvens som nätet. Beroende på hur snabbt rotorn roterar kommer antigen effekt konsumeras eller genereras från rotorn. Ungefär 30 % av märkeffekten kan maximalt genereras från rotorn till nätet. Då en omriktare används innebär det att förlusterna ökar. FPC genererar bara effekt via statorn till nätet och all effekt passerar via en omriktare.

Detta medför att generatorn är ”isolerad” från nätet och kommer därför inte att delta i

Sveriges stamnät (400 kV), där transmissionsnätet och vattenkraftverk inkluderas.

Modellen beskriver en driftpunkt som ska vara jämförbar med låg last under en sommarnatt. Modellen beskriver också vattenkraftverkens individuella karakteristika såsom turbin, synkrongenerator, fältspänningsregulator (exciter), transformator, shuntar, regulatorer etc. Modellen av stamnätet byggs i elkraftsimuleringsprogrammet Simpow. Resultatet jämförs mot tidigare studier.

Från resultaten av linjäranalysen fås slutsatsen att stabiliteten försämras något då en vindkraftpark ansluts till nätet jämfört med då ingen vindkraftspark är ansluten. DFIG- tekniken försämrar stabiliteten något mer jämfört med FPC-tekniken. DFIG-tekniken har även samma påverkan på nätet oberoende var i nätet vindraftparken ansluts. För FPC-tekniken varierar stabiliteten mer beroende på var i nätet vindkraftsparken ansluts. Vidare, hur rotorvinkel m.m. i vattenkraftverket påverkas kunde med hjälp av transientstabilitet (tidsdomänsimuleringar) ett liknande mönster ses som i linjäranalysen. Beroende på var vindkraftparken ansluts konsumerade/producerade vattenkraftverket mer/mindre reaktiv effekt. Man kunde fastställa att resultatet ej beror på var DFIG ansluts men för FPC-tekniken varierar de beroende på var en FPC ansluts.

När lastvinkeln analyserades fås den högsta amplituden under den första svängningen då vindkraftparken är ansluten till Node1 och felet är i Node1. Detta gäller oberoende vilken teknik som används. Vidare är lastvinkelamplituden för DFIG högre under tredje svängningen jämfört med första svängningen. DFIG inför alltså dynamisk besvärliga egenskaper som kan påverka vattenkraftsgeneratorerna. För FPC minskar däremot amplituden för varje svängning.

Ytterligare en viktig slutsats som visas är att vattenkraftverket absorberar mindre reaktiv effekt då en vindkraftpark ansluts jämfört med fallet då ingen vindkraft är ansluten. Då den aktiva effekten producerad från vindkraftsparken ökar minskade den konsumerade reaktiva effekten i den närliggande vattenkraftgeneratorn. Inverkan från en vindkraftspark på vattenkraftverken skulle kunna bli ännu större för svagare nät.

Avslutningsvis, när en vindkraftspark med antingen DFIG- eller FPC-teknik ansluts till nätet har dynamiken försämras något och försämras något mer med DFIG än med FPC. Detta visas både genom linjäranalys och med simuleringar i tids-domänen. Om ytterligare studier skulle göras inom detta område skulle det vara intressant att använda modeller från leverantörer, då modellerna som använts i denna studie kanske

Engström [1].

1 INTRODUCTION 1

1.1 Background and motivation 1

1.2 Purpose of the project 2

1.3 Limitations 2

1.4 Previous work 2

2 THEORY 3

2.1 Variable speed wind turbine 3

2.1.1 Doubly-Fed Induction Generator Wind Turbine 5

2.1.2 Full Power Converter 6

2.1.3 Wind farm 8

2.2 Short-circuit theory 8

2.2.1 Characteristics of voltage sags 9

2.3 Power system stability 11

2.3.1 Rotor angle stability 11

2.3.1.1 Small-signal stability 12

2.3.1.2 Transient stability 13

2.3.2 Voltage stability 13

2.4 Regulations 13

2.4.1 The Swedish grid code 14

2.4.1.1 Tolerance against Stationary Disturbances 14

2.4.1.2 Voltage Control 16

2.4.1.3 Power Control 16

2.4.1.4 Communication and Controllability 16

2.4.1.5 Verification and Documentation 17

3 MODELS 17

3.1 Simpow Models 17

3.1.1 DFIG-Model 17

3.1.2 FPC-Model 19

3.1.3 Differences and similarities between the models 20

3.1.4 Hydropower models 21

3.2 Scaling-up the wind farm models in Simpow 21

3.2.1 Scaling the DC-capacitor in the FPC-model 22

3.2.2 Power factor 23

3.3 PSCAD/EMTDC Models 23

3.4 The grid model 24

5 RESULTS 29

5.1 Small-signal stability analysis 29

5.1.1 Analysis 31

5.2 Transient stability (Time-domain simulations) 31

5.2.1 Active power in Gen 1 31

5.2.1.1 Analysis 33

5.2.2 Reactive power in Gen 1 33

5.2.2.1 Analysis 35

5.2.3 Rotor angle in Gen 1 35

5.2.3.1 Analysis 37

5.2.4 The connection point for the wind farm is fixed at Node1 and the location of

the fault is varied 37

5.2.4.1 Analysis 40

5.3 Capability curve 40

5.4 Critical Fault Clearing Time 41

5.4.1 Analysis 42

5.5 Wind powers affect on reactive power production in neighbouring hydropower

plants 42

5.5.1 Analysis 43

6 CONCLUSION 43

7 DISCUSSION 44

8 FURTHER WORK 44

9 ACKNOWLEDGEMENTS 45

10 REFERENCES 46

APPENDIX pp

APPENDIX A

Aerodynamic performance for a wind turbine APPENDIX B

Summary of articles related to this report APPENDIX C

Active and reactive power for DFIG and FPC during fault

APPENDIX D

Wind Farms' Influence on Stability in an area with High Concentration of Hydropower

1

17

1

5

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1 Introduction

1.1 Background and motivation

The amount of wind power installations has increased considerably during the last years world wide. During the last years an increase of wind power connected to the Nordic grid has become reality. Therefore factors such as the stability and security of the power system operation must be considered when adding wind farms to the power system. Further, it is not longer likely to treat wind power as has been done traditionally, as a distributed small generation or small negative load. Wind turbines have been allowed to disconnect from the grid when a fault appeared in the power system, which is not the case today, see Svenska Kraftnät [3]. When a wind turbine disconnects the loss in generation is also considered which affect the grid stability, see Manwell [4].

