emt validation of fault-ride- through capabilities of …

Jiawei Liu， s080893

EMT VALIDATION OF FAULT-RIDE-THROUGH CAPABILITIES OF WIND TURBINES INDUCTION GENERATORS WITH FULL-RATING CONVERTER

Master 's Thesis, September 2010

2

EMT VALIDATION OF FAULT-RIDE-THROUGH CAPABILITIES OF WIND TUR-BINES INDUCTION GENERATORS WITH FULL-RATING CONVERTER,

Author : Jiawei Liu， s080893 Supervisor(s): Assistant professer, Rodrigo Garcia-Valle, DTU Phd student, Ivan Arana Aristi, Dong Energy Phd student, Ranjan Sharma, Siemens Wind Power

Department of Electrical Engineering Centre for Electric Technology (CET) Technical University of Denmark Elektrovej 325 DK-2800 Kgs. Lyngby Denmark www.elektro.dtu.dk/cet Tel: (+45) 45 25 35 00 Fax: (+45) 45 88 61 11 E-mail: [email protected]

Release date:

30 September 2010

Class:

1 (public)

Edition:

1. Edition

Comments:

This report is a part of the requirements to achieve Master of Science in Engineering (MSc) at Technical University of Den-mark. The report represents 30 ECTS points.

Rights:

© Jiawei Liu, 2010

3

ABSTRACT

This report is prepared as part of the requirements to achieve the Master of Science in Electrical Engineering at Technical University of Denmark. In this thesis project, transients that occur due to switching operation of large offshore wind farms are investigated. Issues concerning modeling of the wind turbines induction generators with full-rating converter for electro-magnetic transient studies are discussed. Measurements with switching transients in Burbo offshore wind farm are provided by the wind farm owner Dong Energy to carry out this project. The measuring system used in Burbo wind farm is introduced briefly in this report. Analysis and calculation to the measurements are done in this project. The measurements are also used to validate the wind turbine model built in this work. The turbines installed in Burbo are 3.6MW Siemens STW-3.6-107 wind turbine, which are equipped with induction generator and full-rating converter. The type of induction generator wind turbine with full converter is studied in this work. The study focuses on the converter system in the wind turbine and its control out of the consideration that the converter stands a good chance of contributing to the switching transients. Vector con-trol for the converter system is introduced and the tuning methods for the controller are also mentioned. A simplified model of full converter wind turbine is presented in this work which can be used to carry out transient study without losing accuracy. The simplified model is im-plemented in PSCAD and Burbo wind farm model is built based on the simplified model. Switching simulation is taken to the wind farm model and switching transients can be obtained. The transients get from the simulation are compared with the meas-urements in order to validate the wind turbine model. Sensitivity analysis is performed to test the effect of components and parameters in the model on the switching transients

5

ACKNOWLEDGEMENT

My thesis would not have been possible without the support of many people. I wish to express my gratitude to those who, during the past several months, contribute their in-sight, guidance and encouragement to help me complete the thesis project. First, I would like to thank Ivan for introducing me the project in the field of full con-verter wind turbine modeling for switching transients study. Throughout my thesis, Ivan provides invaluable guidance on how to carry out the project. Without his help, I could not complete the project with such efficiency, not mention to pick up so much important knowledge that will also be valuable for my future career. Additionally, many thanks go to my supervisor Rodrigo in my Master project for his constant help. Through our regular discussions, we exchange important ideas which this project and my final thesis report have greatly benefited from. Besides, I would like to express my sincere gratitude to my industrial supervisor Ranjan, for the valuable guidance and advice he gave me. For many times, Ranjan helps me out of the bottle neck problems and inspires me to debug and validate the wind turbine model. Finally, an honorable mention goes to my friends in DTU for their supports on me in completing this project. Without the support, strength and help from people mentioned above, I would not solve the many difficulties while doing this project.

7

TABLE OF CONTENT

1 Introduction ........................................................................................................... 15

1.1 Background ....................................................................................................... 16

1.2 Problem formulation ......................................................................................... 16

1.3 Method and limitations ..................................................................................... 17

1.4 Work by others ................................................................................................. 18

1.5 Reading Guide .................................................................................................. 19

2 Measurments at Burbo Offshore Wind Farm .................................................... 21 2.1 Burbo Offshore Wind Farm .............................................................................. 21

2.2 Measurements ................................................................................................... 24

2.3 Analysis of Voltage and Current Measurements .............................................. 29

2.4 Conclusion ........................................................................................................ 36

3 Full Power Converter Wind Turbine With Induction Generator ................... 38

3.1 Introduction ....................................................................................................... 38

3.2 System Configuration of FCWT with IG ......................................................... 40

3.3 Aerodynamics and Pitch Angle Control ........................................................... 42

3.4 Induction Generator Model ............................................................................... 43

3.5 Full-Scale Frequency Converter Configuration ................................................ 44

3.6 Full-scale Frequency Converter Control........................................................... 49

3.7 Simplified Model of FCWT for Transients Study ............................................ 60

3.8 Conclusion ........................................................................................................ 61

4 Simulation and Validation ................................................................................... 63 4.1 Simplified Models of FCWT for transient study in PSCAD ............................ 64

4.2 Burbo Wind Farm Model and Switching Operation ......................................... 81

4.3 Sensitive Analysis of the Model ....................................................................... 87

4.4 Conclusion ........................................................................................................ 94

5 Conclusion and Implication ................................................................................. 95

5.1 Conclusion ........................................................................................................ 95

5.2 Implication for future development .................................................................. 97

References ...................................................................................................................... 99

A User built models in PSCAD .................................................................................. 102

9

LIST OF FIGURES

Figure 2-1: Siemens SWT-3.6-107 wind turbine calculated power curve. ................... 22

Figure 2-2: The Layout of Burbo Bank Offshore Wind Farm....................................... 23

Figure 2-3: The measurement locations in Burbo Offshore Wind Farm ....................... 24

Figure 2-4: measurement points in the wind turbine, adopted from ............................. 25

Figure 2-5: Current Measurements 0.0s - 1.2s ............................................................. 26

Figure 2-6: Current Measurements 0.0s - 0.1s ............................................................. 27

Figure 2-7: Voltage Measurements 0.0 s – 1.2 s .......................................................... 28

Figure 2-8: Voltage Measurements 0.0 s – 0.1 s .......................................................... 29

Figure 2-9: Power calculation results for BB22 ........................................................... 31

Figure 2-10: Power calculation results for BB38 ......................................................... 32

Figure 2-11: Power calculation results for Radial ........................................................ 33

Figure 2-12: FFT Analysis for BB22 currents within the first cycle after switch off ............................................................................................................... 34

Figure 2-13: FFT Analysis for BB38 currents within the first cycle after switch off ............................................................................................................... 35

Figure 2-14: FFT Analysis for the voltages within the first cycle after switch off .......................................................................................................................... 36

Figure 3-1: Scheme of a fixed speed concept with SCIG ............................................. 39

Figure 3-2: Scheme of OptiSlip concept with Wound rotor IG.................................... 39

Figure 3-3: Scheme of DFIG concept ............................................................................ 39

Figure 3-4: Scheme of FCWT concept with SCIG ........................................................ 40

Figure 3-5: Variable speed FCWT with induction generator configuration ................. 42

Figure 3-6: Full-scale power converter in FCWT ......................................................... 44

Figure 3-7: Simplified representation of induction generator with full converter in steady state computation ................................................................... 45

Figure 3-8: Active power and reactive power flow in the converter connected to the IG. ................................................................................................................ 46

List of figures

10

Figure 3-9: The optimized relation between the generator electric frequency and the wind turbine power output. ....................................................................... 47

Figure 3-10: grid-side converter schematic .................................................................... 49

Figure 3-11: structure of IMC ........................................................................................ 50

Figure 3-12: structure of IMC with active damping ...................................................... 51

Figure 3-13: Grid-side converter control diagram ......................................................... 52

Figure 3-14: Structure of the current controller ............................................................. 53

Figure 3-15: SPWM generation procedure .................................................................... 56

Figure 3-16: Principle of SPWM generation SPWM generation …….……….………60

Figure 3-17: Generator-side converter control diagram ................................................. 58

Figure 3-18: Simplified models for FCWT. .................................................................. 61

Figure 4-1: Simplified PSCAD model for BB22 ........................................................... 64

Figure 4-2: Single phase grid-side converter circuit…………………………………. .66

Figure 4-3: Phasor diagram for determining the maximum inductance of 𝐿𝑓…………67

Figure 4-4: Illustration diagram of the first step in vector control ................................. 67

Figure 4-5: Phase angle calculation in PSCAD ............................................................. 67

Figure 4-6: Phase angle found by calculation ................................................................ 68

Figure 4-7: PLL parameters setup .................................................................................. 68

Figure 4-8: Phase angle found by PLL........................................................................... 69

Figure 4-9: Park transformation in PSCAD ................................................................... 69

Figure 4-10: Illustration diagram of the second step in vector control .......................... 70

Figure 4-11: DC-link voltage regulator in PSCAD ........................................................ 70

Figure 4-12: DC-link voltage simulation results in PSCAD .......................................... 71

Figure 4-13: Grid voltage regulator in PSCAD ............................................................. 71

Figure 4-14: Current regulator in PSCAD ..................................................................... 72

Figure 4-15: Simulation results of id and iq in PSCAD ................................................. 73

Figure 4-16: Illustration diagram of the first step in vector control ............................... 74

Figure 4-17: Inverse Park transformation in PSCAD .................................................... 74

Figure 4-18: Illustration diagram of the firth step in vector control .............................. 74

Figure 4-19: SPWM Modulation block in PSCAD ........................................................ 75

Figure 4-20: Firing pulse pattern generated in PSCAD ................................................. 75

Figure 4-21: Simple system built for steady state simulation of BB22 in PSCAD ................................................................................................................... 76

Figure 4-22: Steady state currents of BB22 in PSCAD ................................................. 76

Figure 4-23: Steady state voltages of BB22 in PSCAD ................................................. 76

List of figures

11

Figure 4-24: Steady state power output of BB22 in PSCAD ........................................ 77

Figure 4-25: Simplified PSCAD model for BB38 ......................................................... 78

Figure 4-26: Current control of id and iq for BB38 ...................................................... 79

Figure 4-27: DC-link voltage control for BB38 ............................................................ 79

Figure 4-28: Simple system built for steady state simulation of BB38 in PSCAD……81

Figure 4-29: Steady state currents of BB38 in PSCAD ................................................. 80

Figure 4-30: Steady state voltages of BB38 in PSCAD ................................................ 81

Figure 4-31: Steady state power outputs of BB38 in PSCAD ....................................... 81

Figure 4-32: Simplified wind farm model of Burbo in PSCAD .................................... 83

Figure 4-33: Simulation Results of Switching operation in PSCAD. ........................... 85

Figure 4-34: Simulation results of switching operation for WT model with 63 uH filter in PSCAD. .............................................................................................. 89

Figure 4-35: Simulation results of switching operation for WT model with grid voltage regulator in PSCAD…………………………………………………………………….94

13

LIST OF ABBREVIATIONS

Abbreviation Meaning

p.u. Per unit

TSO Transmission System Operator

FFT Fast Fourier Transform

WT Wind Turbine

FCWT Full Converter Wind Turbine

IG Induction Generator

SCIG Squirrel-Cage Induction Generator

DFIG Doubly Fed Induction Generator

DC Direct Current

AC Alternating Current

SPWM Sinusoid Pulse Width Modulation

IMC Internal Model Control

BB22 (38...) Burbo wind turbine No. 22 (38…)

PSCAD PSCAD/HVDC

RMS Root Mean Square

15

1 INTRODUCTION

Because of energy shortage and environmental concerns, the renewable energy, espe-cially the wind energy, has drawn much more attention recently. At the end of 2009, worldwide name-plate of wind-powered generators was 159.2 gigawats . Energy pro-duction was 340 TWh, which is about 2% of worldwide electricity usage [1]. The UK is perusing the development of renewable electricity generating system in re-sponse to concerns regarding emissions from fossil fuel based electricity generators. In 2007 the UK Government agreed to an overall European Union target of generating 20% of EU’s energy supply from renewable sources by 2020. The government's overall tar-get is to get at least 33 GW of wind power capacity installed by 2020. Until the January of 2010, the installed capacity of wind power in the UK is over 4 GW, which is the second largest source of renewable energy in the UK. Due to the space shortage on land and better wind energy resource, more offshore wind farms are under construction. Compared to onshore wind farm, offshore wind power has several key advantages. Wind is typically stronger and more stable at sea, resulting in significantly higher production per unit installed. Wind turbines can also be bigger than on land because it is easier to transport very large turbine components by sea. By 2020, 40 GW of offshore wind capacity will be reached in the EU, targeted by European Wind Energy Association [2]. UK has ample offshore wind resource, it is estimated to have one third of total offshore wind resource of Europe, and it is a leading country in offshore wind power. Currently it has 1,041 MW of operational nameplate capacity, with a further 1,452 MW under construction [3]. The development of UK offshore wind power progressed in three rounds. The first round started negotiation in 1998, 18 applications were granted permission to proceed in 2001, including UK first large scale offshore wind farm North Hoyle (2003), Scroby Sands (2004), Kentish Flats (2005) and Barrow Offshore (2006). Based on the lessons learned from the first round, the second round starts in December 2003, with 15 projects with a combined capacity of 7.2 GW announced to proceed. By far the largest of these are the 1 GW London Array and the 1.2 GW Triton Knoll. The third round was

Master Thesis Report

16

launched in 2008, the scale of the third round is much bigger with total capacity 25 GW, as the combination of the first and second round capacity is 8 GW.

1.1 Background As the offshore wind power penetration into the grid is increasing quickly, the influence of offshore wind farm on power quality is becoming an important issue, and interest to fully understand and quantify the impact of this development on the performance of the interconnected system has also grown. Unlike the onshore individual wind units which are only required to maintain the power factor range at the connection point, the off-shore wind farm must take more responsibility such as low voltage fault ride through capability, voltage support following gird faults, and provide voltage and frequency control. Otherwise the breakdown of the offshore wind farm may cause serious result such as breakdown of whole power system and large blackout. The large offshore wind farms connected to the transmission network are subject to the Grid Specifications regulated by the Transmission System Operator (TSO). The Nation-al Grid Code [4], for instance, is the grid specifications for TSO and other players to comply with in UK, which is designed to permit the development, maintenance and operation of an efficient, co-ordinate and economical system for the transmission of electricity, to facilitate competition in the generation and supply of electricity and to promote the security and efficiency of the power system as a whole. The offshore wind farm connected to the transmission grid need to fulfill the minimum technical, design and operational criteria specifying in the grid code. Most TSOs now require that wind farms must tolerate system disturbances. For instance, wind farms must not trip during faults and other system disturbances, and wind farms must remain connected to the system following disturbances. In other words, to provide necessary support to the system once disturbances are cleared. In addition, TSOs require that in normal operation wind farm should be capable of regulating voltage or reactive power to maintain a smooth voltage profile at the point of interconnection, protecting against voltage flicker caused by wind gusts, and even performing power curtailment, if system has superfluous generation in off-peak load mode. System security issues associated to the integration of wind power have been mostly important for the TSO. Much effort have been taken to develop requirements and me-thods that makes wind turbines able to withstand critical system events, which eventual-ly could lead to dynamic, transient or voltage instability of the system. High-frequency, high-voltage transients are suspected to have contributed to failures in offshore Wind farms. The current state of wind turbines and wind farm facilities used for offshore in-stallations fulfill the TSO requirements related to system security.

