Design, Control, Simulation and Energy Evaluation of a DC Offshore Wind Park

Andr Madeira Marques

Dissertao para obteno do Grau de Mestre em

Engenharia Electrotcnica e de Computadores

Jri:

Presidente: Prof. Paulo Jos da Costa Branco Orientador: Prof. Jos Fernando Alves da Silva Vogal: Prof. Joo Jos Esteves Santana

Setembro de 2009

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Acknowledgments

First, I would like to thank my supervisor in Chalmers University of Technology in Gteborg, Dr. Torbjrn Thiringer. I would also like to thank my VESTAS contacts, Dr. Lars Helle. Also to help finishing my supervisor in Portugal, Dr. Fernando Silva.

I also would like to thank my friends that gave me support and fun moments in 4 years in Tcnico and in the last one in ERASMUS in Chalmers, it was really a pleasure being with you!

Also I want to thank my mother, father and brother for giving me support, love and advice.

Andr Marques Lisbon September, 2009

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Resumo

Esta tese investiga as capacidades de controlo e produo de energia de um parque elico de 200MW DC, situado a 300km da costa. O dimensionamento e o controlo de velocidade e binrio da Gerador Sncrono de mans Permanentes (PMSG) feito para 3 conversores: o conversor elevador, o conversor de ponte completa e o Rectificador Trifsico Activo (ATR). O controlo de tenso e corrente explicado para o Conversor de Tenso (VSC) em terra que entrega potncia para a rede. Simulaes so feitas usando o MATLAB/Simulink. Clculos de Perdas so feitos para todas as velocidades de vento operveis.

O tempo de resposta do conversor elevador 8ms, 5ms para o ATR e 20ms para o conversor de ponte completa. Usando 12kV como tenso de sada, o conversor com menos perdas o ATR seguido pelo conversor elevador (ambos com 1%). Se a tenso de sada for 60kV, o melhor conversor o de ponte completa com controlo de factor de ciclo (1.62% potncia nominal).

O controlo de corrente do VSC em terra feito desacopulando Id e Iq para controlar a tenso do cabo submarino DC e a potncia reactiva entregue rede independentemente. O sistema responde rpido e aguenta perturbaes grandes e pequenas.

A melhor topologia para a rede DC ligando 5 turbinas em paralelo para 12kV, depois subir 60kV, e depois para 200kV, onde o cabo submarino transporta a energia para terra.

Palavras-chave: Parque Elico DC offshore, conversor elevador, conversor de ponte completa, Rectificador Trifsico Activo, Conversor de Tenso, Gerador Sncrono de mans Permanentes.

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Abstract

This thesis investigates the control capabilities and energy production of a 200MW DC wind park, placed 300km offshore. The design as well as the torque and speed control of the Permanent Magnet Synchronous Generator (PMSG) is done for three converters: the boost converter, the full bridge, and the Active Three-phase Rectifier (ATR). The voltage and current control is explained for the Voltage Source Converter (VSC) onshore that delivers power to the grid. Simulations are made using MATLAB/Simulink. Loss calculations are done for all wind speeds operable.

The response time for the boost converter is 8ms, for the ATR is 5ms and 20ms for the full bridge. Using 12kV as output voltage, the converter with less losses is the ATR followed by the boost converter (both around 1%). Using 60kV as output voltage the best converter is the full bridge using duty cycle control (1.62% at rated power).

The current control of the VSC onshore is done by decoupling Id and Iq to control the voltage in the DC submarine cable and the reactive power to the grid independently. The system responds fast and able to withstand small and large perturbations.

The best topology for the DC grid is connecting 5 turbines in parallel to 12kV, then to 60kV, then to 200kV, where a submarine cable transports the energy to shore.

Keywords: DC offshore wind park, boost converter, full bridge converter, Active three-phase rectifier, Voltage Source converter, Permanent Magnet Synchronous Generator.