However, wind power generation is required to maintain a certain reliability of supply and a certain level of stability. To meet the requirements mentioned above the Transmission System Operators (TSO) have grid codes that must be followed when connecting wind power, as well as all other power production units, to the power system. Wind power manufacturer’s have developed Fault Ride Through (FRT) functions in the wind turbines to meet the new requirements. On the market there are different concepts of wind turbines in terms of efficiency, economics, maintenance, technique, etc.

In the literature, studies have focused on detailed performance of generator’s instead of focusing on the behaviour of the power system when adding a wind farm. There are a limited numbers of studies in the literature that compare how the power system reacts when adding different wind power technologies. When studies have been performed, simplified models of the grid and the wind turbines have been used in a majority of the studies.

There are also a large number of on-going wind power projects in Sweden e.g.

Markbygden which plans to install 2101 MW wind power in northern Sweden [5] and Statkraft SCA Vind AB [6] plans to install 1140 MW in northern Sweden. Huge wind farms are connected directly to the Swedish transmission system. Therefore it is interesting to investigate if neighbouring hydropower plants become affected during faults on the grid. Also if the stability changes depending on which technique used in the wind farm would be an interesting approach, as well as to compare the result with the circumstances before the wind farm was installed.

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1.2 Purpose of the project

Two generator concepts that are widely used when building wind power today are the Doubly-Fed Induction Generators (DFIG) and Full Power Converters (FPC). Different wind turbine manufacturers use diverse concepts to meet the grid requirements from the TSOs which cause differences in the FRT performance as Dahlgren describes in [7].

By comparing a DFIG wind farm with a FPC wind farm when connecting to the national grid (400 kV) in an area with high concentration of hydropower in northern Sweden, it is possible to examine how the dynamics in the power system change depending on selection of technology (DFIG or FPC) in the wind farm. The Master’s Thesis compares models from one power system simulation software Simpow . The aim of the thesis is to estimate whether there are differences in the power system dynamics depending on selected wind power technology and if differences can be identified depending on the geographical distance from close-located hydropower stations when a detailed model of the power system is used. From the performed simulations the following parameters will be studied after a short circuit has been applied to the grid at different distances from a hydropower station:

- The eigenvalues of the system, to determine the stability.

- Rotor angle oscillations in the hydropower station.

- Active and reactive power oscillations in the hydropower station.

1.3 Limitations

- The power flow in the network model only represent a summer night.

- The grid model is limited to follow Lule älv and neighbouring hydropower plants. A model that describes the whole Swedish national grid is therefore not built. Instead an infinite bus behind a short circuit impedance is used to represent the excluded part of the Swedish national grid, 456.8 km from the studied area.

1.4 Previous work

Previous works that have been done in the area of this Master’s Thesis, i.e., how wind turbines affect the power system will here be presented. There is a limited number of articles that relate to how different branches of the power system react when connecting wind farms close to an area of hydropower stations or a weak part of the grid. However, three articles that have investigated the impact of wind power integrated to a small network are Slootweg [8], Fernàndez [9], and Hagstrøm [10] by using small-signal analysis. The articles use a simple grid model without generator

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regulators such as governors and exciters. Further, how the grid models were built differ between the articles which can be an explanation to why the results from the articles not are the same.

The conclusions that can be drawn from the articles are:

- Variable speed wind turbines have a limited impact on the stability on the grid, see Slootweg [8].

- A DFIG wind farm has limited impact of the stability on the grid, see Fernàndez [9].

- Integration of wind power has an influence of the stability. Both FPC and a DFIG decrease the damping, Hagstrøm [10].

The three articles give different conclusions. Two of the articles, [8] and [9], conclude that a limited impact is observed. Article [10] concludes that there is an impact on the power system when adding wind farms with either a DFIG or FPC generators.

Therefore, there is no common knowledge in the literature concerning this issue which shows the need for this project.

A more detailed presentation of previous work can be read in Appendix B where 37 articles related to this thesis are summarized.

2 Theory

A more detailed explanation of the two wind turbine configurations, DFIG and FPC, are presented here to understand the technical differences. Also a clarification of how the symmetrical fault theory and small-signal analysis is presented. Finally, a brief overview of the grid requirements from the Swedish TSO regarding connection of wind power to the grid in Sweden is given.

2.1 Variable speed wind turbine¹

In this Master’s thesis two variable speed wind turbine generators are compared. A variable speed wind turbine generator can operate at rated power at different wind speeds which is not possible for wind turbines with constant speed. To be able to operate at variable speed the supplied power by the generator need to be adjusted to keep the extracted frequency at a constant level. One way of solving the problem is by

1 This section has references to Perdana [11] due to the logic and comprehensible explanation of the two wind turbine concepts DFIG and FPC.

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the use of electrical converters that adjust the frequency and then feeds the grid side with voltage and current with correct grid frequency.

The power extraction from a wind turbine model can be calculated by the following equations (2.1), (2.2) and (2.3).