1.2 Problem formulation The offshore wind power features large investment and high maintenance. The need for accurate simulations is major for offshore wind farms as consequences of faults are more severe in terms of repair cost and lost revenue than on land wind farm. The TSO


17

and wind farm owners require dynamic wind turbine models to evaluate the fault-ride-through performance and to carry out assessment for the dynamic wind turbine impact on the power system stability. A good simulation model can help predict and evaluate the faults, as well as improve the stability of the system. In 2007 field measurements were done in Burbo Bank offshore wind farm, where three GPS synchronized measurements were built and used for simultaneous measurements at three different locations in the wind farm. The purpose of the measuring system is to record high frequency transients in the large offshore wind farm. Transients from switching of circuit breaker and fault situations in the collection grid can result in break-ing down of components. Simulations with reliable measurements performed in a real large wind farm can improve the accuracy of models and give more reliable results. Several switching transients were generated and recorded, but only the disconnection of the line breaker for the middle radial in the collection field is covered in this work. The project is on the basis of the measurements of radial switch operation and answers the following questions:

• What information can be extracted from the measurements? What do the mea-surements imply about how the wind turbines react against the switch operation?

• How does the wind turbine with induction generator and full converter work? How does the control work inside the turbine? What determines the dynamic be-havior of this kind of turbine?

• What information is needed to simulate the switch transients in Burbo? • How complicated should the model be for the transient studies? Which parts of

the turbine are necessarily involved in the model and which parts can be ignored? • How good can the simulation model predict the transients in PSCAD?

1.3 Method and limitations The applied specification for dynamic wind turbine models, which designed for tran-sients study and short term stability studies, can be outlined [5],

• Only the grid relevant components and control are represented using a common standardized model core. This will give sufficient and realistic evaluation of power system stability and fault-ride through capability of wind turbine. At the same time, it reduces the model implementation efforts, improve numerical ro-bustness of the wind turbine model and the entire network system model.

• The wind turbine is a RMS based positive-sequence model due to comply with the common standards and complexity of the applied transmission power-grid model.


18

• Since positive-sequence equivalents of the transmission power grids are applied , the system stability investigations are carried out for balanced grid events

• Credibility of the wind turbine model is proved by validation test. Based on the specifications for the dynamic model introduced above, an simplified model is proposed and used in this thesis. The model is validated by the measurements recorded in Burbo offshore wind farm. The grid information for modeling Burbo offshore wind farm is provided by Dong Energy, which includes the details of the cables, transformers and fixed capacitor banks used in the wind farm. However, no real data are used for parameterizing the wind tur-bine model because of confidentiality agreements with various manufacturers. Instead, typical parameters have been used for all components.

1.4 Work by others Transients in collection grids of offshore wind farm have aroused wide concern and many investigations and researches about this issue have been done. Sørensen per-formed the switching transients study for Nysted offshore wind farm in [6], he used three different cable models to simulate the switching transients with DIgSILENT and compared the results with the measurements. He concluded that the distributed parame-ter model of the cable is more accurate for the transients study. Liljestrand et al. [7] stu-died switching transients in large wind farm based on simulations with PSCAD. Issues concerning modeling of components have been discussed in his work; it is shown by the simulation results that the wave propagation has a crucial impact on magnitude and time derivatives of transient overvoltage. Abdulahovic simulated the energization of a wind park radial with PSCAD in [8], the phenomena of cable energization and transformer magnetization are discussed in this work. The current project uses the lumped parameter model of the cable, a switch for the cir-cuit breaker and standard PSCAD three-phase transformer model for the transformers, because it is focused on the discussion of the impact of power converter on switching transients in this project. A dynamic simulation model for the Siemens SWT-3.6-107 wind turbine was developed by Siemens Wind Power; the model was implemented in PowerFactory and validated with certified fault ride through tests. [5] describes the performed tests and shows the model validation results. The NetConverter system provides grid voltage support during the two different voltage dips and fault durations.


19

Some details of full load converter connected IG are described in the works [9,10,11]. In [9] emphatically describes a generic model for this type of turbine. The details of the model including the generator model, shaft system model, rotor and pitch control and converter control are introduced in this paper. Fault-ride-through tests were done with this model and the author concluded that the fault-ride-through capability of such wind turbines may be improved by the use of specific converter control, combined with pitch control. In [10] the design and performance comparisons of the full-size converters ap-plied for wind turbines have been carried out. It describes the design of modulation me-thod of the converter, the DC link design of the converter and the design of the LC filter respectively. Marta [11] presents the vector control of the full-rated power converter. The control of generator-side converter and grid-side converter are analyzed respective-ly and voltage sag response of the converter is test experimentally. Markus et al. in [12, 13] proposed an simplified model of full converter wind turbine for dynamic analysis. The simulation results of this model are compared to those obtained with the detailed models. Markus concluded that the simplified model provides ade-quate accuracy for transient and dynamic analysis.

1.5 Reading Guide There are totally five chapters in this thesis. The first chapter is an introduction about the project background, why it is important to have a switching transient model for the offshore wind farm, which methods are used to model the wind turbines and wind farm, and the assumptions and limitations of the me-thods. In the second chapter, the details of the Burbo offshore wind farm are given in the first section. The details are about the wind turbines employed in the wind farm and the wind farm itself. The measuring system used in the measurement campaign in Burbo Off-shore Wind farm is introduced in the second section. The measurements with the switching transients are also presented in this section. In the last section of this chapter, power calculation and FFT analysis are done to the measurements and the results are plotted. The third chapter focuses on studying the structure and control of the full power conver-ter wind turbine with induction generator. The system configuration of the full converter wind turbine is introduced in 3.2. In section 3.3 the induction generator model is dis-cussed shortly. It is given a brief introduction about the aerodynamics and pitch control of the wind turbine in 3.4. In section 3.5 it is focused on the configuration of the full


20

converter, the characteristics of the generator-side converter, DC-link and grid-side converter are also discussed respectfully in this section. The full converter is controlled utilizing vector control, which is introduced in 3.6, the details about the vector control can be found in this section. At last in section 3.7, a simplified model for full converter wind turbine is presented. The simplified model can be used in transient study without losing accuracy. In the fourth chapter, the models of the wind turbines and the Burbo wind farm are built in PSCAD. In the first section simplified models are built for both wind turbines BB22 and BB38, the models are tested in steady state operation. In the second section, the model of Burbo wind farm is built based on the wind turbine models built in the first section. The switching operation is carried out and the transients from the simulation results are compared with the measurements. In the third section, sensitivity analysis is done on the purpose of finding how the components and parameters of the wind turbine model affect the switching transients. At last, in the fifth chapter, the conclusions are drawn and the implication for the future work is given.

21

2 MEASURMENTS AT BURBO OFFSHORE WIND FARM

As mentioned in Chapter 1 that the credibility of the wind turbine model need to be proved by validation test, however the credibility of the validation test is based on the accuracy of the measurements recorded in the real power system. On the basis of the usage of the model, corresponding applicable measurements are chosen for the purpose of validation, and different measuring tests in the real field were conducted. The traditional methods of measuring wind turbine performance are under laboratory conditions in ideal circumstances, the results always tend to be optimistic and rarely reflect how the turbine actually behaves in real situation. The real performance will be affected by many factors, for example, the wind conditions, power demand profiles, nearby obstructions, wear and tear of the turbine and a range of other factors. Some of the factors are not easy to be predicted and they may be the critical factors that affect the performance of wind turbine. What is more important is that how the turbine actual-ly reacts and delivers power on site can be certain without proper measurement data. In this chapter, a brief introduction of Burbo offshore wind farm is given in 2.1, the measuring activity and the measuring system is presented in 2.2, after that in 2.3 the measurement data is calculated and analyzed, the information derived from the calcula-tion and the conclusions are then conducted in 2.4.

2.1 Burbo Offshore Wind Farm The Burbo Bank Offshore Wind Farm comprises twenty five Siemens SWT-3.6-107 wind turbines and is situated on the Burbo Flats in Liverpool Bay at the entrance to the River Mersey, approximately 6.4km from the Sefton coastline and 7.2km from North Wirral. The location was selected after a careful process of environmental screening. The Burbo wind farm is fully owned by DONG Energy and its commissioning began from 2007 [14].


22

Each wind turbine in the wind farm is designed to run for approximately 6000 hours each year over 20 years. With a total production capacity of 90 MW, the 25 wind tur-bines will be able to produce 315 million kWh annually, which is equivalent to the year-ly consumption of 80,000 households.

2.1.1 Rotor and Blade Details

The rotor of the SWT-3.6-107 turbine is a three-blade cantilevered construction, mounted upwind of the tower. The power output is controlled by pitch regulation. The rotor speed is variable in order to maximize the aerodynamic efficiency and the speed compliance during power regulation minimizes the dynamic loads on the transmission system. It cuts-in at 3-5 m/s increasing power output linearly until rated wind speed at 13-14 m/s where the power is kept constant until cut-out at 25 m/s. The power curve of SWT-3.6-107 WT is presented in Fig. 2-1 [15].

Figure 2-1: Siemens SWT-3.6-107 wind turbine calculated power curve [15]

The blades are made of fiberglass-reinforced epoxy resin and are manufactured by Sie-mens. No glue joints between spars and shells, no weak points, no easy access for water or lightning. The aerodynamic design of the blades represents state-of-the-art wind tur-bine technology, and the blades have been thoroughly tested at Siemens' test site under both static and dynamic loadings. The blades are mounted on pitch bearings and can be feathered 80 degrees for shutdown purposes. Each blade has its own independent fail-safe pitching mechanism capable of feathering the blade under any operating condition, and allowing fine-tuning to maximize power output [16].


23

2.1.2 Generator Details The SWT-3.6-107 wind turbine utilizes a squirrel cage induction generator connected to the grid via a full rated power converter. The generator is rated at 3.6 MW, the syn-chronous speed of the generator is 1500 rpm, the nominal output voltage is 690 V. The full rated power converter allows the generator works in vary speed. The generator rotor construction and stator windings are specially designed for high efficiency at partial loads. The generator is fitted with a separate thermostat-controlled ventilation arrangement, and by ensuring a very efficient cooling, the generator can be operated at temperatures well below the normal level of the standard insulation class, thereby providing the best possible lifetime of the winding insulation.

2.1.3 Site Details The WTs are connected in ‘rows’ with 36kV three-core AC submarine cable. Figure 2-2 shows the layout of the WF. Electric cables buried under the seabed connect the wind turbines to the land. Onshore, these cables travel a further 3.5km underground, follow-ing existing roads, to a substation at Wallasey. This substation steps up the electricity from internal wind farm voltage 33kV to 132kV so that it can be fed into the national electricity grid.

Figure 2-2: The Layout of Burbo Bank Offshore Wind Farm

The 132 kV and 33 kV networks comprise sections of underground cable or overhead lines or combinations of each. The cables and overhead lines in the network can create


24

harmonic resonances dependent on the system configuration characterized by the sys-tem impedance.

2.2 Measurements The measurement campaign in Burbo Offshore Wind farm took place from the end of November to the beginning of December 2007. Several switching transients were gen-erated and recorded during the measurement campaign in Burbo in 2007, but only the transients caused by opening the line breaker of the middle radial are covered in this work.

2.2.1 Measuring System Used In Burbo The measurements were carried out with a PC equipped with National Instruments data acquisition card, running by a program developed in LabVIEW programming environ-ment. There are six measurement channels in total, three voltages and three currents. The maximum sampling rate is 2.5 MHz with a resolution of 14bit [17]. The measurements used in this work were recorded simultaneously at three different locations in the collection grid in Burbo. The measuring points can be seen in Figure 2-3 and were located at:

• The radial station after the circuit breaker in the middle radial • The wind turbine BB22, the first turbine of the middle radial • The wind turbine BB38, the last turbine of the middle radial

Figure 2-3: The measurement locations in Burbo Offshore Wind Farm

The synchronization is based on the GPS timing device where one pulse per second and a 10MHz clock signal are available together with a time stamp via serial interface. The precision of the synchronization is better than or equal to one sample e.g. 400 ns.


25

In the wind turbine BB22 and BB38, the measuring equipment was placed between the MV switchgear and the high voltage side of the transformer, as shown in Figure 2-4.

Figure 2-4: measurement points in the wind turbine, adopted from [8]

2.2.2 Measurement Data The currents recorded at the three measurement locations are plotted for duration of 1.2 s in Figure 2-5. The top plot is the current at the radial station from 0 s to 1.2 s, the mid-dle plot is the current at the BB22 during that same period and the bottom is the current plot for BB38 during that period.


26

Figure 2-5: Current Measurements 0.0s - 1.2s

From the top plot in Figure 2-5, it can be seen that the currents at the radial station drop to zero just when the line breaker opens. In the middle plot, the current output of BB22 is zero before the switching operation. It means BB22 was not generating, in other words, it was in idle state. But as soon as the line breaker opens, the transient currents emerge in the three phases. The transient currents last about 200 ms before attenuating to zero. In the bottom plot, a similar phenomenon happens for BB38. Practically the system for BB22 and BB38 are same, the only difference is that BB38 was generating before the line breaker opens. Transient currents can also be seen in the three phases until they decay to zero after around 200 ms. In Figure 2-6, the currents measurements are plotted for duration of 100 ms. The top plot is the current at the radial station from 0 s to 100 ms, the middle plot is the current at the BB22 during that same period and the bottom is the current plot for BB38 during that period. It gives a better view of what happens at the time of line breaker opening. From the radial current it can be seen the switching operation happens at 0.036 s, when the cur-rent of phase A turns into zero. Besides, the shapes of the transient currents of BB22 and BB38 can be seen in the middle and bottom plots. In the following section, the tran-


27

sient current during the first cycle after line breaker opening will be analyzed for both BB22 and BB38.

Figure 2-6: Current Measurements 0.0s - 0.1s

The voltages recorded at the three measurement locations are plotted for duration of 1.2 s in Figure 2-7. The top plot is the current at the radial station from 0 s to 1.2 s, the mid-dle plot is the voltage at the BB22 during that same period and the bottom is the voltage plot for BB38 during that period.


28

Figure 2-7: Voltage Measurements 0.0 s – 1.2 s

The transient voltage overshoots can be observed at the time of switching off at all the three locations. The voltages fade to zero after about 600 ms after the line breaker is open. Besides, the frequencies of the voltages at each location decrease from 50 Hz to zero along with the decaying of the amplitude. In Figure 2-8 the voltage measurements are plotted within 100 ms, it shows that the transient voltages with high frequency harmonics emerge during the first cycle after line breaker is open. After that cycle the harmonics disappear and the voltages start fading. As the transients and voltage overshoot happen within the first cycle after line breaker is open, how the wind turbines and the power grid react against the switching operation within this 20 ms is the most interesting issue and is the supreme goal for the model in this work to simulate. In the following section, the voltage transients in the first cycle will be analyzed.


29

Figure 2-8: Voltage Measurements 0.0 s – 0.1 s

2.3 Analysis of Voltage and Current Measurements By doing the analysis of the measurements, much useful information can be obtained about the wind turbine and the power grid. In this section, power calculation and FFT analysis are done to the measurements. The calculation results are also important para-meters to compare the measurements and the results from the simulation.