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Table of Contents

Acknowledgments ..................................................................................................................2 Resumo ..................................................................................................................................3 Abstract..................................................................................................................................4 Table of Contents ...................................................................................................................5 Symbols .................................................................................................................................8 Glossary ...............................................................................................................................11 List of Figures ......................................................................................................................12 Chapter 1 Introduction.......................................................................................................14

1.1. Problem background Why wind power?..................................................................14 1.2. Why study offshore wind turbines? ............................................................................14 1.3. Why develop DC wind farms? ...................................................................................14 1.4. Layout of the Report ..................................................................................................15 Chapter 2 Background Theory and park specifications...................................................16 2.1. Aerodynamic principals of Wind Turbines .................................................................16

2.1.1. Power from the Wind ..........................................................................................16 2.1.2. Mechanical Power Extracted from the Wind........................................................17 2.1.3. Blade Pitching System.........................................................................................18 2.1.4. Pitch control........................................................................................................18 2.1.5. Model of the turbine and gearbox........................................................................19 2.1.6. Model of the generator ........................................................................................20

2.2. The problem specifications ........................................................................................21 2.2.1. Wind Park Specifications ....................................................................................21 2.2.2. Characteristics of the turbine ...............................................................................21 2.2.3. Characteristics of the Generator...........................................................................21 2.2.4. Characteristics of the Gear Box ...........................................................................22 2.2.5. Characteristics of the Transformers .....................................................................22

Chapter 3 Control Fundamentals........................................................................................23 3.1. Method of dominant pole ........................................................................................23

3.1.1. Setting ...........................................................................................................24 3.1.2. Setting the bandwidth of the system .................................................................24

3.2. Symmetry criterion method........................................................................................24 3.3. Method of Ziegler Nichols .........................................................................................26

Chapter 4 Torque control solutions ....................................................................................27 4.1. Boost converter connected to PMSG..........................................................................27

4.1.1. Description..........................................................................................................28 4.1.2. Sizing..................................................................................................................28 4.1.3. Control................................................................................................................28 4.1.4. Simulation Results: .............................................................................................30

4.2. Full Bridge Converter connected to the PMSG...........................................................32

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4.2.1. Description..........................................................................................................32 4.2.2. PMSG, transformer and full bridge converter ......................................................33 4.2.3. Sizing the output inductor and input capacitor .....................................................34 4.2.4. Control and determination of the controller parameters .......................................34 4.2.5. Simulation results................................................................................................36

4.3. PMSG with a ATR.....................................................................................................39 4.3.1. Determination of the LATR and Udc.......................................................................39 4.3.2. Control and Simulation .......................................................................................41

4.4. Efficiency calculation of the three previous converters...............................................42 4.4.1. 60kV Boost converter..........................................................................................42 4.4.2. 60kV Full Bridge ................................................................................................44 4.4.3. 60kV ATR ..........................................................................................................45

4.5. Conclusion:................................................................................................................46 Chapter 5 Speed and pitch control of the turbine................................................................48

5.1. Description: Presentation of the matlab model used ...................................................48 5.1.2. Block Turbine Model.......................................................................................49 5.1.3. Block Drive Train ............................................................................................49 5.1.4. Block PMSG and ATR ....................................................................................49 5.1.5. Block Speed Control........................................................................................49

5.2. Simulation .................................................................................................................50 5.3. Conclusion.................................................................................................................51

Chapter 6 - Control of the main inverter onshore ..................................................................52 6.1. Block diagram of the Plant .........................................................................................52 6.2. Inner Current Control.................................................................................................54

6.2.1. Determination of the voltage level on the primary side of the transformer ...........56 6.2.2. Determination of the PI parameters for the current control...................................57

6.3. Simulation of the system with current control ............................................................57 6.3.1. Test with Id and Iq coupled ..................................................................................59

6.4. Voltage control ..........................................................................................................60 6.5. Simulation of the voltage control for large perturbations ............................................61 6.6. Simulation of the voltage control for small perturbations ...........................................62 6.7. Conclusion.................................................................................................................63

Chapter 7 Analysis of the connection of the wind park.......................................................64 7.1. Best Connection: Parallel or Series?...........................................................................64

7.1.1. Wake effect .........................................................................................................66 7.2. Option 1: 6kV PMSG with ATR to 12kV...................................................................66

7.2.2. Loss calculation ..................................................................................................66 7.3. Calculation of the cable length ...................................................................................70

7.3.1. Length and resistance for 12kV cables ................................................................70 7.3.2. . Length and resistance for 60kV cables...............................................................71 7.3.3. Length and resistance for the main cable .............................................................73

7.4. Option2: 10kV PMSG with Full Bridge Converter to 60kV .......................................73 7.5. Energy production of the park....................................................................................74 7.6. Conclusion.................................................................................................................75

Conclusion: ..........................................................................................................................76 Future Work .....................................................................................................................77