) , 2 (

1



_{2 3 p}

 

mech R v C

P  (2.1)

v



R



 (2.2)



mech m

T  P (2.3)

where Pmech stands for the produced mechanical power, ρ stand for the air density, R is the rotor radius, v is the wind speed, Cp describe the rotor performance of the wind turbine (a value between 0 and 1), β is the pitch angle and λ is the tip speed ratio which is defined by the rotational speed,



R, of the blade divided by the wind speed, see equation (2.2). When operating a variable wind speed turbine, most of the kinetic energy from the wind can be extracted by keeping the tip speed ratio at a constant level according to Betz-theorem, see Manwell [4], varying the rotor speed meanwhile the wind speed changes makes this possible. Thus, the tip speed ratio can be kept at a constant level which matches to the maximum power coefficient Cp because the power coefficient is dependent of the tip speed ratio. The power coefficient Cp defines the amount of power from the wind that can be converted in to mechanical power. By keeping Cp constant, the mechanical torque Tm can also be kept constant if thw wind speed change, see equation (2.3), see Manwell [4] and Ackermann [12]. For a graphical presentation see Appendix A.

Even though a variable speed wind turbine increases the aerodynamic efficiency, losses appear in the power converter. The losses are comparable to the gain in energy production compared to a fixed speed wind turbine. The main reason why a variable speed wind turbine is a good choice is instead explained by the reduction in fatigue damage on the turbine, see Ackermann [12]. A variable speed wind turbine can also control parameters such as the reactive power, voltage and power factor by the use of the power converter, see Lei [13].

Below, a more detailed description of the two wind turbine concepts (DFIG and FPC) is presented.

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2.1.1 Doubly-Fed Induction Generator Wind Turbine

The DFIG wind turbine concept was in 2008 the most common on the wind turbine market, see Perdana [11]. The concept is based on a wound rotor induction generator (asynchronous generator) but a difference is that a DFIG can supply voltage from both the stator and rotor when the rotational speed is above the synchronous speed, there-by the name “Doubly-Fed”. The stator operates synchronously with the grid but the rotor does not, to be able to operate outside the synchronous speed. This is applied to all asynchronous generators. The rotor is instead controlled by a power converter that connects the grid and the rotor. The power converter enables to vary the electromagnetic torque and the generator excitation which implies that a DFIG enables to operate at sub-synchronous speed (below the grid frequency) or super-synchronous speed (above the grid frequency).

Roughly, one third of the rated power can be supplied from the rotor to the grid when operating at rated power, but the span varies between manufacturer’s, see Manwell [4]. There is also a possibility to get a unity power factor for a DFIG wind turbine due to the power converter, see Gole [14]. When the rotor operates at sub-synchronous speed, the DFIG supply power from the stator and the rotor then consumes both active and reactive power. Further, when the rotor operates at super-synchronous speed, the DFIG supply active power from both the rotor and the stator, see Manwell [4].

The drive train in a DFIG is built up of a gear box so that the turbine has a low rotational speed and few pole pairs in the generator. The gear box is designed from the knowledge of the optimal rotational speed of the generator. The optimal generator speed is chosen by knowing the wind distribution and the size of the power converter for the site where the wind turbine should be built.

The stator and rotor are generally provided with isolated three-phase windings which enable to fit a rotor with either two or four poles. A common voltage supplied from the generator is 0.69 kV.

The power converter in a DFIG is smaller and less expensive compared to a FPC since all the power from the generator does not need to be supplied through the power converter which is shown in Figure 1, see Melicio [15]. The power converter has a rotor side and a grid side, and the two sides are controlled independently of each other.

The function for the rotor side of the power converter is to control the active and reactive power by using PWM-modulation (Pulse-width modulation). The function of the grid side of the converter is to adjust the reactive power that should be consumed or produced depending on the operation conditions. PWM-modulation is used also on the grid side. The converter in a DFIG consists mainly of a back-to-back converter, normally with an IGBT (Insulated gate bipolar transistor) in parallel with a diode, see Boulanger [16].

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Between the grid side and the rotor side of the converter a capacitor is positioned. The reason why the capacitor is used between the rectifier and the inverter is to make it possible to decouple the control of the two systems and if transients appear from the grid side. Secondly, the capacitor will help to magnetize the generator and to keep the connection with the grid and being synchronized with the grid frequency. The energy of the capacitor will be kept constant to satisfy the magnetisation demand from the generator.

Below in

Figure 1 a DFIG in detail is shown.

Figure 1 A detailed figure of a DFIG wind turbine with all its components, Perdana [11].

Between the grid and the grid side of the converter it is common that a crowbar is added to protect the rotor from over-currents and over-voltages. By short-circuiting the rotor-side of the converter via the crowbar it is possible to protect the rotor. When designing the size of the resistance in the crowbar it is taken into account that a high resistance protect from high current transients, but a high resistance can also cause high voltage transients. Therefore, the size of the crowbar resistance must be a compromise between the two factors.

2.1.2 Full Power Converter

A full power converter is the latest wind turbine concept on the market of today, see Perdana [11]. An FPC wind turbine has new features like a high resistance against faults on the grid and it can control whether reactive power should be supplied to or

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consumed from the grid. However, the advantages of an FPC are many but the advantages imply some disadvantages.

Electrical losses in the FPC-converter are higher compared to the losses in the DFIG- converter and the investment cost is also higher. But, the trend of the cost of an FPC is decreasing due to that the concept is becoming more established on the market.

The generator in an FPC wind turbine can either be a synchronous generator with or without a gearbox or an induction generator with a gearbox or with permanent magnets. In this study synchronous generators have been used with a gearbox due to that the used models have been designed that way. The synchronous generator excites its own fields. When comparing the different concepts for FPC, advantages such as lower investment costs, lower maintenance requirements and the robustness of the generator are benefits for a synchronous generator, see Ackermann [12].

The converter in the DFIG and the FPC are similar, but the connection of the converters to the grid differs. A wind turbine with FPC does not feed power directly to the grid from the stator as the DFIG does. Instead, all the power supplied needs to pass through the converter. This leads to that all parts of the generator are disconnected from the grid which is an advantage. If a fault occurs on the grid, the generator is less affected and if a fault occurs at the generator side of the converter the grid is less affected by voltage and current transients.

Below in Figure 2 an FPC in detail is shown.

Figure 2 A detailed picture of the FPC wind turbine with all its components, Perdana [11].