2.3.1 Power Calculation There are many industrial applications that require the knowledge of the instantaneous value of the active and reactive power. The instantaneous active and reactive powers are also used in the control of converters connected to the electric network. These conver-ters can control the flow of active and reactive power in the power system to improve voltage regulation, and increasing transient stability margin. In this work, an instantaneous power calculation method employed in the 𝛼𝛽 frame is applied. The application of Clark (α-β) transformation to balanced three phase system in order to calculate the instantaneous active and reactive power is a useful tool for study and analysis of electrical systems. The Clark transformation converts the grid in-formation from the abc frame into the 𝛼𝛽 frame. The matrix for transformation is given by [18]


30

�𝑥𝛼(𝑡)𝑥𝛽(𝑡)� = 2

3�1 −1

2− 1

2

0 √32

− √32

� . �𝑥𝑎(𝑡)𝑥𝑏(𝑡)𝑥𝑐(𝑡)

� (2-1)

The instantaneous active p(t) and reactive power q(t) can be calculated from the space vector given below

�𝑝(𝑡)𝑞(𝑡)� = 3

2�𝑒𝛼(𝑡) 𝑒𝛽(𝑡)−𝑒𝛽(𝑡) 𝑒𝛼(𝑡)� . �

𝑖𝛼(𝑡)𝑖𝛽(𝑡)� (2-2)

Because the measuring system contains 3 channels for measuring the current and 3 channels for measuring the voltage, each channel connects one phase of the output of current or voltage. Before doing the instantaneous power calculation, the measurements need to be verified so that the same channel in the three measuring places connects the same phase of current or voltage. Otherwise, the calculation results would be wrong. In this work, the output voltage at the three measuring points should be in phase. As the measurements of the same voltage channel in each of the three measuring places are already in phase with each other, so we don’t need to change the sequence of voltage measurement. However, the current measurement sequence can’t be verified easily through observation. After testing all the 6 combinations of the sequence of the three phase current, the correct sequence can be found which gives a reasonable instantaneous power output. The instantaneous active and reactive power calculated by using equation (2-1) and (2-2) for BB22 are plotted in Figure 2-9. The power output for both active power and reactive power are zero before 0.04 s because BB22 is in idle state before line breaker is open. Within the first cycle after the switch off, BB22 has positive reactive power output and majority part of negative active power output. In Figure 2-10 and Figure 2-11 show the power calculation results for BB38 and the Radial using the same method as BB22. From Figure 2-10, it can be learned that the instantaneous active power of BB38 oscillates around the average value of 1.7 MW and the instantaneous reactive power oscillates around the average value of 0 MVAr before disconnection of the line breaker. However, within the first cycle after 0.04 s, BB38 has majority part of positive active power output and majority part of negative reactive power output. In Figure 2-11, the instantaneous active power of the radial oscillates around the aver-age value of 6MW. The whole radial supplies 6MW to the grid before it is disconnected. The instantaneous reactive power of the radial oscillates around the average value of -2MVAr. The whole radial consumes 2MVAr reactive power from the grid before it is disconnected. After it is disconnected, both the active and reactive power drop to zero.


31

(a)

(b)

Figure 2-9: Power calculation results for BB22 (a) Active power (b) Reactive power


32

(a)

(b)

Figure 2-10: Power calculation results for BB38 (a) Active power (b) Reactive power


33

(a)

(b) Figure 2-11: Power calculation results for Radial (a) Active power (b) Reactive power


34

2.3.2 FFT Analysis As mentioned in the previous sections, the transients during the first cycle after the line breaker disconnection are most interesting in this work, which are plotted in Figure 2-6. By doing the FFT analysis for the currents and voltages during this period, the frequen-cy characteristics can be found for the transients. Figure 2-12 shows that the fundamental frequency of the BB22 currents within the first cycle after switch off is around 50Hz, the dominating harmonics are from 200 Hz to 400 Hz in the three phases.

Figure 2-12: FFT Analysis for BB22 currents within the first cycle after switch off

Figure 2-13 shows the results of FFT analysis for BB38 currents within the first cycle after switch off. It can be seen that the fundamental frequency is also around 50Hz for BB38, but there are fairy big harmonics at 400 Hz in phase a and phase c. In phase b, the frequency spectrum is relatively flat from 100 Hz to 600 Hz.


35

Figure 2-13: FFT Analysis for BB38 currents within the first cycle after switch off As seen from Figure 2-8, the voltage transients within the first cycle after switch off also contain high frequency harmonics. The results of FFT analysis for the Voltages within the first cycle after switch off is shown in Figure 2-14. The fundamental frequen-cy of Voltage is around 50 Hz, the dominating harmonics are at 200 Hz and 400 Hz in the three phases.


36

Figure 2-14: FFT Analysis for the voltages within the first cycle after switch off

2.4 Conclusion The details of Burbo offshore wind farm are introduced in the first section, which are important when modeling the wind farm in PSCAD. The Measuring system and switching operation are introduced in the second section; the measurements are presented in this section as well. From the measurements we know that BB22 is in idle state and BB38 is in normal operation before the switching opera-tion. After the radial switch is turned off, both BB22 and BB38 have transient currents appeared at the output. The voltage of the radial is also affected by the switching tran-sients; overvoltage emerged at the voltage output after the disconnection. By doing the power calculation in the third section, we can get the steady state power output at all the three measuring points as shown in the table below


37

BB22 BB38 Radial

Active Power (MW) 0 1.7 6

Reactive (MVar) 0 0 -2

Table 2-1: Steady state power output at the three measuring locations

The FFT analysis shows that during the first cycle after the switching operation, the fundamental frequency of the BB22 is around 50Hz, the dominating harmonics are from 200 Hz to 400 Hz in the three phases. The fundamental frequency of the BB38 is around 50Hz, but there are fairy big harmonics at 400 Hz in phase A and phase C. In phase B, the frequency spectrum is relatively flat from 100 Hz to 600 Hz. The fundamental fre-quency of Voltage is around 50 Hz, the dominating harmonics are at 200 Hz and 400 Hz in the three phases.

38

3 FULL POWER CONVERTER WIND TURBINE WITH INDUCTION GENERATOR

In this chapter, the induction generator wind turbine with full power converter is dis-cussed. The system configuration of the full converter wind turbine is introduced in 3.2. In section 3.3 the induction generator model is discussed shortly. It is given a brief in-troduction about the aerodynamics and pitch control of the wind turbine in 3.4. In sec-tion 3.5 it is focused on the configuration of the full converter, the characteristics of the generator-side converter, DC-link and grid-side converter are also discussed respectfully in this section. The full converter is controlled utilizing vector control, which is intro-duced in 3.6, the details about the vector control can be found in this section. At last in section 3.7, a simplified model for full converter wind turbine is presented. The simpli-fied model can be used in transients study without losing accuracy.

3.1 Introduction The development of modern wind turbine technology has been going on since 1970s, and the rapid development has been seen from 1990s. Various wind turbine concepts have been developed and different wind generators have been built. Nowadays The ma-jority of wind turbines concepts are IG based, because they are robust, cheap and have low maintenance cost. Four types of typical generator systems equipped IG for large wind turbines exist. A detailed comparison of these types of turbines are given in [19,20] The first concept is a fixed-speed wind turbine system equipped with squirrel-cage IG (SCIG), directly connected to the grid. The scheme of this concept is shown in Figure 3-1. This is termed fixed-speed because the speed may only vary up to 2 % from the rated speed in normal operation. Fixed speed wind turbines are either stall control or with blade-angle control. The stall control is divided into passive stall control and active stall control. The main advantage of stall control is that this is a robust and cheap solution. The blade-angle control of fixed-speed wind turbine is usually active stall but applies operations in negative range of pitch angles.


39

Figure 3-1: Scheme of a fixed speed concept with SCIG

The second concept is a limited variable speed wind turbine with variable rotor resis-tance, which is used by Vestas in their Vestas OptiSlip wind turbine class. The scheme of this concept is shown in Figure 3-2. In this concept, the rotor circuit is connected to the power electronics converter, which can realize the dynamic control of the external rotor resistance and continuous operation of the generator rotor slip. This dynamic rotor resistance wind turbine is equipped with pitch control.

Figure 3-2: Scheme of OptiSlip concept with Wound rotor IG

The third concept is a variable speed wind turbine with a partial power converter or a wind turbine with a doubly fed induction generator (DFIG). The scheme of this concept is shown in Figure 3-3. The IG rotor in this concept is connected to the power grid through an AC/DC/AC frequency converter. The rating of this frequency converter is normally less than 30 percent of the generator rating. The frequency converter consists of two back to back voltage-sourced converters (VSC) through a DC-link. The DFIG wind turbines can normally increase the energy production by about 5% compared to conventional fixed-speed concept.

Figure 3-3: Scheme of DFIG concept

The fourth concept is a variable speed wind turbine with IGs and full-rating converter. This concept is employed in the Siemens SWT-3.6-107 wind turbine and is the research priority in this work. The scheme of this concept is shown in Figure 3-4. In this concept, the IG is connected to the power grid through a full rating AC/DC/AC frequency con-verter. Since rotor excitation is absent in a squirrel cage IG, machine excitation must be provided entirely by the stator. This leads to high reactive power consumption, which is one of the biggest tradeoffs in using an IG in a full converter wind turbine (FCWT). Consequently, this topology requires an overrated generator-side converter. This con-cept is termed FCWT because the converter rating must cover the rated apparent power


40

of the IG as well as the losses in the converter.

Figure 3-4: Scheme of FCWT concept with SCIG

In the past, the majority of installed wind turbines were fixed-speed wind turbines with a squirrel cage IG, known as the 'Danish concept.' However, the dominant technology in the market at the moment is DFIG wind turbines. This concept accounts for more than 65% of the newly installed wind turbines (in MW unit). It followed by the fixed-speed wind turbine concept, which accounts for 18% of the market share [21]. The market share of FCWTs is slightly below that of fixed-speed wind turbines. Before 2005, such wind turbines were only available with power ratings in the range of hundreds kW. In 2005, the manufacturer Siemens announced 2.3 MW and 3.6 MW wind turbines of this concept. In England, there are more than 150 SWT-3.6-107 wind turbines have been erected until now. In this chapter, the attention is drawn to the variable speed FCWT with IG, its modeling and control features are described in the following sections.

3.2 System Configuration of FCWT with IG In variable speed wind turbine concepts, the generator is controlled by power electron-ics. The electric frequency of the generator is decoupled from the electric frequency of the grid because the generator is connected to the grid via frequency converter. The classical frequency converter consists of a diode rectifier, an intermediary DC capacitor and the thyristor inverter. However, due to the fast developments in the semiconductor industry, the use of self commuted converters (IGBT) is increasing in adjustable-speed drives and uninterruptible power supplies. Compared with diode rectifier, significantly higher power quality and increased dynamic performance can be obtained with the IGBT converter. For example, the currents harmonics from the inverter are decreased, the power can flow in both direction and any desired power factor can be obtained [22]. As a diode rectifier is usually chosen for its low price and low losses, however, the IGBT converter is more expensive and has higher rectifier losses. A generic configuration of FCWT is introduced in [9], which is depicted in figure 3-5. It consists of:

• wind turbine mechanical level: o Aerodynamics


41

o Gearbox and shaft system o Pitch angle control

• wind turbine electrical level: o Induction generator o Frequency converter and its control

In this configuration, the IG connects the grid through a full scale back to back conver-ter, which controls the power flow and the speed of the generator. The full converter consists of two voltage source converters, a generator-side converter and a grid-side converter. The DC-link between the two converters behaves as an energy storage device, which decouples the generator-side converter and the grid-side converter. The generator in FCWT is driven by the wind turbine through a gearbox system to at-tain a suitable speed range for the rotor. The low rotational speed of the wind turbine (5-13 rpm) is transformed to high rotational speed side (595-1547 rpm for 50 Hz system). For the Siemens 3.6 MW wind turbine, the gearbox ratio is 1:119 according to the tech-nical specification from Siemens. The speed conversion from wind turbine speed to rated grid frequency is shared by the small gearbox and full-rating power converter, so that the power losses caused by mechanical speed conversion are reduced. The whole wind turbine system equipped with both a pitch angle controller and a fre-quency converter controller. The pitch angle controller controls the rotor speed by changing the pitch angle, but it works only at high wind speed, when the power need to be reduced by pitching the blades in order to protect the generator and frequency con-troller. The converter controller is responsible for controlling the generator speed, pow-er output and DC-link voltage of the turbine.


42

Figure 3-5: Variable speed FCWT with induction generator configuration

3.3 Aerodynamics and Pitch Angle Control Because the mechanical part of the wind turbine has little influence on the electrical switching transients studied in this work, only a brief introduction of the aerodynamics and pitch angle control of the turbine is given in this section. As the maximum wind power available in the swept rotor area 𝜋𝑅2 is

𝑃𝑉 = 0.5 ∗ 𝜌𝑎𝑖𝑟 ∗ 𝑉3 ∗ 𝜋 ∗ 𝑅2 (3-1) The rotor mechanical power can be calculated with the use of the power coefficient 𝐶𝑝(𝜆,𝛽) characteristics provided by the wind turbine manufacture.

𝑃𝑀 = 𝑃𝑉 ∗ 𝐶𝑝(𝜆,𝛽) (3-2) Where 𝜆 is the tip-speed –ratio and 𝛽 is the pitch angle. However, the power coefficient of any wind turbine cannot exceed its theoretical Betz limit 𝐶𝑃𝑀𝐴𝑋 ≈ 0.59 [23], so the maxi mum rotor mechanical power that the wind turbine can exact from the wind is limited. In order to optimize the mechanical rotor power 𝑃𝑀, the pitch angle 𝛽 should be at its optimized position so that the optimal power coefficient can be reached. The pitch angle control is employed in the wind turbine to adjust the pitch angle to its optimized posi-tion. Note that the power output optimization is viable only when the wind speed is be-


43

low the rated wind speed, otherwise the pitch angle control will adjust the pitch angle to the position where less wind power is obtained in order to protect the wind turbine.

3.4 Induction Generator Model Depending on the objective of the research, the IG can be represented in different ways, which accordingly determines the level of detail of the IG model. There are several phenomenons in the IG which could be considered when building the model. The num-ber of the phenomenons included in the model determines the complexity of the model. The phenomenon includes the stator and the rotor flux dynamics, magnetic saturation, skin effect and core losses. A detailed generator representation obviously provides more accurate results of generator response during a fault. However, a detailed generator re-presentation does not improve the grid response accuracy of an FCWT model [20]. Fifth-order model Detailed dynamic representation of the induction machine is usually based on a fifth-order model, corresponding to the general differential equations of the idealized induc-tion machine [24]. The magnetic saturation, the skin effect, as well as core losses are omitted in the standard fifth-order model of the induction machine. However, the fifth order model takes into account the transients in the rotor circuit as well as the funda-mental frequency transients in the stator flux and in the stator current. By using the vec-tor notation, the fifth-order model is described by the stator and rotor voltage equations [25].

𝑢𝑠 = � 𝑅𝑠𝜎𝐿𝑠

+ 𝑗𝜔𝑠�Ψs +𝑑Ψs

𝑑𝑡− 𝐿𝑚

𝐿𝑠

𝑅𝑠𝜎𝐿𝑠

Ψr (3-3)

0 = −𝐿𝑚𝐿𝑠

𝑅𝑟𝜎𝐿𝑟

Ψs + � 𝑅𝑟𝜎𝐿𝑟

+ 𝑗(𝜔𝑠 − 𝑝Ω𝑚�Ψr +𝑑Ψr

𝑑𝑡 (3-4)

Where 𝑢𝑠 is the supply voltage vector. Ψs and Ψr are the stator and rotor flux linkage vectors. Ω𝑚 is the mechanical angular speed of the rotor

p is the number of pole pairs 𝜔𝑠 is the angular supply frequency.

Besides the voltage equations, the motion equation is also needed

𝐽 𝑑Ω𝑚𝑑𝑡

= 𝑇𝑒 − 𝑇𝑠 (3-5) Where J is the moment of inertia, 𝑇𝑠 is shaft torque and 𝑇𝑒 is electrical torque

𝑇𝑒 = 𝑝 𝐿𝑚𝜎𝐿𝑠𝐿𝑟

Im � Ψs Ψr∗� (3-6) By transform the equations from (3-3) to (3-6) into d-q frame, the fifth-order model can be obtained. Third-order model In power system analysis, transient and small-signal stability programs are usually based on neglecting the stator and grid transients, and therefore, a third-order induction machine model is commonly used. The third order model of the induction machine can


44

be reduced from the five order model by disregarding the stator flux transients [25]. The derivatives of the stator flux linkages are set at zero in (3-3), and the stator flux linkages are then solved as functions of the rotor flux linkages and the rotor speed. The resulting expressions for the stator flux linkages are inserted into (3-4) and (3-5) giving the basic third-order model. First-order model The simplest model of IG is known as first-order model. There is not any electrical dy-namics are taken into account in this model, only the mechanical dynamics are included. In order to have the first-order model, all the derivatives in (3-3) and (3-4) are needed to be set to zero. The first-order model is always used when the IG works in steady state.

3.5 Full-Scale Frequency Converter Configuration As shown in figure 3-6, the full-scale power converter is made up of generator-side converter, DC-link, Grid side converter and DC-link chopper. Both the generator-side converter and the grid-side converter make use of IGBT switches parallel with freew-heeling diodes to realize the control of the converter.