References............................................................................................................................77 Appendix..............................................................................................................................79

Sizing of the components for the boost converter..............................................................79 Sizing of the components for the full bridge converter ......................................................79

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Sizing of the components for 2MW ATR..........................................................................80 Design and current control of the 2MW 60kV boost converter ......................................81 Design and current control of the 2MW 60kV full bridge converter ..............................82 Design and current control of the 2MW 60kV ATR ......................................................83 Parameters for the VSC onshore ...................................................................................83 Efficiency of the 2MW 12kV VSC and 200MW 200kV VSC onshore ..........................84 Efficiency of the 10MW 12/60kV and 200MW 60/200kV full bridge converters ..........84 Design, Control and efficiency evaluation of the 2MW 60kV boost converter with transformer ...................................................................................................................86 Design of the transformer for the full bridge converter..................................................86 Design of the Inductor ..................................................................................................88

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Symbols Bm rotating damping coefficient [Nmsrad-1] c scale parameter of the Weibull distribution Ci capacitance input capacitor in the full bridge converter [F] Conshore capacitance to be used onshore [F] Ctrl(s) transfer function representing the controller dynamics Cp Power coefficient

Depth_buried depth of the buried cable [m] Depth_sea depth of the sea [m] ed, eq voltages e1, e2, e3 in the dq frame [V] E Energy [J] Em peak line to ground voltage of the PMSG [V] e1, e2, e3 RMS voltage line to ground primary transformer onshore [V] Eproduced energy produced by the park in one year [Wh] Err reverse recovery energy of the diodes [J] f frequency of the PMSG [Hz] fcom switching frequency [Hz] ferated rated electrical speed of the PMSG [Hz]

( )vf Probability density function of the wind F(s) function transfer between V(s) and P(s) Ia current in phase a in the PMSG [A] id, iq currents i1, i2, i3 in the dq frame [A] IDC DC current that enters the VSC onshore [A] Idiode current in the diode [A] IIEGT current in the IEGTs [A] Ig current from the submarine cable [A] Iload current in the load of the converter [A] Iin input current [A] Iqnom rated current in the q axis [A] Iout output current [A] Isec current of the secondary of the transformer [A] Igroup1,2 current of the 12kV cables of group1,2 [A] iL current in the inductor [A] iL current variation in the inductor [A] i1, i2, i3 currents from the VSC to the grid [A] Jeq inertia seen from the generator side [kgm2] Jg inertia from the generator [kgm2] Jw inertia from the turbine [kgm2] K factor relating the time and fall times and switching losses k shape parameter of the Weibull distribution

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Kd derivative constant of the PID controller Ki integral constant of the PI or PID controller

Kp proportional constant of the PI or PID controller

KPcrit critical proportional constant

Kv modulator gain L inductance of the PMSG [H] LATR inductance in the AC side in the ATR [H] L(opt6) length of the cable in option6 [m] L(12kVopt1) length of the 12kV cables for option1 [m] L(60kVopt1) length of the 60kV cables for option1 [m]

edgeL5 Length of the 12kV cables of group 1 [m]

Lboost inductance of the inductor in the boost converter [H] Lcable cable length [m] Ld, Lq inductance of the generator in the dq-axis frame [H] Length_cable_buried Length of the cable buried [m] Lload output inductor inductance in the full bridge converter [H] LG1 cable length in group1 [m] Ltrans inductance of the transformer [H] m& Mass flow rate [kg/s] Mod(s) transfer function of the modulator dynamics n transformer ratio in the full bridge converter ng speed ratio of the gear box np number of pole pairs in the generator ns number of semiconductors in series p pressure of the air [Pa] P Power [W] Pavg average power of the wind park [W] PCDiodes conduction losses in the diodes [W] PCIEGT conduction losses in the IEGT [W] Pfriction friction power [W] Pmain_cable ohmic losses in the main cable [W] Pmech mechanical power in the turbine [W] Pnom rated power [W] Pclusters1in input power in the clusters 1 [W] Pgroup1 power in group1 [W] PlossesDRc conduction losses in the diode rectifier [W] PlossesDRs switching losses in the diode rectifier [W] Pohmic12kV ohmic losses in the 12kV cables [W] Pohmic60kV ohmic losses in the 60kV cables [W] Pout electric power of the PMSG [W]

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Ptrans power losses in the transformer [W] P(s) dynamic perturbation