Page 8 (51) 2.1.3 Wind farm

When building a wind farm there are three different power electronic solutions that can be used according to Ackermann [12], to control the voltage:

1. A completely decentralized structure where each turbine has its own frequency converter and its own control system. An advantage is that each turbine then can operate at its optimum level. One example is Horns rev in Denmark.

2. A partly centralised structure of the wind farm when the voltage is rectified to a DC network and the whole farm is connected through a central inverter. An advantage with this concept is that it provides all the features of the variable speed concept since each turbine is controlled independently. This concept has not yet been implemented.

3. A completely centralised control structure which connect the wind farm to the grid. An advantage of the concept is that the internal behaviour is separated from the grid. A disadvantage is that all turbines need to rotate with the same average angular speed and therefore the wind turbines cannot operate at their optimal speed. It is better to use fixed speed turbines for this concept instead of variable speed turbines.

The first solution above will be used when performing the simulations due to the simplicity of the model. The internal grid for the wind farm is excluded. Instead an aggregated model of a wind farm is used represented by a single generator directly connected to the grid via a transformer, see Slootweg [8], Fernàndez [9], and Hagstrrøm [10].

2.2 Short-circuit theory

Basically, a short-circuit fault in a power system occur when one or more phases come in contact with each other or with ground. If the system was symmetric before the short-circuit happened, the system will also remain symmetric during the fault due to the symmetrical behaviour of the fault. When considering the grid code presented by the Swedish TSO Svenska Kraftnät, (SvK), only symmetrical three-phase faults are considered. Symmetrical faults causes the highest short-circuit currents in the grid which the system must be protected from. Further, the most common fault in the grid is unsymmetrical faults, see Manwell [4], Eliasson [17], Grainger[18]. Approximately, 70 % of the total amount of faults is unsymmetrical on the national grid, see Eliasson [17], Enquist [19].

The basics for symmetrical faults will be discussed below. Focus will be on the symmetrical fault due to that a more negative impact on the grid is achieved during a symmetrical fault compared to an unsymmetrical fault.

Page 9 (51) 2.2.1 Characteristics of voltage sags

A voltage sag or a voltage dip is a drop of the root-mean-square (RMS) voltage during a short period of some milliseconds up to minutes, see Enquist [19]. The International Electrotechnical Commission (IEC) defines a voltage sag by the following: “A temporary reduction of the voltage at a point in the electrical system below a threshold”. Different scenarios such as when a large motor start or a short circuit occurs on the grid can cause a voltage sag. There is no clear definition how a voltage sag should be defined regarding the magnitude and the period. There are different definitions given from both IEEE and the European Standard, EN 50160. IEEE and EN 50160 define a voltage sag as occurring during a period of 0.5 cycles to 60 seconds. But they differ when it comes to how the magnitude of the voltage sag should be defined. IEEE defined the magnitude for a voltage sag between 0.1 and 0.9 pu compared to the nominal voltage but EN 50160 define a voltage sag between 0.01 and 0.9 pu compared to the nominal voltage.

When a fault occur on the national grid a severe voltage dip at one, two or three phases can cause problem on the grid due to the propagation of the fault. A fault that propagates on the grid will decrease its magnitude as a result of the transmission lines and the transformers that is located between the fault position and the generators in the system. A fault on a parallel feeder results in a voltage drop on the substation that affects all the connected feeders until the fault is cleared, see Figure 3.

Figure 3 Description on how a voltage sag propagate through a grid depending on where in the grid the fault occur, Enquist [19].

The high fault currents during a fault create high voltage drops over the impedances close to the fault position. Therefore, generators will not be affected to the same extent

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if they are located far from the fault position. A typical characteristic for a fault is that the fault spread towards lower voltage levels which in turn will affect the customers connected to the grid. For example, when no generation is connected to lower voltage levels the voltage drop will propagate towards that area because there are no generators that can support the voltage.

A balanced voltage dip affects all the three phases e.g. a three-phase fault, see Figure 4.

Figure 4 A simulation of a three phase fault in PSCAD/EMTDC. The fault is applied at 1 sec and the duration of the fault is 0.1 sec.

The fault on the grid can be analysed through sequence components such as the voltage divider described in Figure 5 where the voltage in the Point of Common Coupling (PCC) is analysed during a three-phase fault.

Figure 5 A network describing how the grid reacts depending on how close to the PCC the fault is applied.

The impedance Zf in Figure 5 is large if the fault position is located far from the PCC and the fault position is located close to the PCC. The voltage source is a Thevenin-

U_Rms (t)

U

s

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equivalent with an impedance which describes the grid between the PCC and the ideal voltage source. A Thevenin- equivalent is a simplification of a circuit to be able to use fewer components. By calculating the magnitude of the voltage sag, Us, with equation (2.4) the impact of the position of the fault will be verified. But, the load current before and after the fault must be neglected and the voltage in the PCC before the fault is here set to 1 pu.

s f

f s

Z Z U Z

  (2.4)

This simple example shows that a voltage sag located close to the PCC will cause a severe voltage sag at PCC. But, a voltage sag that occur far away from the PCC will instead have a low impact of the voltage at the PCC.

In some situations the voltage will increase slowly after the fault has been recovered which is called post-fault dips, see Enquist [19]. The frequency of a generator will decrease due to that the torque of the generator is proportional to the square of the voltage. A small decrease in voltage will hardly affect the torque in a hydropower station and a wind farm with either DFIG or FPC technique. But if the voltage drop from 1 p.u. to 0 p.u. both the hydropower station and the wind farm is affected. After clearing the fault, the voltage increases which cause a deacceleration of the generators.

In the beginning will the generator draw a large current flow that will decay when the slip of the generator gets smaller. The post-fault dip can last for several seconds, see Enquist [19].