Figure 3-6: Full-scale power converter in FCWT

In steady state, the IG can be represented with the first-order model as mentioned in the previous section. The generator-side converter and grid-side converter can be represented as shown in figure 3-7 [20].


45

Figure 3-7: Simplified representation of induction generator with full converter in

steady state computation [20] In this steady state full converter scheme, 𝑈𝑠 denotes the voltage at the grid connection terminals 𝑈𝐺 denotes the voltage at the generator terminals, α is the phase difference between the stator voltage and the rotor voltage. The impedance of the stator is 𝑅𝑆 +𝑗𝑋𝑆, the magnetizing reactance is 𝑋𝑀, and the impedance of the rotor circuit is 𝑅𝑅/𝑠 +𝑗𝑋𝑅. The currents in the stator and rotor are 𝐼𝑆 and 𝐼𝑅 respectively. The power converters are represented as current sources, 𝐽1and 𝐽2, in this scheme, which are used to balance the power flow through the DC-link. The voltage source 𝑈𝐶 is induced by the grid-side converter, the impedance of the smoothing inductor is 𝑅𝐶 +𝑗𝑋𝐶 and the current through the smoothing inductor is 𝐼𝐶.

3.5.1 Generator-side converter The generator-side converter absorbs the active power form IG and transfers it to grid-side converter through DC-link. Since rotor excitation is absent in a squirrel cage IG, machine excitation must be provided entirely by the stator. Besides, the IG is decoupled from the grid through DC-link, it cannot be excited from the grid. Consequently, this topology requires an overrated generator-side converter to fulfill the high reactive pow-er consumption from the IG [9]. The converter rating of Siemens SWT-3.6-107, for ex-ample, must be at least 3.6 MVA plus the loss in the converter to cover rated apparent power of the IG. In this case, the power flow is shown in figure 3.8 a. To reduce the reactive power supplied from the generator-side converter, fixed capaci-tors can be used at the generator terminals to compensate for the reactive power con-sumption of the IG. The rating of the generator-side then can be reduced. In high load situation, for example, in strong wind, the IG absorbs more reactive power for excitation. Both the generator-side converter and the fixed capacitor support the reactive power for the IG excitation. The power flow for this case is shown in figure 3.8 b. In the case of low load operation in weak wind, the IG absorbs less reactive power which can be supported totally by the fixed capacitors. When the reactive power from the fixed capacitors is higher than reactive power demand by the IG, the generator-side converter can be set to absorb surplus reactive power from the fixed capacitor in order to prevent the IG from over excitation. The power flow diagram is shown in figure 3.8 c.


46

Figure 3-8: Active power and reactive power flow in the converter connected to the IG. (a) IG excited by generator side converter. (b) in high load operation, IG excited by both fixed capacitors and the generator side converter. (c) in low load operation, IG excited only by fixed capacitors, the generator side converter set to absorb reactive power. [9]

As depicted in Figure 3-7, the IG feeds into the voltage source induced by the generator-side converter. The generator-side converter is responsible for controlling the magnitude and the electric frequency induced at the generator terminal, 𝑈𝐺∠𝛼. The electric fre-quency of the generator, 𝑓𝐸, is propotional to the wind turbine rotor speed, 𝜔𝑀, and set by gnenrator-side converter according to the power reference of the roror.

𝜔𝑀 = 𝑓𝐸 ∗ (1 + 𝑠) (3-7) Where s is the slip. The rated electric frequency is one of design parameters of wind turbine and can be chosen between 10 and 25 Hz for MW-class wind turbines with con-verter-connected IG. The rated electric frequency is reached when the power output is around 30 percent of wind turbine rated power output. The optimized relation between the generator electric frequency and the wind turbine power output is shown in figure 3-9.


47

Figure 3-9: The optimized relation between the generator electric frequency and the

wind turbine power output. The rated 𝑓𝐸 is at 12 Hz. [9]

3.5.2 DC-link The DC-link capacitor provides intermediate energy storage between the generator-side converter and the grid-side converter, which also decouples these two converters. As shown in figure 3-7, the charging current of the DC-link is 𝐽1 = 𝑃𝑠

𝑈𝐷𝐶 and the discharg-

ing current is 𝐽2 = 𝑃𝐸𝑈𝐷𝐶

. Here 𝑃𝑆 denotes the active power transferred from the IG ter-

minals and 𝑃𝐸 denotes the active power supplied to the grid from the grid-side converter terminals. In steady state, in order to keep the DC voltage constant, the charging current 𝐽1 equals the discharging current 𝐽2. In other words, 𝑃𝑆 equals 𝑃𝐸 in case of no loss in DC link. The DC-link voltage in steady-state operation can be calculated by using the following equation [20],

𝑈𝐷𝐶 = 2√2𝑚∗√3

𝑈𝑆 (3-8)

Where 𝑈𝐷𝐶 is the DC link voltage, 𝑈𝑆 is the RMS value of grid voltage, m is the PWM modulation depth of the grid-side converter. The capacitance of the DC link capacitor is relevant to the voltage ripple of DC link voltage, which must be made small enough for the voltage to be virtually constant dur-ing a switch period. Small voltage ripples requires larger capacitor, but on the other hand have a slow response to voltage changes. Small capacitor makes fast changes in the DC voltage but results in higher voltage ripples. Selecting the size of the DC-link has thus to be a trade-off between voltage ripples, lifetime and the fast control of the DC-link. The trade-off relation for the design of the DC-link capacitor in the back-to-back converter is described in [26], as follows:

𝐶𝐷𝐶 = 𝑆𝑛𝑈�𝐷𝐶∗∆𝑈𝐷𝐶∗2𝜔𝑒

(3-9)


48

Where ∆𝑈𝐷𝐶 is allowed voltage ripple, 𝑈�𝐷𝐶 is average DC link voltage, 𝜔𝑒 is electrical frequency and 𝑆𝑛 is apparent converter power. In steady state operation and with no losses in the DC-link, the instantaneous power on the DC side must equal the instantaneous power on the AC side. In the moment that this power balance is broken, the instantaneous difference in power is stored in the DC-link capacitor and this leads to fluctuations in the DC-link voltage. The generator feeds pow-er to the network as long as the DC-link has a constant voltage higher than the peak voltage of the network. By balancing the DC-link voltage, the grid-side converter rece-ives the active power transmitted from DC-link and delivers it to the power grid. The reactive power cannot be exchanged through the DC-link in the converter system. How-ever, the grid-side converter, whose electric frequency and voltage are fixed to the grid, can be set to control the power factor or control the grid voltage, for example, in weak grid.

3.5.3 Grid-side converter The objective of the grid-side converter is to keep the DC-link voltage constant regard-less of magnitude and direction of the power flow from the generator. The grid-side converter then converts the constant DC voltage to the AC grid voltage with fixed pow-er system frequency. The schematic of the grid-side converter is shown in figure 3-10 [27]. Applying the Kirchhoffs voltage law to the circuit in figure 3-10 the following equation can be found:

�𝑣𝑎𝑣𝑏𝑣𝑐� = 𝑅 �

𝑖𝑎𝑖𝑏𝑖𝑐� + 𝐿 d

d𝑡�𝑖𝑎𝑖𝑏𝑖𝑐� + �

𝑣𝑎1𝑣𝑏1𝑣𝑐1

� (3-10)

Where L is the smoothing inductance, R is the smoothing resistance, 𝑣𝑎, 𝑣𝑏, 𝑣𝑐 are the three phase grid voltages and 𝑣𝑎1, 𝑣𝑏1, 𝑣𝑐1 are the three phase grid-side converter ter-minal voltages.


49

Figure 3-10: grid-side converter schematic [27]

Because the reactive power is not able to transfer through the DC-link, all the reactive power exchanged between the wind turbine and the grid should be supported by the grid-side converter. The reactive power arrangement is based on the grid requirement. In normal operation, the wind turbine is set to optimize the power factor, therefore the exchanged reactive power is zero so as to keep cos𝜑 = 1. However, the wind turbine is required to support the grid voltage within a desired range in case of weak grid, the grid-side converter then need to generate the reactive power as the grid requirement.

3.6 Full-scale Frequency Converter Control The full-scale frequency converter control is divided into two controllers: a control for the generator side converter and a control for the grid side converter. The control of the converter can be realized by using different strategies as described in [28]. The common used control strategies include maximum torque control, unity power factor control of the generator and constant stator voltage control. The control strategies determine how the converter works and its performance, each strategy has its own advantages and disadvantages compared with other strategies. The unity power factor control, for example, minimizes the converter rating when generator operates with unity power. However, as the stator voltage is not directly controlled, the stator voltage varies depending on the speed, which could cause overvoltage for the converter and the generator in case of over speed. In the case of constant stator voltage control, generator and converter always operate at rated voltage, so there is no risk of overvoltage and saturation of the converter at high speeds. A disadvantage of this con-trol is the reactive power demand of the generator, which increases the converter rating. The full-scale frequency converter is generally controlled utilizing vector control tech-niques. The vector control enables the converter to control the active and reactive power output independently. The idea is that the three phase currents and voltages are pro-jected to a rotating reference frame, which is rotating along either with AC flux or vol-


50

tage. By selecting a suitable rotating frame, the AC currents and voltages appear as DC quantities in the steady state. Therefore, static errors in the control system can be avoided by tuning PI controllers. When tuning the converter system control, the proportional gains and the integration times of the PI controller need to be determined. In this chapter, the Internal Model Control (IMC) will be introduced to simplify the controllers design and setup the para-meters of the PI controllers.

3.6.1 Internal Model Control (IMC) IMC is considered as a robust control method, it can be used for designing current or speed control of any ac machines [29,30] and simplifying the design of controllers. The IMC structure is depicted in figure 3-11.

Figure 3-11: structure of IMC [30]

The structure in figure 3-11 uses an internal model 𝐺�(𝑝) in parallel with the controlled system G(𝑝). For an ac machine, v and i are the stator voltage and current vectors re-spectively, while 𝑖𝑟𝑒𝑓 = [𝑖𝑑

𝑟𝑒𝑓 , 𝑖𝑞𝑟𝑒𝑓] is the current reference vector. Controller design is

then just a matter of choosing the proper transfer function 𝐶(𝑝), one common way of choosing 𝐶(𝑝) follows the equation below,

𝐶(𝑝) = ( 𝛼𝑝+𝛼

)𝑛𝐺�−1(𝑝) (3-11)

Where ( 𝛼𝑝+𝛼

)𝑛 is a low pass filter, n is the order of the filter and 𝛼 is a design parameter,

which for n=1, is set to the desired bandwidth of the closed-loop system. The controller, F(p), inside the dashed block in figure 3-11, becomes

𝐹(𝑝) = 𝐶(𝑝)1−𝐶(𝑝)𝐺�(𝑝)

(3-12)

The closed loop transfer function can be simplified to


51

𝐺𝑐𝑙(𝑝) = 𝐺(𝑝)𝐶(𝑝) = ( 𝛼𝑝+𝛼

)𝑛 (3-13)

when 𝐺(𝑝) = 𝐺�(𝑝), which means the internal model is perfect. For the first order system, n=1, take (3-11) into (3-12) the controller becomes an ordi-nary PI controller.

𝐹(𝑝) = 𝛼𝑝𝐺�−1(𝑝) = 𝑘𝑝 + 𝑘𝑖

𝑝 (3-14)

The main benefit of using IMC can be found from (3-14). The tuning problem, which for a PI controller involves adjustment of two parameters, is reduced to the selection of only one parameter, the desired closed loop bandwidth 𝛼. In order to improve the disturbance rejection, “active damping” is introduced into the IMC system in the form of an inner feed-back loop, the structure can be changed to fig-ure 3-12

Figure 3-12: structure of IMC with active damping [30]

The transfer function from load disturbance E to output i is

𝐺𝐸𝑖(𝑝) = 𝑝𝑝+𝛼

𝐺(𝑝)1+𝐺(𝑝)𝑅

= 𝑝𝑝+𝛼

1𝐺−1(𝑝)+𝑅

(3-15)

For a first order system it is possible to choose R so that the transfer function can be reduced to

𝐺𝐸𝑖(𝑝) = 𝐾 𝑝(𝑝+𝛼)2

(3-16)

(3-16) means that the disturbance is damped with the same time constant as the dynam-ics of the control loop.

3.6.2 Control of Grid-Side Converter The main objective of the grid-side converter is to control the dc-link voltage constant. The control of the grid-side converter consists of a fast inner current control loop, which controls the current through the grid filter and an outer slower control loop that controls the dc-link voltage.


52

3.6.2.1 Vector Control Scenario of Grid Side Converter The vector control of Grid-side converter uses a reference frame oriented along with the stator vector position. Under stator voltage orientation, the direct component of the AC side smoothing current, id, is proportional to the active power output and is used to con-trol the DC-link voltage. The quadrature current component, iq, represents the reactive power and directly determines the power factor of the converter. The vector control schematic is shown in figure 3-13 [11]. The smoothing currents are transformed to id and iq using the park transformation

�xdxq� = �cos (φ) −sin (φ)

sin (φ) cos (φ) � ∗ �xαxβ� (3-17)

id and iq are controlled in the d-q axis through PI controllers. The PI controllers design is shown in the following section.

Figure 3-13: Grid-side converter control diagram [11]

In steady state operation and with no losses in the DC-link, the instantaneous power on the DC side must equal the instantaneous power on the AC side. This gives

𝑃 = Vdcidc = 32

vdid (3-18)


53

Where Vdc is the DC-link voltage and idc is the DC-link current. From (3-18) it can be concluded that the active power and the DC-link voltage can be controlled by id. The reactive power generated by the grid-side converter can be expressed as

𝑄 = 32

vdiq (3-19)

Then it is possible to use iq to control the reactive power and further to control the grid voltage. Using the park transformation given in (3-17), the equation (3-10) is transformed from phase values into dq reference frame rotating at grid voltage frequency 𝜔𝑒.

𝑣𝑑 = 𝑅𝑖𝑑 + 𝐿 d𝑖𝑑d𝑡− 𝜔𝑒𝐿𝑖𝑞 + 𝑣𝑑1 (3-20)

0 = 𝑅𝑖𝑞 + 𝐿d𝑖𝑞d𝑡

+ 𝜔𝑒𝐿𝑖𝑑 + 𝑣𝑞1

As the d-axis of the reference frame aligns the grid voltage vector, we have 𝑣𝑞 = 0 in (3-20). It is possible to control the d axis current by controlling the d-component of the SPWM output voltage and the q axis current via the q component. However, this leads to a poor control system response, because attempting to change 𝑖𝑑 also causes 𝑖𝑞 to change tran-siently [31]. Hence, modifications have to be made to the basic PI controller structure so that a decoupled response is possible, and a request to change 𝑖𝑑 changes only 𝑖𝑑 without affecting 𝑖𝑞 ; and vice-versa. The modified current controller structure is shown in figure 3-14.

Figure 3-14: Structure of the current controller


54

In this current controller structure, 𝐿𝑥1 and 𝐿𝑥2 are chosen to control the currents, the resulting equations are then decoupled. Using the feedback PI control, it is set the error in the 𝑖𝑑 loop affect 𝐿𝑥1 and the 𝑖𝑞 loop to affect 𝐿𝑥2. The quantity 𝜔𝐿 is the impedance of the smoothing filter which can be calculated based on the wind turbine design para-meters. The output voltages of the current regulator, 𝑣𝑑1 and 𝑣𝑞1, are used as reference voltages of the grid-side converter. If 𝑣𝑑1 and 𝑣𝑞1 are applied before the smoothing inductor, the desired currents 𝑖𝑑𝑟𝑒𝑓 and 𝑖𝑞𝑟𝑒𝑓 will flow in the circuit. As long as the reference voltage 𝑣𝑑1 and 𝑣𝑞1 are derived, the vector control heads into the last stage. By using the in-verse Park transformation in (3-21), the reference voltages in dq frame are transformed back into the abc phase values [18].