( )vP Power curve of each turbine [W] Q Reactive Power [Var] Pw Power from the turbine [W] R gas constant [m3PaK-1kg-1] Rb Radius of the rotor [m] Ra resistance of the PMSG in the stator windings [] Rcable resistance per length of the cable [/m] Rgroup1,2 total resistance of the 12kV cables of group1,2 [] RL resistance of the inductor [] Rload output resistance [] Rtrans resistance of the transformer [] Rsec resistance of the secondary of the transformer [] S Cross section area of the cable [m2] T switching period [s] Tair Temperature of the air [K] TCcrit critical period of the oscillations [s] Td time constant of the derivative part in the controller [Nm] Te Electromagnetic Torque [Nm] tf fall time of the semiconductor [s] Ti time constant of the integral part in the controller [Nm] Tower Height of the tower [m] tr rise time of the semiconductor [s] Tw torque in the turbine side [Nm] Tw_g Aerodynamic torque in the turbine from the generator side [Nm] Tz time constant of the zero of the PI controller [s] U, U Alpha and Beta Voltages [V] Ub voltage line-to-line base [V] Uc control voltage [V] Udiode ON voltage of the diode [V] ud, uq voltages u1, u2, u3 in the dq frame [V] Udc DC voltage for the VSC onshore and offshore [V] Uin input voltage of the converter [V] UP voltage across the switch in the boost converter [V] Urated, Prated Rated voltage and Power of the PMSG [V, W] Uqnom rated voltage in the q axis [V] Uo output voltage in the converter [V] u1, u2, u3 RMS voltage line to ground after the VSC onshore [V] v wind speed [m/s]

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v Average wind speed [m/s] VIEGT ON voltage of the IEGT [V] Vref(s) reference of the variable to be controlled V(s) variable to be controlled Zb impedance base [] duty cycle pitch angle [degrees] Tip speed Ratio damping factor copper resistivity of the copper [m] air air density [kg/m3] time constant of Mod(s) [s] flux in the permanent magnets in the rotor [Wb] e angular electrical speed of the PMSG [rad/s] erated rated angular electrical speed of the PMSG [rad/s] grid angular frequency of the grid [rad/s] m angular speed of the generator from the generator side [rad/s] n frequency of the oscillations [rad/s] ref reference speed for the turbine [rad/s] t turbine speed from the turbine side [rad/s] rotor mechanical speed of the rotor from the generator side [rad/s] Z gain of the series of Mod(s) and F(s)

Glossary

ATR Active Three Phase Rectifier

DR Diode Rectifier FD Freewheeling Diodes IEGT Injection Enhanced Gate Transistor IGBT Insulated Gate Bipolar Transistor PMSG Permanent Magnet Synchronous Generator PWM Pulse Width Modulation SVPWM Space Vector Pulse Width Modulation T1 Single Phase Transformer VSC Voltage source converter (in this thesis it is done with IEGT) WS Wind Speed