2.3 Power system stability

In order to simplify the analysis of stability problems, stability is further considered as:

- Rotor angle stability: Small-signal stability and Transient stability (Time- domain simulations)

- Voltage stability 2.3.1 Rotor angle stability

Rotor angle stability is the ability of a power system to ensure a stable operating equilibrium under steady-state conditions and being restored to an acceptable equilibrium after the system has been disturbed. When the number of wind farms in operation is increased a change in the system’s dynamic takes place. Insufficient synchronizing torque results in non-oscillatory instability whereas insufficient damping torque results in oscillatory instability. In order to simplify the analysis of stability problems, rotor angle stability is further considered as Small-signal stability and Transient stability, see Kundur [20].

Page 12 (51) 2.3.1.1 Small-signal stability

According to Kundur [20], small-signal stability is defined as the ability of the power system to maintain synchronism when subjected to small disturbances. The disturbance is regarded as small if the equations describing the system response can be linearized for the purpose of analysis. The small-signal stability problem normally occurs due to insufficient damping torque which results in rotor oscillations of increasing amplitude.

For small-signal stability analysis, the nonlinear equations of the dynamic power system are first linearized around a specific operating point when operating under steady state. The linearization is made with help from Taylor’s series expansion and only first-order terms are included. The resulting set of linear differential equations describes the dynamic behaviour of the power system subjected to a small disturbance around the chosen operating point.

The equations are transformed to the frequency domain with Laplace transform and the eigenvalues are calculated. The eigenvalues identify important information about the system reaction to small perturbations and thus characterize the stability of the system. The eigenvalues represent the conditions for the stability of the power system.

The time-dependent characteristic of a mode corresponding to an eigenvalue, λ=σ+jω, is given by e^λt. A real and positive eigenvalues, σ>0 and ω=0, determines an exponentially increasing behaviour while a negative real eigenvalues, σ<0 and ω=0, represents a decaying mode. A complex eigenvalue with positive real part, σ>0 and ω0, results in an increasing oscillatory behaviour and a negative real part, σ<0 and ω0, results in damped oscillation. The real part of the eigenvalue gives the damping and the imaginary part gives the frequency of oscillation. The frequency of oscillation (f) and damping ratio (ζ) of a complex eigenvalue (λ=σ+jω) can be represented as described in the equations (2.5) and (2.6).





 2

f (2.5)

2 2

 

 

 

 ^(2.6)

The damping ratio (ζ) determines the rate of decay of the amplitude of the oscillation.

The effect of the system parameters on the overall system dynamics can be examined by evaluating the sensitivity of the eigenvalues with respect to variations in system parameters.

In large power systems, the small-signal stability problem can be either local or global in nature. Power system oscillations are usually in the range between 0.1 and 2 Hz

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depending on the number of generators involved. Local oscillations lie in the upper part of the range and consist of the oscillation of a single generator or a group of generators against the rest of the system. Stability (damping) of these oscillations depends on the strength of the transmission system as seen by the power plant, generator excitation control systems and plant output. In contrast inter-area oscillations are in the lower part of the frequency range and comprise the oscillations among groups of generators. Load characteristics, in particular, have a major effect on the stability of inter-area modes, see Vittal [21].

The variable speed generator design consisting of power converter conveys dominant effect on dynamic performance of the generator. The dynamic characteristics of variable speed wind turbines are completely governed by the power electronic converter. The converter decouples the turbine from the grid by not only controlling the rotor speed and electrical power, but also damping out any rotor-speed oscillations that may occur within the wind turbine generator, see Vittal [21]

2.3.1.2 Transient stability

Transient stability is the capability of a power system to maintain synchronism when subjected to a severe disturbance. The severe network disturbances include equipment outages, load changes or faults that result in large changes of generator rotor angles.

The resulting system response is influenced by the nonlinear power angle relationship.

Transient stability depends on both the initial operating state of the system and the severity of the disturbance. Instability is usually due to insufficient synchronizing torque and results in a periodic angular separation. The time frame of interest in transient stability studies is usually 2 to 5 seconds after the power system has been disturbed. But, the duration of the oscillation may extend up to 10-20 seconds for a very large system, see Vittal 21].

2.3.2 Voltage stability

Voltage stability is the ability of a power system to maintain steady within acceptable voltages at all nodes under normal operating conditions and after being subjected to a disturbance. The main factor causing instability is the inability to meet the demand for reactive power, see Vittal [21].

2.4 Regulations

When integrating wind farms to the national grid some aspects need to be taken into account. The Swedish TSO has provided guidelines that describe which requirements wind farms need to meet to be able to connect to the grid. A wind farm needs to meet requirements regarding capabilities to remain connected to the grid due to a fault that causes a voltage sag.

Page 14 (51) 2.4.1 The Swedish grid code

Depending on the size of the wind production unit the Swedish TSO has different regulations that need to be followed called grid code when connecting to the 220 kV grid, 400 kV grid or connecting to neighbouring countries described in [3]. The Swedish TSO defines the size of wind farms as following:

- A large wind farm has the total installed power >100 MW

- A medium sized wind farm has the total installed power between 25 – 100 MW

- A small wind farm has the total installed power between 1.5 – 25 MW

In the grid code a wind farm is defined as a wind turbine with associated equipment such as the internal grid and transformers that is used to link the wind turbine to a group of wind turbines.

Most focus will here be put on large wind farms when describing the grid code. When introducing a wind farm to the grid the owner has the responsibility to investigate and consider the following:

- Tolerance against Stationary Disturbances - Voltage Control

- Power Control

- Communication and Controllability - Verification and Documentation The five items will be discussed below.

2.4.1.1 Tolerance against Stationary Disturbances

A wind farm needs to supply a certain amount of power to the grid for different stationary variations of the voltage and the grid frequency, see Table 1.

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Table 1 Requirements that a medium and a large sized wind farm needs to meet to get permission to connect to the network, see SvK [3].

Independently of the magnitude of the frequency, a medium and a large wind farm need to supply voltage to the network. If the frequency deviates from 50 Hz a reduction in delivered power is needed and depending on the magnitude of the frequency the operational time deviates between the different operational cases.