�𝑖𝛼𝑖𝛽� = �cos(𝜑) − sin(𝜑)

sin(𝜑) cos(𝜑) � �𝑖𝑑𝑖𝑞� , (3-21)

�𝑖𝑎𝑖𝑏𝑖𝑐� =

32

⎣⎢⎢⎢⎡

1 0

−12

√32

−12

−√32 ⎦⎥⎥⎥⎤

�𝑖𝛼𝑖𝛽�

The phase values are compared with a high frequency triangle wave to determine the firing pulse patterns, which are used to control the corresponding IGBTs. The modula-tion process will be discussed in detail in section 3.6.2.3.

3.6.2.2 Parameters Design for PI Controllers Current Regulator of Grid Filter As presented in (3-10), the dynamics of the grid filter can be also written as

𝐿𝑓d𝑖𝑓d𝑡

= 𝑣𝑓−(𝑅𝑓 + j𝜔𝑒𝐿𝑓)𝑖𝑓 − 𝐸𝑔 (3-22)

Where 𝐸𝑔 is the grid voltage, 𝑖𝑓 is the grid-filter current and 𝑣𝑓 is the grid-filter voltage supplied from the grid-side converter. In order to introduce the “active damping” and decouple the d and q components of the grid filter current, the applied grid-filter voltage 𝑣𝑓 is chosen as

𝑣𝑓 = 𝑣𝑓′ − (𝑅𝑎𝑓 − 𝑗𝜔𝑒𝐿𝑓)𝑖𝑓 (3-23) The the inner closed-loop transfer function becomes

𝐺(𝑝) = 𝑖𝑓(𝑝)

𝑣𝑓′ (𝑝)

= 1𝐿𝑓𝑝+𝑅𝑓+𝑅𝑎𝑓

(3-24)


55

The parameters of PI controller can be determined with the bandwidth 𝛼𝑓. By choosing the active damping as 𝑅𝑎𝑓 = 𝛼𝑓𝐿𝑓 − 𝑅𝑓, the transfer function from 𝐸𝑔 to 𝑖𝑓 is

G𝐸𝑔𝑖𝑓 = p𝐿𝑓(𝑝+𝛼𝑓)2

(3-25)

Finally the grid-filter current control can be written as

𝑣𝑓 = �𝑘𝑝𝑓 + 𝑘𝑖𝑓𝑝� (𝑖𝑓

𝑟𝑒𝑓 − 𝑖𝑓) − (𝑅𝑎𝑓 − 𝑗𝜔𝑒𝐿𝑓)𝑖𝑓 (3-26)

Where 𝑘𝑝𝑓 = 𝛼𝑓𝐿𝑓 , 𝑘𝑖𝑓 = 𝛼𝑓�𝑅𝑓 + 𝑅𝑎𝑓� = 𝛼𝑓2𝐿𝑓 , 𝑅𝑎𝑓 = 𝛼𝑓𝐿𝑓 − 𝑅𝑓 (3-27)

DC-link Voltage Regulaor The parameters of PI controller for DC-link voltage control can be determined following the process we’ve used for the current controller. However, linear control techniques need to be applied to transfer the nonlinear DC-link dynamics to equivalent linear system.

12𝐶𝑑𝑐

𝑑𝑊𝑑𝑡

= −𝑃𝑟 − 𝑃𝑓 (3-28)

Where 𝑃𝑟 is the power delivered to generator by the DC-link, 𝑃𝑓 is the power delivered to grid filter by the DC-link, W is the energy in DC-link, 𝑊 = 𝑣𝑑𝑐2 . After adding an active damping into the system,

𝑖𝑓𝑞𝑟𝑒𝑓 = 𝑖𝑓𝑞

′𝑟𝑒𝑓 + 𝐺𝑎𝑊 (3-29) Where 𝐺𝑎 is the gain of “active damping”, the inner closed loop transfer function is

𝐺′(𝑝) = 𝑊(𝑝)

𝑖𝑓𝑞′𝑟𝑒𝑓(𝑝)

= −6𝐸𝑔𝑝𝐶𝑑𝑐+6𝐸𝑔𝐺𝑎

(3-30)

Then by utilizing IMC, the PI controller can be obtained

𝐹(𝑝) = 𝛼𝜔𝑝𝐺−1(𝑝) = − 𝛼𝜔𝐶𝑑𝑐

6𝐸𝑔,𝑛𝑜𝑚− 𝛼𝜔𝐺𝑎

𝑝 (3-31)

Where the active damping is chosen as 𝐺𝑎 = 𝛼𝜔𝐶𝑑𝑐/(6𝐸𝑔,𝑛𝑜𝑚), 𝐸𝑔,𝑛𝑜𝑚 is the nominal value of the grid voltage and 𝛼𝜔 is the bandwidth of the DC-link vlotage loop. The parameters of the PI controller then can be determined as

𝑘𝑝𝑓 = 𝛼𝜔𝐶𝑑𝑐6𝐸𝑔,𝑛𝑜𝑚

, 𝑘𝑖𝑓 = 𝛼𝜔2𝐶𝑑𝑐6𝐸𝑔,𝑛𝑜𝑚

(3-32)

3.6.2.3 Sinusoidal Pulse Width Modulation Although the basic circuit for an inverter may seem simple, accurately switching these devices provides a number of challenges. The most common switching technique is called Pulse Width Modulation (PWM) [22, 32]. PWM is employed in a wide variety of applications, ranging from measurement and communications to power control and conversion. In ac motor drives, PWM inverters make it possible to control both fre-quency and magnitude of the voltage and current applied to a motor. The energy, which


56

is delivered by the PWM inverter to the ac motor, is controlled by PWM signals applied to the gates of the power switches at different times for varying durations to produce the desired output waveform. There are several PWM modulation techniques, well-known among these are sinusoidal PWM (SPWM), hysteresis PWM, space vector modulation. While the SPWM and the hysteresis PWM can be implemented using analog techniques. In the wind turbine mod-el in chapter 4, the SPWM is used to control the IGBT converter. The following illustra-tion describes the procedure of SPWM method.

Figure 3-15: SPWM generation procedure [22]

As seen from figure 3-15, three-phase reference voltages transformed from dq frame with variable amplitude and frequency are compared in three separate comparators with a common triangular carrier wave of fixed amplitude and frequency. Each comparator output forms the switching-state of the corresponding inverter leg.


57

Figure 3-16: Principle of SPWM generation [22]

Figure 3-16 shows the principle of the SPWM method; SPWM produces an average voltage value that is equal to the reference voltage within each PWM period. Therefore, the fundamental of the switched pulse pattern equals the corresponding reference vol-tage. This method is called sinusoidal PWM because the pulse width is a sinusoidal function of the angular position in the reference signal.

Since the PWM frequency is equal to the frequency of the carrier wave, and it is usually much higher than the frequency of the reference voltage. Normally, the proportion of the carrier frequency to the reference voltage frequency is multiple of three and is an odd number in order to have fewer harmonics. With high switch frequency used, the harmonics caused by PWM can be attenuate by small line filter. Maximum feasible sampling frequency is twice the switching frequency. Drawback of high switching fre-quency is that the loss in the valves is high due to high frequency distortion. Besides, the triangular-shaped carrier wave is always symmetric with respect to the center of each PWM period. The symmetrical PWM is often preferred, since it generates less current and voltage harmonics.


58

3.6.3 Control of Generator-Side Converter

3.6.3.1 Vector Control Scenario of Generator Side Converter The function of the generator-side controller is to optimize the power output by the IG and control the generator speed. Be similar with the vector control of grid-side converter, the stator currents and voltages are transformed to dq frame with d axis aligned along the rotor flux vector position. In this specific dq frame, the control of electromagnetic torque and reactive power can be decoupled. The vector control schematic for the generator-side converter is shown in figure 3-17 [11]. The 𝑖𝑑𝑟𝑒𝑓 comes out of the flux regulator and 𝑖𝑞𝑟𝑒𝑓 comes out of speed regulator. The current regulator then utilizes the current references in dq frame and generates the voltage references which can be used to control the generator-side converter.

Figure 3-17: Generator-side converter control diagram [11]

To calculate the rotor flux vector, first the stator flux is calculated in (3-33)

𝜓𝑠 = ∫(𝑣𝑠 − 𝑅𝑠𝑖𝑠)𝑑𝑡 (3-33) Where 𝑣𝑠 , 𝑅𝑠 and 𝑖𝑠 are the stator voltage, resistance and current respectfully. The sta-tor flux is then transformed to 𝛼𝛽 frame to calculate the angle position 𝜙𝑠. The angle 𝜙𝑠 gives the instantaneous position of the stator’s rotating magnetic field. As the rotor is rotating as well and is instantaneously located at the rotor angle 𝜙𝑟, with a reference frame attached to the rotor, the stator’s magnetic field vector is at the loca-tion 𝜙 = 𝜙𝑠 − 𝜙𝑟. 𝜙 is used in Park transformation in order to achieve field orientation.


59

Apart from this, together with 𝜙𝑟𝑒𝑓 , 𝜙 is imported to current regulator to generate d-axis current reference, which will in turn control the reactive power flow. The electromagnetic torque of the induction machine is calculated as

𝑇𝑒 = 23𝑝 𝐿𝑚𝐿𝑟𝜓𝑑𝑖𝑞 (3-34)

Where p is the number of pole pairs, 𝜓𝑑 is the d component of rotor flux, 𝐿𝑚, 𝐿𝑟 are the magnetizing and rotor inductances. 𝑖𝑞 is then used to control the electromagnetic torque. This will in turn control the active power flow.

3.6.3.2 Parameters Design for PI Controllers Current Regulator The stator current is controlled with the field orientation aligned with the rotor flux.

𝑑𝑑𝑡𝜓𝑠��(𝑡) = −𝑅𝑠𝚤𝑠�(𝑡) − 𝑗𝜔1𝜓𝑠��(𝑡) + �̅�(𝑡)

𝜓𝑠��(𝑡) = 𝐿𝑠𝚤𝑠�(𝑡) + 𝐿𝑚𝚤𝑟�(𝑡) (3-35) 𝑑𝑑𝑡𝜓𝑟��(𝑡) = −𝑅𝑟𝚤𝑟�(𝑡) − 𝑗𝜔2𝜓𝑟��(𝑡)

𝜓𝑟��(𝑡) = 𝐿𝑚𝚤𝑠�(𝑡) + 𝐿𝑟𝚤𝑟�(𝑡) (3-36) Where 𝚤𝑠�, 𝜓𝑠��(𝑡), and 𝚤𝑟� , 𝜓𝑟�� are the grid and rotor current and flux, �̅� is the stator vol-tage, 𝑅𝑠, 𝑅𝑟 and 𝐿𝑠, 𝐿𝑟 are the stator and rotor resistance and self-inductances, respect-fully. 𝐿𝑚 is the magnetizing inductance. In order to derive stator-current control law, it is advantageous to eliminate 𝚤𝑟� and 𝜓𝑠�� among the above equations,

𝐿𝜎𝑑𝚤�̅�(𝑡)𝑑𝑡

+ 𝑅𝐼𝑀𝚤�̅�(𝑡) + 𝑗𝜔1𝐿𝜎𝚤𝑠�(𝑡) = �̅�(𝑡) + 𝐿𝑚𝐿𝑟

(𝑅𝑟 𝐿𝑟− 𝑗𝜔𝑟)𝜓𝑟��(𝑡) (3-37)

Where 𝐿𝜎 = 𝐿𝑠 − 𝐿𝑚2 /𝑅𝑟, 𝑅𝐼𝑀 = 𝑅𝑠 + (𝐿𝑚𝐿𝑟

)2𝑅𝑟 and 𝜔𝑟 = 𝜔1−𝜔2.

By treating the 𝜓𝑟�� as a disturbance, the inverse transfer function with the modified sta-tor voltage vector can be written as

G−1(s) = �p𝐿𝜎 + 𝑅𝐼𝑀 −𝜔1𝐿𝜎𝜔1𝐿𝜎 p𝐿𝜎 + 𝑅𝐼𝑀

� (3-38)

The standard PI current controller for the rotor flux oriented IM is

F(s) = αp�p𝐿𝜎 + 𝑅𝐼𝑀 0

0 p𝐿𝜎 + 𝑅𝐼𝑀� (3-39)

The parameters of the PI controller then can be determined as 𝑘𝑝𝑓 = 𝛼𝐿𝜎 , 𝑘𝑖𝑓 = 𝛼𝑅𝐼𝑀 , 𝑅𝐼𝑀 = 𝑅𝑠 + (𝐿𝑚

𝐿𝑟)2𝑅𝑟 (3-40)

Speed Regulator The mechanical dynamics of the generator can be expressed as (3-41)


60

𝐽𝑛𝑝

𝑑𝜔𝑟𝑑𝑡

= 𝑇𝑒 − 𝑇𝑠 (3-41)

Where J is the inertia, 𝑛𝑝 is the number of pole pairs, 𝜔𝑟 is the rotational speed, 𝑇𝑒is the electrical torque and 𝑇𝑠 is the shaft torque.

As the current regulator is much faster than the speed control, we can consider 𝑇𝑒 =𝑇𝑒𝑟𝑒𝑓. After introducing the active damping 𝐵𝑎, the reference torque becomes

𝑇𝑒𝑟𝑒𝑓 = 𝑇𝑒

′𝑟𝑒𝑓 − 𝐵𝑎𝜔𝑟 (3-42) The transfer function can then be written as

𝐺(𝑝) = 𝜔𝑟(𝑝)

𝑇𝑒′𝑟𝑒𝑓 = 1

𝐽𝑛𝑝𝑝+𝐵𝑎

(3-43)

Using IMC, the following PI controller can be found 𝐹(𝑝) = 𝛼𝑠

𝑝𝐺−1(𝑝) = 𝐽𝛼𝑠

𝑛𝑝+ 𝐵𝑎𝛼𝑠

𝑝 (3-44)

By choosing the active damping as 𝐵𝑎 = 𝛼s𝐽/𝑛𝑝, the parameters of the PI controller then can be determined as

𝑘𝑝𝑓 = 𝐽𝛼𝑠𝑛𝑝

, 𝑘𝑖𝑓 = 𝐽𝛼𝑠2

𝑛𝑝 (3-45)

3.7 Simplified Model of FCWT for Transients Study Because wind generators are much smaller compared with conventional power genera-tors and their number is therefore much larger, the model aggregation techniques have to be applied for being able to carry out dynamic simulations within reasonable calcula-tion time. It reduces calculation speed considerably compared to a fully detailed model. Detailed dynamic model with all wind generator components including wind turbine rotor, induction generator, and converters are introduced in the previous sections. How-ever, for investigating transient phenomena, the detailed model of FCWT is not neces-sary and it can be simplified without reducing accuracy [12,13]. The grid disturbances considered in this thesis are of a short duration, maximum a few tens of milliseconds. Such disturbances are the most common in the grid. Since the con-sidered grid disturbances are much faster than wind speed variations, the wind speed can he assumed constant. Moreover, the mechanical behavior has generally no big im-pact on voltages and power flow within such short duration, so the impact of the pitch regulation and shaft system can be also ignored in the simulations. Because the DC-link decouples the grid-side converter from the generator-side conver-ter and IG, the generator-side converter and IG cannot interact with the grid directly and on the other hand avoid directly affecting by the grid disturbance. With proper assump-tion, only the grid-side converter fed by a DC-voltage needs to be considered in the simplified model. A simplified model can be derived based on the assumption that the DC-link voltage is constant. This assumption can be justified by the large DC-link capa-citance and by the DC voltage controller.


61

The simplified models are shown in figure 3-18. In the case that the wind turbine works in idle state, the FCWT model can be simplified as depicted in figure 3-18 a. when the wind turbine is in idle state, there is no power output from the generator. The IG and generator-side converter can be neglected, and the grid-side converter is set to keep the DC-link voltage constant and control the reactive power output to zero. For the wind turbines in normal operation, the simplified model is shown in figure 3-18 b. In figure 3-7, it is known that the generator-side converter can be modeled as current source in steady state. The IG and converter-side converter is replaced by current source in the simplified model in figure 3-18 b. the active power output is determined by the size of current source. The reactive power is controlled by the grid side converter.