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List of Figures

Fig. 2.1 Cp as function of and . Fig. 2.2 Power curve that will be followed by the pitch angle control. Fig. 3.1 Block diagram used in the method of the dominant pole. Fig. 3.2 Block diagram simplified. Fig. 3.3 Block diagram using the symmetry criterion. Table 3. 1 Ziegler-Nichols and Tyreus-Luyben tunning rules. Fig 4.1 Diagram with the first implementation using the boost converter. Fig 4.2 Current control block used in the simulation of the boost converter. Fig 4.3. Block diagram representing the dynamics of the system. Fig 4.4 Inductor current Response. Fig 4.5. Voltage and Current in the diode. Fig 4.6. Voltage and Current in the IEGT. Fig 4.7. Currents Ia, Iq and Id in the stator in the PMSG and electromagnetic torque. Fig 4.8. Full bridge converter used in this application. Fig 4.9 Schematic of the inverter. Fig 4.10 Phase shift control block. Fig 4.11 Waveforms for the control of switch 1 and switch 3 (switches 2 and 4 are the negative). Fig 4.12 Step response of the full bridge with different controllers. Fig 4.13 Input voltage, control voltage Uc and input and output currents of the full bridge converter. Fig 4.14 Stator Ia, Iq, Id and electromagnetic torque of the PMSG. Fig 4.15 Voltage Vp and the current in the primary side of the transformer. Fig 4.16 Current in the Rectifier1 and in the IEGTs. Fig 4.17 Equivalent electric circuit. Fig 4.18 Simulation model to determine the maximum percentage of voltage harmonics. Fig. 4.19. Current control for Id and Iq in the ATR. Fig. 4.20. PMSG measurements with the ATR control. Table 4.1 Losses for all wind speeds for the diode rectifier plus boost converter to 60kV. Table 4.2 Losses for the full bridge converter to 60kV using phase shift control. Table 4.3 Losses for the full bridge to 60kV using duty cycle control. Table 4.4 Losses for the 60kV ATR. Fig. 4.21. Losses for the three converters discussed in this chapter in percentage of transmitted power. Fig. 5.1 Simulink model for the simulation of the one turbine. Fig 5.2 Frequency reference and the frequency of the generator. Fig 5.3 Electric power in generator and mechanical power in the turbine. Fig 6.1 Wind park from the submarine cable to the grid. Fig 6.2 Electric circuit that represents the wind park from the submarine cable to the grid. Fig 6.3 Simplified electric circuit. Fig 6.4 Block diagram of the Plant, relating Ud and Uq with Id and Iq. Fig 6.5 Block diagram with the Current Control System and the Plant. Fig 6.6 Block diagram with the Plant and the Current Control System altered in order to de-couple Id and Iq. Fig 6.7 Block diagram with Id and Iq de-coupled. Fig 6.8 Id and Iq using the Simulation Model. Fig 6.9 Transient of Id zoomed in. Fig 6.10 Transient of Iq zoomed in.

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Fig 6.11 Id and Iq with the control system with Id and Iq coupled, Fig 6.5. Fig 6.12 Transfer Function of the Current Control System and the Plant (Fig 6.6) in close loop. Fig 6.13 Circuit with the currents and Voltages used in the voltage control system. Fig 6.14 Block diagram with Voltage control in close loop. Fig 6.15 Id response simulated in Simulink (Large perturbations). Fig 6.16 UDC response simulated in Simulink (Large Perturbations). Fig 6.17 UDC response simulated in Simulink for small Perturbations. Fig 6.18 Idref response simulated in Simulink for small Perturbations. Fig. 7.1 Proposed connections for the Wind park. Fig. 7.2 Losses for 12kV converters in this thesis. Table 7.1 Losses for the 12kV converter, currents and power in the 2 groups. Table 7.2 Losses for cables and 12/60kV full bridge converter. Fig. 7.3 Losses for the 12/60kV converter. Fig. 7.4 Losses for the 60/200kV converter. Table 7.3 Losses in the main cable, VSC onshore and output power of the park. Fig. 7.5 Losses in the VSC onshore. Fig. 7.6 Representation of one quarter of the wind park. Each circle is one turbine. Fig. 7.7 Representation of half of the wind park. Table 7.4 Losses for 60kV converters and currents in both groups. Table 7.5 Losses in the 60kV cables, 60/200kV converter and in the main cable. Fig. 7.8 Efficiency of the whole park using option1 and option2. Fig. A.1 Dimensions of the single-phase transformer. Fig. A.2 Total Losses and relative price for the transformer for the best iron area. Fig. A.3 Dimensions of the Inductor.

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Chapter 1 Introduction 1.1. Problem background Why wind power?

Nowadays there is a huge demand for electric power in order for societies to develop. In countries with quickly growing economics like China and India where the electricity consumption is increasing exponentially daily, there is a necessity for reliable and cheap sources of electric power.

The usual sources have a huge problem that cannot be hidden: they cause very serious environmental problems like green house effect on the long run. An alternative that doesnt have this problem is wind power.

1.2. Why study offshore wind turbines?

In most of the western European countries there is already a great utilization of wind power inland. There are so many wind turbines operating that there is a lack of space in land for wind power to continue to increase. Also too many wind turbines inland have the problem that they can spoil the view of the landscape.

For these reasons engineers all over the world start to focus their attention to place wind turbines offshore. Offshore turbines have a lot of advantages over inland turbines: the wind offshore is more constant and has higher effective speed over the year, there is space in the North Sea and Atlantic Ocean more than enough to supply the consumers, there is no spoil in the landscape, no people live nearby to be affected by the noise. More energy can be extracted, with less environment problems compared to what inland turbines have. Studies even say that offshore turbines are beneficial for the fauna in the sea. The great downside is that installing turbines offshore is much more expensive than inland, but bigger turbines can be installed.