However, a wind farm should be able to keep the connection to the grid during a variation in voltage in one or more phases or a transient fault such as lightning strikes or operation of circuit breakers. The recommendations by the Swedish TSO state that a wind farm should remain connected down to 0 % of the nominal voltage during 0.25 seconds. The voltage sag is followed by a jump in voltage to 25 % of the nominal voltage and then a linear increase in voltage during 0.5 seconds up to 90 % of the nominal voltage which the system then remain at. For a graphical representation, see Figure 6. The voltage profile describes a failed disconnection of a short circuit fault.

The slow rise of voltage after 0.25 seconds is due to the magnetization of the induction generator that needs reactive power and the lower voltage level after the fault depend on a weaker grid because some transmission lines probably have become decoupled, see Larsson [22].

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Figure 6 The grid code from the Swedish TSO that a large wind farm needs to meet to be able to be connected to the national grid, see SvK [3].

2.4.1.2 Voltage Control

Large wind farms when the installed power is above 100 MW should be provided with an automatic voltage controller and the voltage should be adjustable between at least +/- 5 % of the nominal voltage of the wind farm. Moreover, the control system that adjusts the reactive power in the wind farm should be able to direct the reactive power towards 0 Mvar if desired.

2.4.1.3 Power Control

A wind turbine in a wind farm should have the possibility to independently stop to supply power to the grid. Further, when the wind speed is too high all wind turbines should not be disconnected at once. Instead, not more than 30 MW/min should be disconnected. The same limitation is used when a wind farm should start up. At most 30 MW/min could be connected to the grid at once. The supplied active power should be able to be controled in order to not exceed the rated power. Further should the possibility exist to control the power by an external signal and change the power algorithm during operation. Finally should the ability exist to limit the supplied power from rated power to 20 % of the rated power within 5 seconds.

2.4.1.4 Communication and Controllability

A wind farm should be equipped in such a way that the Swedish TSO should be able to get online information regarding voltage, controllability, operation status, active, and reactive power. Further, the wind farm must be equipped in such a way that within 15 minutes after a disruption it is possible to control the wind farm manually. The manual control device manages to connect to the grid, disconnect from the grid and to control the active and reactive power by changing the set point.

Page 17 (51) 2.4.1.5 Verification and Documentation

A wind farms ability to fulfill the requirements described above needs to be verified by full scale tests, simulations or technical calculations. Documentation of the wind farm needs to be accessible for the Swedish TSO and if changes are made within the documentation it needs to be reported.

3 Models

In the upcoming section a description is given of how the wind turbine models are configured and how the grid model was approximated in northern Sweden. The power system simulation tool Simpow was used. Simpow perform simulations in the time- domain and under steady-state conditions (using phase-vectors). Simpow has models that are implemented and describe different electrical components e.g. transformers, wind turbines, generators, transmission lines etc. There are many models that describe the same components, some models need much input-data and other less. The user can choose the level of detail for the model, depending on how a large amount input-data that is possible to get. All the models need input-data to be able to describe a component and approximations can be made if data is missing. To be able to perform calculations in the dime-domain an implicit predictor-corrector method of integration for simultaneous solution of all algebraic and differential equations is employed. The output variables from the simulation can either be power, voltage, current, frequency or other electrical or mechanical variables. The output variables are shown in graphs or as a set of data that can be plotted in another program.

3.1 Simpow Models

The main objective of the models built in Simpow is to perform system analysis of power flow and electromechanical transients. The models of DFIG and FPC wind turbines in Simpow are valid for both constant and variable wind speeds and both models are limited to the fundamental frequency components of voltage and current.

The electrical state in the AC-system is assumed to be sinusoidal in the used mode of simulation (Transta). The object for both the models is to investigate the impact of wind power generation in an area with high concentration of hydropower and give an accurate description of the interaction between the wind farm and the hydropower stations. The wind turbine models include both the mechanical part and the electrical part of a wind turbine.

3.1.1 DFIG-Model

The DFIG-model that is implemented in Simpow is shown in Figure 7 and for an overall over view of the DFIG concept see Figure 1. The model uses a wound rotor induction generator (asynchronous generator). Between the rotor and the grid a power converter is connected. The power converter consists of a rectifier, an intermediate

Page 18 (51)

DC-system and an inverter with a voltage of 0.69 kV at the grid side of the converter.

The stator is directly connected to the grid with a frequency of 50 Hz and a voltage of 0.69 kV.

Figure 7 Block diagram of the DFIG-model in Simpow, see Simpow [23].

First, there is a block that converts the kinetic energy into rotational energy at the generator which includes the pitch control system, speed control system, and the wind turbine that is approximated with a one-mass model. The wind turbine needs the speed of the wind and the pitch angle to be able to calculate the torque (TM), see equations (2.1), (2.2) and (2.3). To be able to calculate the pitch angle, tables that describe how Cp and the tip speed ratio are related to each other for different pitch angles is added to the model. A crowbar block is also added in order to protect the rotor from over/under voltages. In Perdana [11] a recommendation is to set the span for the voltage between 0.9 and 1.12 p.u. Regarding the control parameters, default values were used for the regulators in the DFIG-model.

Page 19 (51) 3.1.2 FPC-Model

The FPC-model implemented in Simpow is shown in Figure 8 and for an overall over view of the FPC concept see Figure 2. The generator is a synchronous generator which is connected to the generator-side of the converter (the PWM-rectifier) and the grid- side of the converter (the PWM-inverter). In between there is a DC-capacitor that acts as a small energy storage, to keep the voltage variation small. The size of the DC- capacitor depends on the rated power of the synchronous generator, see section 3.2.1.

The main task of the frequency converter is to control the active rotor power in such a way that the rotation speed of the generator is following the wind speed in the most effective way. The voltage provided by the generator is set to 0.69 kV, the DC-voltage is set to 2 kV and the grid side voltage is set to 0.69 kV. The DC-voltage (2 kV) is higher compared to the AC-voltage (0.69 kV) because the DC-voltage describe a single phase and the AC-voltage describe the peak value for all three-phases.