(a)

(b)

Figure 3-18: Simplified models for FCWT. (a) Simplified model for FCWT in idle state, (b) Simplified model for FCWT in normal operation

In Paper [12] the author introduces the simplified dynamic model of FCWT shown in figure 3-18, a series of simulation are performed with this model to test the dynamic characteristic by the author. For example, a simulation of voltage sag of 80% at the connection point is carried out with this simplified model. The simplified wind turbine models are benchmarked against detailed, not-simplified models. The results from the simplified and detailed models match very well. It confirms that the simplified model is adequate and the best for transient study.

3.8 Conclusion The full rating frequency converter equipped in the induction generator wind turbine is a back-to-back frequency converter system consisting of a generator-side converter and a grid-side converter connected by a DC-link capacitor. The full-rating frequency con-verter enables the induction generator to work at fully variable frequencies.


62

The induction generator supplies the active power to the grid through the DC-link capa-citor. However, the reactive power cannot be transferred through the DC-link. The in-duction generator is excited by the generator-side converter. The grid-side converter is in charge of generating reactive power for the turbine in case of needed. Vector control technique is employed to control the converter system. The vector con-trol enables the converter to control the active and reactive power output independently. The grid-side converter is set to balance the DC-link voltage and control the reactive power supply to the power grid and grid voltage support. The generator-side converter is used to control electromagnetic torque and reactive power. Internal model control is introduced to turning the PI controllers used in the controls since it simplify the process of the parameterizing the PI controllers. The 𝑘𝑝 and 𝑘𝑖 for the PI controllers can be cal-culated based on the equations (3-27), (3-32), (3-40), and (3-45). For doing the transient study of the induction generator wind turbine with full converter, an simplified model is introduced in order to reduce the model’s complexity speed without losing accuracy. The simplified model can be applied to both the wind turbine in idle state and the wind turbine in normal operation.

63

4 SIMULATION AND VALIDATION

In this chapter, an simplified model of FCWT is built and implemented using PSCAD. The simplified model can be applied to simulate the switching transients for both the WT in idle state, e.g. BB22 and the WT in normal operation, e.g. BB38 in Burbo off-shore wind farm. The component models and the control scenarios utilized in the FCWT model are based on philosophies introduced in chapter 3. With this simplified model of FCWT wind turbine, the model of Burbo offshore wind farm can be built easily in PSCAD. The switching operation is taken with the wind farm model according to the measurements introduced in Chapter 2. The switching transients from the simulation results are compared with the measurements to validate the model. The grid information for modeling Burbo offshore wind farm is provided by Dong Energy, which includes the details of the cables, transformers and fixed capacitor banks used in the wind farm. However, no real data are used for parameterizing the wind tur-bine model because of confidentiality agreements with various manufacturers. Instead, typical parameters have been used for all components. PSCAD is a powerful electromagnetic time domain transient simulation tool. With proper design of the simulation model, PSCAD can help improve the power system per-formance and reliability. Various electric power researches can be taken using PSCAD, for example, transmission system design, power quality studies, power electronics de-sign, electric machine performance study, control system design and optimization [33]. However, it is most suitable for simulating time domain instantaneous responses, also known as electromagnetic transients, in both electrical and control systems. There is a vast work and research done for modeling and simulation of wind turbines induction generators within their components and control elements suitable for steady state and electromechanical transients (e.g. small, long term dynamics, etc) based on different simulations tools(e.g. Matlab, PowerFactory, PSS, etc). However, there is a lack of generic EMT models based on PSCAD, therefore the research work will be fo-cused on the model, develop and simulation of wind turbines induction generators with full-rating converter and fault-ride-through capability based on the PSCAD simulation package.


64

4.1 Simplified Models of FCWT for transient study in PSCAD As discussed in section 3.7, with proper assumption, only the grid-side converter fed by DC-voltage needs to be considered in the simplified model. The simplified FCWT mod-el is benchmarked against detailed model in the work [12] and the simulation results confirm that the simplified model is adequate and the best for transient study. In this current project, the FCWT in Burbo offshore wind farm is simplified as grid-side converter fed by DC-voltage source to carry out the switching operation. It is shown in figure 3-18 that the simplified model for the wind turbine in idle operation is a little different from the simplified model in normal operation. Because the available mea-surements are for wind turbine at BB22 and BB38, which are operating in idle state and in normal operation state respectively before the radial switch is turned off. The PSCAD model for BB22 and BB38 will be introduced separately in this section.

4.1.1 PSCAD Model for BB22

4.1.1.1 Model Schematic and Component Parameters Design

The simplified PSCAD model for BB22 is shown in figure 4-1, the model consists of a DC-link capacitor, a three-phase voltage source inverter, and line filter. The structure of the model is same with the grid-side converter schematic shown in figure 3-6. A DC voltage source is connected across the DC-link capacitor in the circuit, which is used to initialize the DC-link voltage to the steady state value. After the DC-link voltage reach-es that value, the DC voltage source is disconnected.

Figure 4-1: Simplified PSCAD model for BB22

The DC-link voltage in steady-state operation can be calculated by using the equation (3-8). For the wind turbine BB22, the RMS value of line-to-line grid voltage 𝑈𝑆 is 0.69 kV, and the modulation depths m is chosen as 0.751, the DC-link voltage can be calcu-lated as

𝑈𝐷𝐶 =2√2𝑚 ∗ √3

𝑈𝑆 =2√2

0.751 ∗ √3∗ 0.69 = 1.5 kV


65

The value of DC-link capacitance is determined using the equation (3-9). For the wind turbine BB22, the average DC link voltage 𝑈�𝐷𝐶 is 1.5 kV, the allowed voltage ripple ∆𝑈𝐷𝐶 is 2% of average DC link voltage, ∆𝑈𝐷𝐶 = 2% ∗ 1.5 = 0.03 kV , the electrical frequency 𝜔𝑒 = 2π ∗ 50 = 314.16 rad/s and the apparent converter power 𝑆𝑛 is 3.6 MW . After putting these values to (3-9), the value of the capacitance can be calculated,

𝐶𝐷𝐶 =𝑆𝑛

𝑈�𝐷𝐶 ∗ ∆𝑈𝐷𝐶 ∗ 2𝜔𝑒=

3.6 𝑀𝑊1.5 𝑘𝑉 ∗ 0.03 𝑘𝑉 ∗ 2 ∗ 314.16 𝑟𝑎𝑑/𝑠

= 0.127 𝐹

The single phase circuit diagram is shown in figure 4-2. Because the inductance of the line filter 𝐿𝑓 is related to the converter output voltage 𝑈𝐶�� and the grid voltage 𝑈𝑠��, the maximum inductance of the filter 𝐿𝑓 can be decided as long as the 𝑈𝐶�� and 𝑈𝑠�� are known.

Figure 4-2: Single phase grid-side converter circuit

In the current model, the maximum magnitude of 𝑈𝐶�� is |𝑈𝐶|𝑚𝑎𝑥 = 𝑈𝐷𝐶 ∗ 𝑚𝑚𝑎𝑥 = 1.5 𝑘𝑉 ∗ 0.42 = 630 𝑉 𝑚𝑚𝑎𝑥 is the maximum modulation index for single phase L-N value. The single phase L-N value of grid voltage 𝑈𝑠 can be calculated as

|𝑈𝑠| =690 𝑉√3

= 398 𝑉

When the grid-side converter is with unity power factor and the power output is at the rated value 3.6 MW, the maximum inductance of 𝐿𝑓 can be derived according to the phasor diagram shown in figure 4-3


66

Figure 4-3: Phasor diagram for determining the maximum inductance of 𝐿𝑓

The single phase line current 𝑖𝑠 is evaluated as

𝑖𝑠 =1.2 𝑀𝑊398 𝑉

= 3000 𝐴

The maximum voltage drop of the line filter can be calculated as

|𝑈𝐿|𝑚𝑎𝑥 = �(|𝑈𝐶|𝑚𝑎𝑥)2 − |𝑈𝑠|2 = �6302 − 3982 = 488 𝑉 As long as we have the maximum voltage drop of the line filter and the line current, the maximum inductance of the filter can be derived.

𝐿𝑚𝑎𝑥 =|𝑈𝐿|𝑚𝑎𝑥

𝑖𝑠 ∗ 2𝜋𝑓=

4883000 ∗ 2𝜋 ∗ 50

= 0.518 𝑚𝐻

In the current model, in order to achieve high quality filter properties, a 0.5 mH inductor is used as a filter to fill out the harmonics generated in the process of SPWM. The mod-el with smaller filter will be discussed in the sensitive analysis in section 4.3.

4.1.1.2 Converter Vector Control Design in PSCAD The principle of vector control of grid-side converter has been introduced in section 3.6.2. The design of vector control for grid-side converter in PSCAD follows the vector control schematics shown in figure 3-13. In this section, the design process of vector control is divided into four steps; the details for each step are illustrated below. First step: Park Transformation.


67

Figure 4-4: Illustration diagram of the first step in vector control

The detection of the ac grid voltage reference angle can either be done by calculating the phase angle in 𝛼𝛽 frame or using a PLL (Phase Lock Loop). By using the equation (4-1), it is not hard to find the phase angle in 𝛼𝛽 frame.

φ(t) = atan (xβ(t)xα(t)

) (4-1)

The phase calculation can be realized in PSCAD as shown in figure 4-5. The grid phase voltages V1a, V1b,V1c are firstly imported to a abc to 𝛼𝛽 transformation block, which is a user built component. The abc to 𝛼𝛽 transformation block works on the basis of equation (2-1), the script of this block can be found in Appendix A. After the phase val-ues are transformed to 𝛼𝛽 values, a PSCAD built in block can be used to change the rectangular 𝛼𝛽 values to polar value. The phase angle can be easily found from a polar value.

Figure 4-5: Phase angle calculation in PSCAD

The grid voltage reference angle calculated in 𝛼𝛽 frame is plotted in figure 4-6


68

Figure 4-6: Phase angle found by calculation

However, the phase angle of the grid voltage can be only calculated in steady state. As shown in (4-1), if the grid voltage becomes zero, for instance, after switching off the radial in the thesis, the grid angle becomes infinitive which means the system would lose the phase. Instead of calculating the phase angle in 𝛼𝛽 frame, PLL is employed in this work in order to hold the phase of the grid-side converter during switching off transients. The PLL model is available in PSCAD Master Library; the parameters in the model are set as shown in figure 4-7.

Figure 4-7: PLL parameters setup

Because the output phase angle range is from 0 to 2𝜋 by using PLL, in addition, the

phase angle generated by PLL leads the phase angle calculated in 𝛼𝛽 frame by 5𝜋2

. By

subtracting 𝜋2 from the PLL output, the phase angle if PLL is equivalent to the phase

angle calculated in 𝛼𝛽 frame when doing trigonometric calculation. The phase angle found from PLL is plotted in figure 4-8.


69

Figure 4-8: Phase angle found by PLL

As long as the phase angle is found, the phase values of grid voltages and currents need to be transformed into dq frame in order to utilizing vector control. The transformations are done as shown in figure 4-9.

Figure 4-9: Park transformation in PSCAD

In figure 4-9 the 𝛼𝛽 to dq transformation block is a user built block, which is ground on the equation (3-17). The script of this block is given in Appendix A.

Second step: Currents and DC voltage regulators The second step of the vector control is to find the reference voltages of the converter output which will be used to control the converter in the further step. As shown in figure 4-10, there are totally four PI controllers that are used in this step to regulate the DC-link voltage, the grid voltage and the currents.


70

Figure 4-10: Illustration diagram of the second step in vector control

As described in chapter 3, the DC-link voltage can be regulated by controlling the direct axis current 𝑖𝑑 in the voltage vector-oriented reference frame. Thus, a reference current 𝑖𝑑𝑟𝑒𝑓 is derived from the DC-link voltage error of the power converter by a PI controller. The reference of the DC-link voltage is 1.5 kV in this model, the DC-link voltage regu-lator can be built as shown in figure 4-11 in PSCAD. The PI controller is a built in model in PSCAD master library.

Figure 4-11: DC-link voltage regulator in PSCAD

The simulation result of DC-link voltage is shown in figure 4-10, the blue curve is the DC-link reference voltage and the green curve is the real DC-link voltage. From 0 to 0.05 s, the DC-link capacitor is initialized by a 1.5 kV DC voltage source as shown in figure 4-1. At the point 0.05 s, the voltage source is disconnected and the DC-link vol-tage is regulated constant by the controller. As we can see the controller works pretty well which keeps the DC-link voltage at the rated value 1.5 kV


71

Figure 4-12: DC-link voltage simulation results in PSCAD

The design of grid voltage regulator should meet the grid voltage regulating specifica-tions in the grid code. If the absolute value of grid voltage decrease within 10% of the rated value, the grid voltage 𝑣𝑑 is controlled through a PI controller by 𝑖𝑞. If the abso-lute value of grid voltage decrease beyond 10%, 𝑖𝑞 = 2(𝑣𝑑𝑟𝑎𝑡 − 𝑣𝑑) . However, be-cause the model is designed for simulating switching transients, the grid voltage changes severely after switching operation, the PI controller can be ignored and let 𝑖𝑞 = 0 when the absolute value of grid voltage decrease within 10%. The structure of grid voltage regulator in PSCAD is shown in figure 4-13.

Figure 4-13: Grid voltage regulator in PSCAD

Because the voltage goes up during the switching transient, the grid-side converter theo-retically needs to consume 𝑖𝑞 in order to limit the grid voltage within the tolerable level. However, due to the line breaker is open, the grid-side converter can’t acquire any 𝑖𝑞 from the grid, the grid voltage regulator can’t work properly. Therefore, in this simpli-fied model for switching transient study, the 𝑖𝑞𝑟𝑒𝑓 is set to zero instead of being derived from the grid voltage regulator. The model with grid voltage regulator will be discussed in the sensitive study in section 4.3.

The current controller is built followed the structure shown in figure 3-14 in PSCAD, which can be seen in figure 4-14. The selection of 𝑖𝑑𝑟𝑒𝑓 for the grid side converter is through the control circuit shown in Figure 4-11, which attempts to keep the capacitor voltage at its rated value by adjusting the amount of active power. The 𝑖𝑞𝑟𝑒𝑓 is set to zero in order to have unity power factor.


72

Because vector control uses maximum values to control the converter, the line to line RMS grid voltage need to be changed to maximum value, vd = 0.69 kV

√3∗ √2 = 0.563 kV. The

inductor impedance is calculated as 𝜔𝐿 = 2𝜋 ∗ 50 ∗ 0.5 𝑚𝐻 = 0.157 Ω.

Figure 4-14: Current regulator in PSCAD

The proportional gains and the integration times of the PI controller can be determined by tuning the converter system control. The data of the DC-link and the grid-side con-verter configuration must be taken into account when tuning. There are several ways to turning the parameters of the PI controller in order to give an ideal control performance, for example, the Ziegler-Nichols reaction curve method, the Cohen and Coon tuning method, and the IMC tuning method which is introduced in chapter 3. By tuning the following targets shall be reached [26] The controlled parameters shall reach their respective references The response of the converter to a change in a reference signal shall be as fast

as possible, but without large overshoots and excitation of transients in the grid-side VSC.

The converter must perform damping of the fundamental-frequency transients in the electric parameters of the grid-side converter.

The generic control of the back to back converter is examined by stepping the refer-ences, for instance, 𝑖𝑑𝑟𝑒𝑓, 𝑖𝑞𝑟𝑒𝑓 and 𝑉𝐷𝐶𝑟𝑒𝑓. In this model, the proportional gain and the integral time constant for the PI controllers are given in table 4-1


73

PI controller for id PI controller for iq PI controller for DC-link

Voltage

Kp Ti Kp Ti Kp Ti

100 0.05 s 100 0.05 s 200 0.5 s

Table 4-1: Parameters for PI controllers

The simulation results of 𝑖𝑑 and 𝑖𝑞 in PSCAD can be seen in figure 4-15. The blue curve is the reference current and the green one is the real current in both of the plots. As we can see, during the initialization of the first 0.05 s, the reference currents change strong-ly but the 𝑖𝑑 and 𝑖𝑞are trying to follow the reference. After the initialization, the currents 𝑖𝑑 and 𝑖𝑞 stay at zero just as the reference.