1.3. Why develop DC wind farms?

Studies show the wind speed is higher and more constant in a reasonable distance from the shore. Also people cannot see the turbines when they are placed far from the shore.

When the distances are too large, if all wind turbines are connected in an AC connection there is a problem of reactive power created that lowers the power factor. If the connection is DC instead, there is no reactive power and the frequency in the generators can be independent from the onshore grid frequency. The cable resistance of a DC cable is lower than an AC cable for the same cross section leading to lower losses. With the development of power electronic semiconductors like Insulated Gate Bipolar Transistor (IGBT) and Injection Enhanced Gate Transistor (IEGT) the active and reactive power delivered to the grid can be controlled like in an AC wind farm.

The downside is that nowadays the efficiency of the transformers to raise the voltage is above 99% while the efficiency of DC/DC converters is lower. A DC wind farm will have more losses than a conventional AC park.

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1.4. Layout of the Report

This thesis is going to design, control the torque and speed, simulate and compute the efficiency of 3 converters for 12kV and 60kV DC. These are connected to the PMSG, and they will be compared in order to find the best one to use in a DC offshore wind farm.

With the efficiency data computed, the losses in the whole park are known and thus the efficiency. This will be done for two grid topologies, with two and three voltage levels. They will be compared in order to determine the best efficiency. The yearly energy produced by the park is computed with the wind speed distribution that is assumed to be a Rayleigh distribution with an average wind speed equal to 10 m /s.

In chapter 2 some aerodynamic principals are presented, and the modelling of the PMSG and wind turbine is done. It is also displayed the problem specifications and the characteristics of the equipment used. In chapter 3 the control theory necessary to explain the control strategies ahead is exhibited.

In chapter 4 the torque control, simulation and efficiency calculation are done for the 3 converters: the boost converter, the full bridge converter and the ATR. In chapter 5 is performed the speed control for the same previous three converters.

In chapter 6 the voltage and reactive power control is conducted for the VSC onshore. In chapter 7 the best configuration for the park grid is investigated with the goal to minimize the losses, for all wind speeds. With these results the yearly energy production is computed.

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Chapter 2 Background Theory and park specifications

In this section a model for static and dynamic approach of a wind turbine is developed. For the development of a control of the speed turbine for maximization of power extracted from the wind, the dynamic modelling approach is chosen.

In the first section Aerodynamic principals of Wind turbines the equations that give the Cp, and power from the wind are given.

In the second section Model of the Wind turbine and gearbox, the equations that give the Turbine Torque, Turbine Power and Turbine Speed are presented.

In the third section Model of the PMSG the equations that relate voltage, current and electrical speeds and the equation that gives the electromagnetic torque of the PMSG are presented.

2.1. Aerodynamic principals of Wind Turbines

2.1.1. Power from the Wind

The kinetic energy of the air with mass m and speed v is:

2

21

mvE = . (2.1)

The power is:

2

21

vmdtdEP &== . (2.2)

Where m& is the mass flow rate. When the air passes across an area A, in this case the area swept by the

rotor blades, the power of the air will be:

323

21

21

vRAvP bairair pi == . (2.3)

Where Rb is the radius of the blades, and air is the air density. It will vary with air pressure and temperature along with:

airair RT

p= . (2.4)

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Where p is the pressure, Tair the temperature and R the gas constant. At sea level at a temperature of

Tair=288K=30C, it will have the value air =1.225kg/m3. This will be the value considered in this thesis.

2.1.2. Mechanical Power Extracted from the Wind

In [1] it is explained that no energy converter can extract all the energy of the wind into mechanical energy. The efficiency of this energy conversion is the coefficient Cp. This coefficient depends on two parameters: the tip-speed ratio and the blade pitch angle . The tip-speed ratio is defined as:

v

Rbt = , (2.5)

where Rb is the radius of the blade, t is the angular speed in the turbine side, and v is the wind speed. The blade pitch angle is defined as the angle between the plane of rotation and the blade cross-section

chord. Cp for a three bladed-rotor can be computed with:

=

5.12exp54.011622.0pC . (2.6)

1035.0

08.01

1

3 +

+

=

(2.7)

In [1] and in Fig.2.1 is seen that the best Cp possible for the three-bladed rotor is =7. For this reason, except when the wind speed is higher than the rated speed, the turbine speed is going to be controlled to ensure that is 7 for medium and low wind speeds. This procedure maximizes Cp and consequently maximizes the power that can be converted into mechanical energy from the wind.