As for the DFIG-model there is a block that converts kinetic energy into rotational energy which also includes a pitch control system, speed control system, and the wind turbine that is approximated with a one-mass model. The PWM-converter model can be designed by the user which means that the losses and the size of the converter can be changed. The size of the converter is set to the rated power of the turbine and the losses are set to 2% of the rated power for each converter, according to Perdana [11].

Regarding the control parameters, default values were used for the regulators in the FPC-model.

The AC-voltage control system control the reactive power production/consumption of the PWM-converter. By calculating the imaginary current order from the two input parameters, the AC-voltage reference and the AC-bus voltage, it is possible to control the reactive power flow.

Page 20 (51)

Figure 8 Block diagram of the FPC-model in Simpow, see Simpow [23].

3.1.3 Differences and similarities between the models

There are many similarities between the two models. Both models uses:

- Speed control - Pitch control - AC-voltage control

- A one-mass model of the wind turbine The two main differences between the models are:

- The size of the DC-capacitor cannot be chosen in the DFIG-model but can be chosen in the FPC- model.

- Crowbar control is used in the DFIG-model but is not used in the FPC-model.

Page 21 (51) 3.1.4 Hydropower models

Hydropower plants included in the Simpow- model are built to reflect how they behave in reality. Parameters that describe the characteristics of each hydropower plant are therefore individual for each hydropower generator. To be able to build an accurate model of a hydropower station an exciter, a generator, a governor, a stabilizer, a transformer and a turbine need to be included in the model, for description see below.

- Exciter: Regulate the excitation of the synchronous generator.

- Generators: Synchronous generators.

- Governor: Provide the electrical field voltage from the terminal voltage.

- Stabilizer: Provide an input signal to the regulator to be able to damp power system oscillations.

- Transformer: Step voltage levels up and down.

- Turbine: Induce the mechanical torque.

3.2 Scaling-up the wind farm models in Simpow

To be able to model a wind farm, the rated power for the generators need to be scaled up, the default rated power for the models was set to 2.05 MVA. When deciding the size of the wind farm, Lillgrund (110 MVA) [16], was used as a reference due to that Lillgrund is one of the largest wind farms built in Sweden today. Further, by almost doubling the size of Lillgrund a size of 200 MVA is obtained which would be regarded as a larger wind farm, see section 2.4.1. An aggregated model was assumed which mean that one single generator is used to represent a wind farm due to simplifying the modelling code, see Slotweg [8], Fernàndez [9], and Hagstrøm [10].

Depending on the aim of the study it is possible to use an aggregated model of a wind farm. In this case when the power system is studied, it is possible to consider an aggregated model of a wind turbine. Further, if the aim is to examine the behaviour of the network within the wind farm, it is not convenient to use an aggregated model.

Parameters such the rated power of the frequency converters, rated power for the generators, and rated power for the wind turbine need to be changed. Also the active power supplied from the turbine need to be scaled-up. An assumption was made that the nominal active power production by the wind turbine supplied to the grid, was set to 150 MW.

The loss in the FPC-model is higher compared to the DFIG-model. Therefore the production from the synchronous generator in the FPC was set to 158 MW due to losses that correspond to 8 MW so that both the DFIG and the FPC supplied the same amount of power to the grid. The higher amount of losses in the FPC is due to that all the power goes through both the rectifier and the inverter which has considerable

Page 22 (51)

amount of losses. In the DFIG only about a third of the power goes through the converter and the inverter.

3.2.1 Scaling the DC-capacitor in the FPC-model

Conversely, when the size of the generator increases, the size of the DC-capacitor also needs to be increased. In the DFIG-model it is not possible to set the size, but for the FPC-model it is possible.

First, the DC-voltage level must be chosen so the modulation index, MI, is within the range 0-1, see equation (3.1).



DC Phase AC

U MI U

2

 , (3.1)

UAC, Phase stands for the phase AC-voltage produced by the generator and UDC stands for the nominal DC-voltage for the capacitor. Using equation (3.2) UAC, Phase is calculated.

, ,

,

[ ] 3

0.69 0.4

3

AC LN AC Phase

AC Phase

U U kV

U kV kV

 

 

(3.2)

then, UDC was chosen to 2 kV and the modulation index become, MI=0.31.

The size of the DC-capacitor is calculated with equation (3.3),

] 2 [

2

CU J

E  ^DC (3.3)

and by re-writing equation (3.3) we get an expression for the DC-capacitor C. Below the relation E=PDCT was used, see equation (3.4).

] 2 [

2

2

2 F

U T P U

C E

DC DC DC



 (3.4)

where

C is the DC-capacitance in Farad [F].

E is the energy stored in the DC-capacitor in Joule [J].

PDC is the nominal DC power in Watt [W].

T is the time constant in Seconds [s].

UDC is the nominal DC voltage in Voltage [V].

Page 23 (51)

If the time constant T is assumed to be 10 ms, see Simpow [23], the size of the DC- capacitor calculated, see equation (3.5)



^{21010 10}



^{10 1 [ ]}

200 2

3 2

3 6

F

C 









  ^ (3.5)

3.2.2 Power factor

Both the DFIG and the FPC wind turbine operate according to an active power/wind speed curve which contains of three parts namely constant rotational speed at low wind speed, constant Cp and constant maximum power at high wind speeds, see Appendix A. When the wind speed change the power also change, due to that the power is proportional to the cube of the wind speed, see equation (2.1). To be able to control this behaviour a speed control is implemented in the model. A speed reference (w – wref) for the turbine is calculated from the actual real power production, see equation (3.6).

0 1

2

2P AP A

A w

w _ref  _eg  _eg  (3.6)

where

Peg is the actual power production in p.u.

A0, A1 and A2 are coefficients.

How the calculations of the coefficients are performed can be seen in the Simpow manual [23] page. 1239-1241. Values for the coefficients of the power curve is presented in Table 2.

Table 2 Coefficients that describe the power curve.