(a)

(b)

Figure 4-15: Simulation results of id and iq in PSCAD. (a) plot of id and its reference idref. (b) plot of iq and its reference iqref.


74

Third step: Inverse Park transformation.

Figure 4-16: Illustration diagram of the first step in vector control

The reference voltages in dq frame are transformed back to phase values so that they can be used in SPWM modulator. The inverse Park transformation follows the equation (3-21) in chapter 3. The model of inverse Park transformation is built as shown in figure 4-17 in PSCAD. A magnitude limiter is used to limit the magnitude to the maximum rating of the grid side VSC converter. Both the dq to 𝛼𝛽 and the 𝛼𝛽 to abc blocks are user built, the scripts of these two blocks can be found in Appendix A.

Figure 4-17: Inverse Park transformation in PSCAD

Firth step: SPWM Modulation

Figure 4-18: Illustration diagram of the firth step in vector control

Figure 4-19 shows the SPWM controller model built in PSCAD, the model is based upon the SPWM principle introduced in section 3.6.2.3. Each of the phase voltages is compared with a high frequency triangle wave to determine the firing pulse patterns. The switching frequency is chosen as 𝑓𝑘 = 21 ∗ 50𝐻𝑧 = 1.05 𝑘𝐻𝑧 .


75

Figure 4-19: SPWM Modulation block in PSCAD

The firing pulse pattern for the IGBT switch T1s is shown in figure 4-20.

Figure 4-20: Firing pulse pattern generated in PSCAD

4.1.1.3 Steady state simulation of BB22 As long as the simplified model of BB22 is built as shown in figure 4-1 and it utilizes the vector control introduced in 4.1.1.2, the steady state simulation can be carried out. A simple system is built as shown in Figure 4-21.


76

Figure 4-21: Simple system built for steady state simulation of BB22 in PSCAD

The steady state phase currents measured after the turbine transformer are shown in figure 4-22. As we can see, the currents turn to zero after the initialization because BB22 is in idle state in steady state. It can be verified by the measurement of BB22 be-fore the radial switch is turned off.

Figure 4-22: Steady state currents of BB22 in PSCAD

The steady state voltages of BB22 are shown in Figure 4-23. They are three phase sinu-soid voltages with a maximum value 27 kV. It is also same with the measurements.

Figure 4-23: Steady state voltages of BB22 in PSCAD


77

In figure 4-24 it is shown that the steady state active power and reactive power of BB22 in steady state. The upper plot of figure 4-24 is the active power output of BB22, after assume some active power during initialization, the active power becomes zero. The lower plot of figure 4-24 is the reactive power output of BB22, it also turns to zero after initialization. The power plots verify BB22 works in idle state.

Figure 4-24: Steady state power output of BB22 in PSCAD. Upper plot: active power output of BB22 in steady state. Lower plot: reactive power output of BB22 in steady state.

4.1.2 PSCAD Model for BB38

4.1.2.1 Model Schematic and Control of BB38 The schematic of the simplified model of BB38 is shown in figure 4-25. Compared with the simplified model of BB22 in figure 4-1, a DC current source is placed in parallel with the DC-link capacitor. The DC current source is used to replace the generator and the generator-side converter for the purpose of simplification. As we know from chapter 2, the BB38 generates 1.7 MW active power in steady state, the magnitude of the DC current source can be calculated using equation (3-18) as

𝑖𝐷𝐶 =𝑃𝑉𝐷𝐶

=1.7 𝑀𝑊1.5𝑘𝑉

= 1.133 𝑘𝐴


78

Figure 4-25: Simplified PSCAD model for BB38

The control of the BB38 follows the vector control steps implemented in BB22, and the parameters in the control are same as the parameters used in BB22. Some important controlling signals are shown below. Figure 4-26 shows the 𝑖𝑑 and 𝑖𝑞 in the BB38 model. The upper plot is 𝑖𝑑 and its refer-ence and the lower plot is 𝑖𝑞 and its reference receptively. From equation (3-18) we know that,

𝑖𝑑 =𝑉𝐷𝐶 ∗ 𝑖𝐷𝐶1.5 ∗ vd

=1.5 kV ∗ 1.133 kA

1.5 ∗ 0.563 kV= 2.012 kA

. As we can see from the upper plot of figure 4-26, the 𝑖𝑑 equals to -2.07 kA after initiali-zation in steady state. The negative sign results from the current measuring direction of I1a, I1b and I1c in figure 4-25. Therefore, the simulation result of 𝑖𝑑 complies with its theoretical value. Because BB38 has unity power factor in steady state, the reactive power output is zero. 𝑖𝑞 of BB38 is kept to zero which means there is not any reactive power generated by BB38.


79

(a)

(b) Figure 4-26: Current control of id and iq for BB38 (a) plot of id and its reference idref. (b) plot of iq and its reference iqref. Figure 4-27 gives the plot of DC-link voltage of BB38. The DC voltage controller keeps the DC-link voltage at its reference value 1.5 kV during steady state operation.

Figure 4-27: DC-link voltage control for BB38


80

4.1.2.2 Steady state simulation of BB38 By utilizing the simplified model of BB38 introduced in the previous section, a simple system is built for simulating the steady state operation of BB38. The simple system is shown in figure 4-28.

Figure 4-28: Simple system built for steady state simulation of BB38 in PSCAD

The simulated steady state currents of BB38 are shown in figure 4-29. The maximum values of the currents are 0.041 kA after initialization in steady state, which are same as the current measurements of BB38 in steady state.

Figure 4-29: Steady state currents of BB38 in PSCAD

The steady state voltages of BB38 are shown in Figure 4-30. They are three phase sinu-soid voltages with a maximum value 27 kV. It is also same with the measurements.


81

Figure 4-30: Steady state voltages of BB38 in PSCAD

The active power and reactive power outputs are plotted in figure 4-31. The upper plot is the active power generated by BB38, which equals 1.7 MW consistent with the calcu-lated value in chapter 2. The lower plot is the reactive power generated by BB38, it is zero after the initialization period because BB38 is with unity power factor in steady state.

Figure 4-31: Steady state power outputs of BB38 in PSCAD. Upper plot: active power output of BB38 in steady state. Lower plot: reactive power output of BB38 in steady state.

4.2 Burbo Wind Farm Model and Switching Operation On the condition that the simplified models for BB22 and BB38 work properly in the steady state, the model of Burbo offshore wind farm can be built in PSCAD and the switching operation can be taken with these models. As known in chapter 2, there are totally 25 wind turbines arranged in three radials in Burbo wind farm, however, only the


82

switching operation of the middle radial is considered in this project. In order to reduce the complexity of the wind farm model and simplify the calculation of the simulation, an simplified wind farm model is employed to do the switching transients simulation. Because the measuring points are all in the middle radial and the turbines in the other two radials have no effect on the switching transients at the measuring points, only the middle radial of Burbo wind farm is maintained in the wind farm model. Besides, from chapter two, we can know that only BB24, BB26, BB27, and BB38 are in normal opera-tion before the switching operation, the other turbines including BB22, BB23,BB25 and BB37 are in idle state. The turbines in the idle state can be eliminated as they don't con-tribute any power in steady state and their switching transients have little effect on BB38 and BB22. In the simplified wind farm model of Brubo in this work, only six of the eight turbines in the middle radial are reserved with BB25 and BB37 being eliminat-ed. The grounding transformers and the capacitor bank in Burbo wind farm are not included in the simplified wind farm model as well because they are not in the radial which takes switching operation and they have no effect on the switching transients of BB22 and BB38. The parameters of the cables, wind farm transformer and wind turbine transformer are provided by the wind farm owner Dong Energy. In this wind farm model, the cables are modeled as Pi section out of the consideration that the cables don't make strong impact on the switching transients at the measuring points compared with the converter. The transformers are modeled using the three-phase transformer model based on the classic-al approach in PSCAD. The transformer windings in the 34 kV grid are delta-coupled for the radial transformer as well as for the wind turbine transformer. The grounding on the secondary side of the transformer is through a small resistor. The simplified wind farm model is shown in figure 4-32. There are six wind turbines included in this model. Wind turbine BB22, BB23 are in idle state and BB24, BB26, BB27, BB38 are generating before the switching operation is taken. From the calcula-tion of the measurements in chapter 2, it is known the total active power output of the radial is 6 MW and reactive power output is -2 MVar. As BB38 generates 1.7 MW ac-tive power and 0 MVar reactive power, we can assume each of the other three generat-ing wind turbines output 1.43 MW and -0.67 MVar.


83

Figure 4-32: Simplified wind farm model of Burbo in PSCAD

The line breaker is turned off at 0.3 s and the wind turbines are disconnected at 0.325 s out of the consideration of protecting the wind turbines against high overvoltage. The radial currents and voltages are measured before the line breaker and the wind turbine currents and voltages of BB22 and BB38 are measured behind the wind turbine trans-former. The simulation results with the switching transients at the three measuring points are shown below in figure 4-34. The simulation results are moved to align with the time coordinate of measurements in order to compare the simulation results with the measurements. In the time coordinate of measurements in figure 4-33, the line breaker is turned off at 0.036 s, and the wind turbines are disconnected from the grid at 0.061 s.


84

(a) (b)

(c) (d)

(e) (f)


85

` (g) (h)

(i) (j)

(k) (l)

Figure 4-33: Simulation Results of Switching operation in PSCAD. Plot (a),(b),(c) are the three phase radial currents respectively. Plot (d),(e),(f) are the three phase currents measured at the output of wind turbine BB22. Plot (g),(h),(i) are the three phase currents measured at the output of wind turbine BB38. Plot (j),(k),(l) are the three phase voltages measured at the radial


86

From figure 4-33 (a)-(c), we can see the radial currents from the simulation results match the measurements perfectly. The phase A of radial current turns into zero at the time of breaker is open, the currents in phase B and phase C reach zero at 0.04s and keep zero afterwards. Figure 4-33 (d)-(f) show the three phase currents of BB22. Before the switching opera-tion at 0.036 s, the three phase currents of BB22 maintain at zero exactly the same as the measurements, which means the BB22 is at idle state. When the line breaker is turned off, the transient currents come out of BB22 in all the three phases. Compared with the measurements, the switching transients from the simulation follow the shapes of the measurements. The peak values and the phase of the transients from the simula-tion results are almost identical with the measurements; however, the high frequency oscillations in the measurement are not represented by the simulation. In figure 4-33 (g)-(i) the three phase currents of BB38 are displayed. Before the switch-ing operation at 0.036 s, BB38 was in normal operation with active power output of 1.7 MW. The currents of BB38 match the measurements perfectly in steady state. When the line breaker is turned off, the transient currents of BB38 from the simulation follow the shape of the measurement during the first cycle before the wind turbines are discon-nected from the grid at 0.06 s. Similar to the transients in BB22, the simulation results of current transient from BB38 cannot represent the high frequency oscillations. Figure 4-33 (j)-(l) give the voltages comparisons between the simulation results and the measurements. As we can see, the transient voltages from the simulation are different from the measurements. First, in all the three phases, the overvoltages from the simula-tion are more severe than the overvoltages in the measurements. Second, the phases of the transient voltages from simulation lag behind the measurement. Third, just like the currents, the simulation cannot represent the high frequency oscillations in the mea-surements. The preliminary analysis suggests that the high frequency oscillations in the switching transient currents could be caused by the resonance between the cables, transformers and the filters. The lumped Pi model of the cable used in this wind farm model may be not adequate for obtaining ideal switching transients. More accurate models for the cables and the transformers can be built following the methods described in [6,7,8], however, it is very difficult to find the precise parameters for modeling the grid cables and transformers and it is out of the scope of discussion in this project which focuses on investigating how the wind turbine reacts against the switching operation. Besides the inadequacy of the cable and transformer models, because the parameters used in the wind turbine model are all practical values instead of the real values used by the manu-facture, it can also cause the simulation results be different from the measurements. Since it is hard to acquire the real values from the manufactures in the current stage, sensitive analysis can be performed to the preliminary model so as to investigate how the uncertain factors in the wind turbine model affect the switching transients. The sen-sitive analysis is performed in the following section.


87

4.3 Sensitive Analysis of the Model The aim of the sensitive analysis of the model is to evaluate the preliminary model and to verify the effect of the parameters of components on the switching transient simula-tion results and indirectly improve the accuracy of the model. In the current project, two kinds of sensitive analysis of the model are performed, sensitive analysis of the filter inductance and sensitive analysis of the grid voltage regulator.

4.3.1 Sensitive analysis of the filter inductance Instead of using 0.5 mH inductor as a line filter, a smaller inductor is used in this part for the new wind turbine model. The other parameters in the new model are exactly the same with the model implemented in section 4.2. The value of the new inductor is de-termined by calculation based on the practical modeling experience. A rule of thumb for designing the inductor filter is to employ an inductor with imped-ance of 0.15 p.u. In the current case, the inductance of the filter can be acquired by ap-plying this rule as follows

ZL = 𝑈𝑠2

𝑆∗ 0.15 = (0.69 𝑘𝑉/√3)2

1.2 𝑀𝑉𝐴∗ 0.15 = 0.0198 Ω

As long as the single phase impedance of the inductor filter is known, the inductance of the filter can be easily calculated,

L =ZL

2πf=

0.01982π ∗ 50

= 63 μH

After replacing the 0.5 mH inductor with the 63 μH inductor, the vector control of the converter need to be tuned again so that optimal control characteristic is obtained. The parameters of the PI controller are derived after tuning the system as shown in table 4-2.

PI controller for id PI controller for iq PI controller for DC-link

Voltage

Kp Ti Kp Ti Kp Ti

100 0.01 s 100 0.01 s 300 1 s

Table 4-2: Parameters for PI controllers

The wind farm model is identical with the model used in section 4.2 except the induc-tance of the filter in the wind turbine model being changed to 63 μH.


88

As long as the wind farm model is built, the switching operation can be taken with the model. The line breaker is turned off at 0.036 s in the measurements time coordinate, and the wind turbines are disconnected from the grid at 0.061 s. the simulation results together with the comparison with the measurements are shown in figure 4-34.

(a) (b)

(c) (d)

(e) (f)


89

(g) (h)

(i) (j)

(k) (l)

Figure 4-34: Simulation results of switching operation for WT model with 63 uH filter in PSCAD. Plot (a),(b),(c) are the three phase radial currents respectively. Plot (d),(e),(f) are the three phase currents measured at the output of wind turbine BB22. Plot (g),(h),(i) are the three phase currents measured at the output of wind turbine BB38. Plot (j),(k),(l) are the three phase voltages measured at the radial


90

From figure 4-34 (a)-(c) it is seen that the radial phase currents follows the shape of the measurements. However, high frequency oscillations can be found in the radial currents. Figure 4-34 (d)-(f) plot out the currents measured at the output of BB22. Before the radial breaker is turned off at 0.036s, the currents of BB22 were oscillating within the range of -0.01 to 0.01. Besides, the currents of BB22 were polluted by high frequency harmonics in steady state. At the moment of switching operation at 0.036s, transient currents are obtained by the simulation and the transients follow the shape of the mea-surements. Compared with the switching transients of BB22 shown in figure 4-33 (d)-(f), high frequency oscillations appear in the transients in this case which are more simi-lar to the measurements. In figure 4-34 (g)-(i) the currents measured at the output of BB38 are shown. Similar to the case of BB22, the current outputs of BB38 are polluted by high frequency harmon-ics in steady state. But for the switching transients, the high frequency oscillations ap-pear in the simulation results with make it look more like the measurements compared the transients of BB38 shown in figure 4-33 (g)-(i). From the voltage plots shown in figure 4-34 (j)-(l), we can see the transient voltages from the simulation results lag behind the measurements and they are shortage of oscil-lations which appear in the measurements. But compared with the transient voltages shown in figure 4-33 (j)-(l), the peak values of overvoltages decrease to 40 kV other than the 60 kV in figure 4-33. In summary, smaller line filter improves the accuracy of the model during switching transients. The high frequency oscillations appear in the transient currents of BB22 and BB38 which make the simulation switching transients look more similar to the mea-surements. In addition to this, the peak values of the transient overvoltages decrease after changing to the smaller line filter. However, smaller filter causes the deterioration of the current outputs of BB22 and BB38 in steady state. The currents are polluted by the high frequency harmonics because the filter efficiency becomes lower with smaller filter.