Fig. 2.1 show Cp as a function of and .

Fig. 2.1 Cp as function of and .

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It can be seen that in order to maximize Cp the pitch angle should be as low as possible, for example 2 degrees like in Fig. 2.1 and in [2]. This will be possible unless the wind speed is higher than the rated speed as explained in the next section.

2.1.3. Blade Pitching System

There are two ways of controlling the amount of mechanical power extracted from the wind: the stall and pitch control. The first is used in fixed-speed turbines and the second in variable speed turbines.

In many previous works it was concluded that the pitch control has numerous advantages over stall control, like less noise and less power fluctuation. For these reasons, in this thesis only variable speed turbines with pitch control are studied.

2.1.4. Pitch control

This control system consists of having a motor that according to the direction and speed of the wind will position the blades in order to get the reference mechanical power. This reference power varies as a function of the wind speed as described in Fig. 2.2 :

Fig. 2.2 Power curve that will be followed by the pitch angle control.

This figure was taken from [6], which is a wind turbine model with the desired rated power for the turbines of the wind park in study: 2 MW. The wind turbine will start operating at 4m/s and stops rotating at

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25m/s. It can be seen in the figure that for the lowest sound level the rated speed will be 15m/s, but for the highest sound level the rated speed is 12m/s. As these turbines will be placed 300km from the shore, almost nobody will hear them. So the rated speed will be chosen to be 12m/s, more power can be extracted at medium wind speed.

In order for the turbine profile to follow Fig. 2.2 , the following steps must be taken: -for wind speeds lower than 12m/s (this value for the rated wind speed was chosen in [6]), the goal is to

extract the maximum power possible from the wind, so Cp should be maximum, equal to 0.4. From Fig. 2.1 it is obtained =7 and =2.

-for wind speeds higher than 12m/s, Cp is should be lowered in order for the power from the turbine to be constant and equal to its nominal value, in this example 2 MW.

The control of the maximum extraction point will follow these rules. From (2.3)(2.3.) it is known:

33232650

225.140222

vv

MWvR

PCb

mechp =

==

pipi. (2.8)

Since the rated power of the turbine is 2MW, the mechanical power will have to be a bit higher than 2MW to take into account the mechanical and electrical losses. Those losses were computed in latter simulations, and knowing the electric power (2MW) the mechanical power is known and thus the constant that relates wind speed and Cp in (2.8). However the results wont be altered significantly by the losses.

2.1.5. Model of the turbine and gearbox

The turbine mechanical system could be considered as a two mass lumped system; if the mechanical stresses in the shaft are to be studied (detailed models are needed). However, here a rigid shaft is considered.

Between the wind turbine and the generator there is a gear box to raise the speed and decrease the torque in order for the generator to be smaller (lower torque gives lower current which gives lower losses). Newtons law of motion for this system gives:

( )mmgweeq

m BTTJdt

d

=

_

1 (2.9)

Where m is the angular speed of the shaft in the generator side, Te is the electromechanical torque in

the generator, Tw_g is the aerodynamic torque from the turbine seen from the generator side, Bm is the rotating damping coefficient and Jeq is the inertia seen from the generator side as well. Jeq and Tw_g can be computed as:

2g

wgeq

n

JJJ += . g

wgw

n

TT =

_

. (2.10)

Where Jg is the inertia of the generator, Jw is the inertia of the turbine, ng is the speed ratio of the gear box, and Tw is the torque in the turbine side. This torque, with Cp and computed, can be calculated as:

20

pip

bw

CvRT

23

21

=

. (2.11)

And the power from the turbine can be computed as:

wtw TP = . tgm n = . (2.12)

The reference frequency for the generator is:

pgb

ref nnRv

= . (2.13)

where ng is the speed ratio of the gear box and np is the number of pole pairs in the generator. As a conclusion, the turbine is modelled using Newtons equation. The Cp and give the torque and the

reference speed of the turbine. The reference speed will give the current that will give the torque Te from the generator. With this torque and the torque from the turbine Tw_g, with the Newton equation, the speed can now be computed.

2.1.6. Model of the generator

In this thesis the generator could be the Synchronous Generator, either wound or with permanent magnets. However, from now forward only the option of permanent magnets is going to be used.