A0 A1 A2

0.4039 1.018 0.4428 3.3 PSCAD/EMTDC Models

Before the start of the Thesis it was said that PSCAD/EMTDC should be included to verify the model built in Simpow. Two models, one DFIG-model, see Gole [14] and one FPC-model, see Boulanger [16] were chosen to represent the wind farms in the grid in a PSCAD/EMTDC-model. The DFIG-model was scaled up to 50 MW by help from the PSCAD-support. The FPC-model did not however behave correct; instead of supply power the model consumed power. An attempt was made to debug the model.

The conclusion that was made proposes that there is something wrong with the converter and the control of the converter. A rather brief explanation of how the converter was built made it difficult to identify the problem in the FPC-model.

Page 24 (51)

Therefore, the attempt to build a DFIG and FPC wind farm in PSCAD/EMTDC was abandoned due to the lack of functional models.

3.4 The grid model

A model built in the software PSS/E² of the hole Swedish national grid that illustrate a summer night with low load was used when approximating the grid-model. The grid includes:

- Transmission lines which are approximated with PI-equivalents see Figure 9. A PI-equivalent describes length, resistance (R), reactance (X) and susceptance (B) of a transmission line.

- Shunt impedances.

- Constant loads was added to some buses were transmission lines was cut in order to describe the power flow in the original PSS/E model as accurate as possible.

- Hydropower plants which is built up by exciters, governors, stabilizers, synchronous generators and turbines.

- Transformers.

Figure 9 Picture of a PI-equivalent that describe the resistance (R), the reactance (X) and the susceptance (B).

From the PSS/E-model a 400 kV-grid was approximated following the river Lule älv in northern Sweden, see Figure 10. A map of the National grid from the Swedish TSO was used when approximating the grid model. Both series and parallel nodes need to be included in the model in order to get an accurate power flow. The reason behind that is because the voltage is straight proportional to the power and a simulation of a too simplified model will give an unlikely result, see PSCAD [24]. To be able to perform the simulation in Simpow the code that described the model was transferred from PSS/E to Simpow. All the exciters could not be modelled in Simpow with the standard library of exciters, therefore some of them needed to be coded in the graphical editor DSL Code Generator of Simpow. In the model three different voltage

2 Power System Simulation tool for Engineers

Page 25 (51)

levels were used 0.69 kV within the wind farm, 15 kV from the hydropower stations and 400 kV at the national grid.

Figure 10 The grid that was used when simulating how wind power affects hydropower. There are nineteen hydropower generators with transformers, one wind farm with a transformer and one infinite bus included in the network. The indexation in the figure is used below.

An important aspect when modelling the grid following Lule älv is to find a point of an equivalent of the rest of the system. At the point Node 6 a fictional bus is added and an ideal voltage source (an infinite bus) is connected. The infinite bus is positioned behind a short-circuit impedance (R and X) to simulate the remaining nodes of the national grid that not is included in the grid model, see Lenasson [25] and Wall [26]. By the use of the electromagnetic simulation tool PSS/E it was possible to calculate the short-circuit impedance. Only one fictional bus with an ideal voltage source was used, otherwise there will be problem with the load angles in the grid model, Olsson [27]. The point where the infinite bus was added in Node 6, has a reasonable large distance to the studied area.

3.4.1 Simplifications in the model

A PI-model cannot accurately represent the frequency dependent parameters of a line (such as skin effects). But the described effects are not important for this project and can therefore be ignored, see PSCAD [28]. Further, no cables have been used when

Page 26 (51)

connecting the wind turbines, this implies that the distance between the connection point and the wind turbine is zero meters. Another assumption dealt with the rated voltage for the hydropower stations. In the PSS/E-file the rated voltage was not mentioned. Instead, the rated voltage was assumed to be 15 kV for all hydropower stations.

3.5 Model verification

The model has been verified with a load-flow analysis to identify if the grid model built in Simpow equals the model in PSS/E. The active power production is set to fix values in the load flow calculation in Simpow and therefore the same power flow will be simulated in both software. But, the reactive power that flows in/out to the network from the synchronous generators is variable, see Table 3.

Table 3 The reactive power flow in the Simpow and the PSS/E-model and its deviation between the two software.

Reactive power flow [Mvar]

Synchronous generators Simpow-model PSS/E-model Deviation³

Node1, Gen 1 -74.5 -71.3 -3.2 (4.6%)

Node14, Gen 2 -6.6 -5.4 -1.2 (22.2%)

Node14, Gen 3 -6.6 -5.4 -1.2 (22.2%)

Node14, Gen 4 -6.6 -5.4 -1.2 (22.2%)

Node13, Gen 5 -8.2 -8.3 0.1 (1.2%)

Node13, Gen 6 -8.2 -8.3 0.1 (1.2%)

Node13, Gen 7 -8.2 -8.3 0.1 (1.2%)

Node12, Gen 8 -14.4 -14.3 -0.1 (0.7%)

Node12, Gen 9 -14.4 -14.3 -0.1 (0.7%)

Node12, Gen 10 -14.4 -14.3 0.1 (0.7%)

Node8, Gen 11 -52.0 -26.4 25.6 (97.0%)

Node7, Gen 12 -32.1 -32.1 0 (0.0%)

Node10, Gen 13 17.9 18.0 -0.1 (0.6%)

Node10, Gen 14 18.3 18.6 -0.3 (1.6%)

Node5, Gen 15 48.8 40.5 8.3 (20.5%)

Node5, Gen 16 47.9 55.5 -7.6 (13.7%)

Node2, Gen 17 -22.4 -20.9 -1.5 (7.1%)

Node2, Gen 18 -22.4 -20.9 -1.5 (7.1%)

Node2, Gen 19 -22.0 -20.9 -1.1 (5.2)

The difference in reactive power flow between the models almost equals each other except for the stations named Node8, Gen 3; Node5, Gen 1 and Gen 2; and Node14,

3 The deviation in percent was calculated by dividing the deviation with the absolute value from the PSS/E-model