4.3.2 Sensitive analysis of the grid voltage regulator The function of voltage regulator is to help maintain the grid voltage at the rated value regardless whether the wind turbine is in normal operation and during fault. The struc-ture of the voltage regulator can be seen in figure 4-13 and the design of voltage regula-tor is introduced in section 4.1.1.2.


91

Instead of keeping the reference current in q-axis 𝑖𝑞𝑟𝑒𝑓 as zero, the model in this sec-tion utilizes the voltage regulator to provide 𝑖𝑞𝑟𝑒𝑓 to the current regulator. . If the abso-lute value of grid voltage decreases within 10% of the rated value, the grid voltage 𝑣𝑑 is controlled through a PI controller. If the absolute value of grid voltage decrease beyond 10%, 𝑖𝑞 = 2(𝑣𝑑𝑟𝑎𝑡 − 𝑣𝑑) . This voltage regulation is required in the grid code for the purpose of supporting the grid voltage in case of voltage sag. Besides the grid voltage regulator, other parameters in the wind turbine model are same with the parameters used by the model in section 4.2. The wind farm model is built in the same way that introduced in 4.2. The line breaker is turned off at 0.036 s in the mea-surements time coordinate, and the wind turbines are disconnected from the grid at 0.061 s. the simulation results together with the comparison with the measurements are shown in figure 4-35.

(a) (b)

(c) (d)


92

(e) (f)

(g) (h)

(i) (j)


93

(k) (l)

Figure 4-35: Simulation results of switching operation for WT model with grid voltage regulator in PSCAD. Plot (a),(b),(c) are the three phase radial currents respectively. Plot (d),(e),(f) are the three phase currents measured at the output of wind turbine BB22. Plot (g),(h),(i) are the three phase currents measured at the output of wind turbine BB38. Plot (j),(k),(l) are the three phase voltages measured at the radial The radial currents are plotted in figure 4-35 (a)-(c). The simulation results follow the shape of the radial currents measurement except that in phase B and phase C the radial currents turn into zero before 0.04 s after the line breaker is turned off. The currents measured at the output of BB22 are shown in figure 4-35 (d)-(f). The cur-rents from the simulation match perfectly with the measurements in steady state, how-ever, there is a big difference between the simulation results and the measurements dur-ing the switching transients. The shape of the simulation result doesn’t match the mea-surement and big transient currents can be found in the simulation result. Similar to the case of BB22, the current outputs of BB38 shown in figure 4-35 (g)-(i) don't match the measurements very well after the radial breaker is turned off. However, the voltage outputs from the simulation shown in figure 4-35 (j)-(l) get better compared with the voltage outputs in figure 4-33 and figure 4-34. The overvoltages be-come smaller and the phase difference between the simulation result and the measure-ment is also reduced. In addition, the harmonics can be found in voltage simulation re-sults which are similar to the measurements. One of the reasons that the current outputs of BB22 and BB38 don't match the mea-surements is that the voltage regulator controls the grid-side converter to consume 𝑖𝑞 in order to pretend the grid voltage going up at the moment of switching operation. How-ever, because the radial breaker has been turned off, the converter can’t consume 𝑖𝑞 from the grid. This could cause the current error during switching transients.


94

4.4 Conclusion In this chapter the simplified model is implemented in PSCAD for both the wind turbine BB22 and BB38. The component parameters are designed based on the theory intro-duced in chapter 3 and the vector control is implemented for the model. In this model, the design process of vector control can be divided into four steps, which are described accordingly below,

• Park transformation • DC voltage and currents regulator design • Inverse Park transformation • SPWM design

In steady state, both the models for BB22 and for BB38 work properly in PSCAD. The currents, voltages, and power match the measurements shown in chapter 2 very well. Based on the wind turbine models for BB22 and BB38, a simplified Burbo wind farm model is built for switching transient study. The switching operation is taken to the wind farm model and the switching transients are measured at the three measuring points as described in chapter 2. The switching transients from the simulation follow the measurements but the high frequency oscillation in the transient currents can be ob-tained by the model. Besides, the transient overvoltage is bigger than the measurement and there is phase difference between the simulation voltage output and the measure-ments. Sensitive analysis is performed to the wind turbine model. In the first case, smaller filter is employed in the model. The switching transients become better compared with the preliminary model but the currents are polluted by high frequency harmonics because the filter efficiency becomes lower with smaller filter. In the second case, grid voltage regulator is added to the model. The transient switching voltages become more similar to the measurements but the currents can’t follow the measurements because the grid voltage regulator in this model can’t work properly after the line breaker is open. According to the sensitive analysis, the simulation result of switching transients could be improved by proper design of the filter. Besides, more accurate cable and transfor-mer model could also contribute to a better simulation result.

95

5 CONCLUSION AND IMPLICATION

5.1 Conclusion In this project, transients that occur due to switching operation in large offshore wind farms are investigated. The measurements of wind turbine BB22, BB38 and the Radial with switching transients acquired in Burbo offshore wind farm are provided to carry out this project. Through the analysis of the measurements, it is found that BB22 was in idle state and BB38 was in normal operation with 1.7 MW active power output before the switching operation. The whole radial was generating 6 MW active power and con-suming 2 MVar reactive power in total. It is also speculated that the wind turbines are disconnected from the grid one cycle after the switching operation out of the considera-tion to protect the wind turbines from overvoltage. The structure and control of the full converter wind turbine with induction generator are introduced in this report. The full power converter equipped in the wind turbine is a back-to-back frequency converter system consisting of a generator-side converter and a grid-side converter connected through a DC-link capacitor. The full-rating frequency converter enables the induction generator to work at fully variable frequencies. The in-duction generator supplies the active power to the grid through the DC-link capacitor. However, the reactive power cannot be transferred through the DC-link. The induction generator is excited by the generator-side converter. The grid-side converter is in charge of generating reactive power for the turbine in case of needed. Vector control technique is employed to control the converter system. The vector con-trol enables the converter to control the active and reactive power output independently. The grid-side converter is set to balance the DC-link voltage and control the reactive power supply to the power grid and grid voltage support. The generator-side converter is used to control electromagnetic torque and reactive power. For doing the transient study of the induction generator wind turbine with full converter, an simplified model is introduced in order to reduce the model’s complexity without losing accuracy. The simplified wind turbine models are benchmarked against detailed, not-simplified models in [12]. It is concluded by the author that the simplified model is adequate and the best for transient study.


96

Issues concerning modeling of the wind turbines induction generators with full-rating converter for switching transient studies are discussed. The generic full converter struc-ture and its vector control scenario are followed when building the dynamic simplified wind turbine model. However, no real data are used for parameterizing the wind turbine model because of confidentiality agreements with various manufacturers. Instead, typi-cal parameters have been used for all components. At the early stage, a series of steady state simulations are carried out to the simplified wind turbine model to gain a complete understanding of the control and test if the model works correctly in steady state. Af-terwards, a simplified model for Burbo offshore wind farm is built. The grid informa-tion for modeling Burbo offshore wind farm is provided by Dong Energy, which in-cludes the details of the cables, transformers and fixed capacitor banks used in the wind farm. The simplified wind farm model consists of six wind turbines in one radial. Switching operation is taken to the radial and switching transients are measured at the three measuring points introduced in chapter 2. The simulation results are compared with the measurements in the same time coordinate. The simulation results show that the currents and voltages match the measurements per-fectly in the steady state. After the radial breaker is turned off, the switching transient currents are generated by the model of BB22 and BB38. For BB22, the shape, peak values and the phase of the transients from the simulation results are almost identical with the measurements; however, the high frequency oscillations in the measurement are not represented by the simulation. The high frequency oscillations could be caused by the resonance in the grid, the discrepancy in relation to the oscillations might be im-proved by employing a more accurate grid model. For BB38, the transient currents from simulation also follow the shape of the measurement. However, similar to the tran-sients in BB22, the simulation results of current transient from BB38 cannot represent the high frequency oscillations. For the switching transient voltages, the overvoltage can be obtained from the simulation but it is bigger than the measurement. In addition the phase of simulation lags behind the measurement shortly. Sensitive analysis is performed to evaluate the dynamic wind turbine model and test the effects of the components and parameters in the model on switching transients output. There are some uncertainties in the wind turbine model such as the design of filter and grid voltage regulator, the study case of sensitive analysis is selected to investigate how the uncertainties would affect the final results. Through analyzing the effect of line filter on the switching transients, we can see small-er line filter could improve the accuracy of the model during switching transients. The high frequency oscillations appear in the transient currents of BB22 and BB38 like the measurements. In addition, the peak values of the transient overvoltages decrease after changing to the smaller line filter. However, smaller filter causes the deterioration of the


97

current outputs of BB22 and BB38 in steady state. The currents are polluted by the high frequency harmonics because the filter efficiency becomes lower with smaller filter. In the second study case, grid voltage regulator is added to the model. The transient switching voltages become more similar to the measurements but the currents can’t fol-low the measurements because the grid voltage regulator in this model can’t work prop-erly after the line breaker is open.

5.2 Implication for future development As discussed in the part of conclusion, a more accurate grid model could contribute to a better simulation result with the wave propagation and resonance being considered in the cables and transformers. The modeling of cables and transformers in the wind farm for switching transients simulation have been discussed in the works [6,7,8], the model-ing methods in [6,7,8] can be employed in the future development of the preliminary model built in this project. From the sensitive analysis we know the design of the line filter could also affect the simulation results of switching transients. A better design of the filter could improve the accuracy of the model for transients study. Because both the wind turbine model and Burbo wind farm model are built using sim-plified methods for switching transient study in this project, detail models can be built for the wind turbine and wind farm to benchmark the accuracy of the simplified models for transient study. The method for benchmarking the simplified model can be referred to the work [12].

99

REFERENCES

[1] World Wind Energy Report 2009, World Wind Energy Association. February 2010. Retrieved 13-March-2010.

[2] European Wind Energy Association, Oceans of opportunity, September 2009

[3] RenewableUK report. Available online : http://www.bwea.com/ukwed/offshore.asp

[4] The Grid Code, Issue 4, Revision 2. National Grid Electricity Transmission plc, UK. March 2010

[5] Jørgen, N., et al. Modeling and fault-ride-through tests of Siemens Wind Power 3.6 MW variable-speed wind turbines, Wind Engineering, vol: 31, issue: 6, pages: 441-452, 2007

[6] Sørensen, P., et al. Switching transients in wind farm grids, European Wind Energy Conference and Exhibition 7-10. May 2007.

[7] Liljestrand, L., et al. Transients in collection grids of large offshore wind parks. Wind Energy Vol.11 Issue.1 2008: 45-61.

[8] Abdulahovic, T., et al. Modeling of the energizing of a wind park radial. Nor-dic Wind Power Conference. Roskilde, 2007.

[9] Vladislav, A., Full-load converter connected asynchronous generators for MW class wind turbines, Wind Engineering, vol: 29, issue: 4, pages: 341-351, 2005

[10] Xiangjun, Z., et al. Design and comparison of full-size converters for large variable-speed wind turbines, Power Electronics and Applications 2007 Euro-pean Conference, pages: 1 - 10 , Sept. 2007

[11] Marta, M., et al. Control of wind turbines with induction generator interfaced to the grid with power electronics converters, Power Electronics and Applica-tions, 2005

[12] Sebastian, A., et al. Direct drive synchronous machine models for stability as-sessment of wind farms, DigSILENT GmbH, available online: http://www.digsilent.de/Consulting/Publications/.

[13] Markus, P., et al. Aggregated wind park models for analyzing power system dynamics, DigSILENT GmbH, available online: http://www.digsilent.de/Consulting/Publications/.


100

[14] DONG Energy, Burbo Bank Offshore Wind Warm, Available online: http://www.dongenergy.com/burbo/index.htm, October 2007.

[15] Lukasz, K., et al, Harmonic models of a back-to-back converter in large off-shore wind farms compared with measurement data. Nordic wind power confe-rence. 2009.

[16] Siemens wind turbine SWT-3.6-107, Available online: http://www.energy.siemens.com/hq/en/power-generation/renewables/wind-power/wind-turbines/swt-3-6-107.htm

[17] Leif, C., et al, GPS synchronized high voltage measuring system, European offshore wind conference & exhibition, 2007.

[18] Kundur, P. Power System Stability and Control, McGraw-Hill, 1994.

[19] H. Li, et al., Overview of different wind generator systems and their compari-sons, IET Renewable Power Generation, vol. 2, no. 2, pp. 123-138, 2008.

[20] Vladislav, A., Induction Generators for Wind Power, Multi-Science Publishing Company Ltd, 2005

[21] A. Hansen, et al., Market penetration of wind turbine concepts over the years, Proc. European Wind Energy Conference and Exhibition 2007, Milan, Italy, May 2007.

[22] Tonny, R. et al., High power electronics, lecture notes, technical university of Denmark, January 2010.

[23] Martin, H., Aerodynamics of wind turbines, second edition, Earthscan, 2008.

[24] H. C. Stanley, An analysis of the induction motor, AIEE Trans., vol. 57, pp. 751–755, 1938.

[25] T. Thiringer, et al., Comparison of Reduced-Order Dynamic Models of Induc-tion Machines, IEEE Transactions on power systems, VOL. 16, NO. 1, Febru-ary 2001

[26] Vladislav, A., Analysis of dynamic behaviour of electric power systems with large amount of wind power, Ph.D. dissertation, DTU, 2003.

[27] R. Pena et al., Double fed induction generator using back-to-back PWM con-verters and its application to variable-speed wind-energy generation, Electric Power Applications, IEE Proceeding, vol. 143, issue 3, pp. 231-241, 1996.

[28] G. Michalke, et al., Control strategy of a variable speed wind turbine with mul-ti-pole permanent magnet synchronous generator, Proc.European Wind Energy Conference and Exhibition, Milan, Italy, May. 2007.

[29] Lennart, H. et al., Model-based current control of AC machines using the inter-nal model control method, IEEE transactions on industry applications, Vol.34, No.1, January 1998.


101

[30] Andreas P., Analysis, Modeling and Control of Doubly-Fed Induction Genera-tors for Wind Turbines, Ph.D. dissertation, Chalmers university of technology, 2005

[31] A. Pujante-lopez. et al., Performance comparison of a 2 MW DFIG wind tur-bine model under wind speed variations, Europ’spremier wind energy event , 2009.

[32] Robert, E. et al., Fundamentals of power electronics, second edition. Springer, 2001

[33] PSCAD/EMTDC, Manitoba HVDC Research Centre, available online: http://www.pscad.com/products/pscad/

102

A USER BUILT MODELS IN PSCAD

Park Transformation

Graphic view of the model:

Script of the model: $Is_alpha = TWO_3RD*($IsA - $IsB*0.5 - $IsC*0.5) $Is_beta = ($IsB - $IsC)*SQRT_1BY3

Clark Transformation Graphic view of the model:

Script of the model: $isD=cos($rho)*$Is_alfa + sin($rho)*$Is_alfa $isQ=-sin($rho)*$Is_beta + cos($rho)*$Is_beta

Inverse Park Transformation


Script of the model:

$IsA=($Is_alfa) $IsB=(-$ Is_alfa + SQRT_3*$Is_beta)*0.5 $IsC=(-$ Is_alfa - SQRT_3*$Is_beta)*0.5

A

B

C

3 to 2 Transform

alfa

beta

103

Inverse Clark Transformation


Script of the model:

$Is_alfa=cos($rho)*$isD - sin($rho)*$isQ $Is_beta=sin($rho)*$isD + cos($rho)*$is

www.elektro.dtu.dk/cet Department of Electrical Engineering Centre for Electric Technology (CET) Technical University of Denmark Elektrovej 325 DK-2800 Kgs. Lyngby Denmark Tel: (+45) 45 25 35 00 Fax: (+45) 45 88 61 11 E-mail: [email protected]

emt validation of fault-ride- through capabilities of …

Documents