In [2] it is explained the background theory. The dynamics of this generator is derived using the two-phase synchronous frame, where two axes are considered the d axis aligned with the rotor position and the q axis which is 90 ahead of the d-axis.

Applying Faradays Law to the three windings in the stator, three equations will be obtained. Applying Parks Transformation to these equations the following can be obtained:

+

+=

++=

qqq

dq

deq

q

aq

dd

qd

qed

d

ad

uLL

iLL

iLR

dtdi

uL

iLL

iLR

dtdi

11

1

(2.14)

where id, iq, ud, uq, Ld and Lq are the currents voltages and inductances in the d-axis and q-axis respectively, Ra is the resistance in the stator windings and is the flux in the permanent magnets in the rotor. For many PMSG, Ld=Lq=L [17]. Then, it will become:

21

+

+=

++=

qdeqaq

dqedad

uLL

iiL

Rdtdi

uL

iiLR

dtdi

11

1

. (2.15)

The electromagnetic torque is computed using:

( )( ) qpdqde iniLLT +=. (2.16)

2.2. The problem specifications

2.2.1. Wind Park Specifications

In this section the specification given for the wind park to study are displayed.

Distance to the shore: 300km.

Nominal power: 200MW.

Number and disposal of turbines: 100 turbines disposed 10*10 squared, each turbine apart of 400 meters.

Nominal power of each turbine: 2MW.

2.2.2. Characteristics of the turbine

Cut-in wind speed: 4m/s

Nominal wind speed (2000kW): 12m/s Cut-out wind speed: 25m/s

Rotor diameter: 80 meters

2.2.3. Characteristics of the Generator

The generator used is going to be a PMSG (Permanent Magnet Synchronous Generator). It will have the following characteristics, taken from [2].

425.0

008.0

=

=

=

p

a

n

puLpuR

.

Nominal Power: 2MW Nominal Frequency: 100Hz

rotor=

pn

fpi2 =

41002pi

=157rad/s

22

The nominal voltage will differ from case to case. It can be a low voltage generator; in this case it will present 690V. It can be a high voltage generator; in this case it could be 5kV. Ra is the stator resistance, L is the stator inductance, np is the number of pole pairs.

For the 690V PMSG, Ra=2m and L=0.09mH. For the 5kV PMSG, Ra=100m and L=5mH.

2.2.4. Characteristics of the Gear Box

The inertia seen from the generator side, Jeq in (2.9) is Jeq=8000 kgm2, and includes the turbine inertia and the inertia of the generator. The turbine data used is the same as in [2]. In [3] the gear box losses are estimated in 3%. This means:

12

2

43.2157

03.02%3 ==== NmsradMWBP

BP

Pm

nom

rotorm

nom

friction (2.17)

In [2] the speed ratio of the gear box used is ng = 77. This value will be used in this thesis.

2.2.5. Characteristics of the Transformers

The three phase transformers that will be used in this thesis will have in each side: Rtrans=0.002pu Ltrans=0.05pu The single phase transformers will have leakage inductance 5% total. The frequency can be 100Hz or

400Hz.

23

Chapter 3 Control Fundamentals

In this thesis the control of power electronics equipment such as IEGTs converters is going to be used. For this reason in this chapter a brief description of the control methods will be given.

In this thesis the current, the voltage or the speed will be controlled, depending of the used converter. Considering the block diagram that describes the dynamics of the system and the problem, different control methods need to be used. The methods that will be used in this thesis will be three: the method of dominant pole, the method of symmetric criterion and the Ziegler-Nichols method.

3.1. Method of dominant pole

The method of dominant pole is the simplest method, and it is used only for the current control in Chapter 6. In this case the block diagram of the system is presented in Fig.3. 1 :

Ctrl(s) Mod(s) F(s)

P(s)

Vref(s) V(s)

+

-

-

+Ctrl(s) Mod(s) F(s)

P(s)

Vref(s) V(s)

+

-

-

+

Fig.3. 1 Block diagram used in the method of the dominant pole.

V(s) is the variable to control (in the current control of chapter 6 Id and Iq), and Ctrl(s) is the function transfer of the controller, in this case a PI controller. Mod(s) is the function transfer of the modulator which is all cases in this thesis a first order function. F(s) is the function transfer between the perturbation and the variable to control. P(s) is the perturbation (the voltage in the grid). As this voltage is constant, it can be removed from the block diagram. The block diagram will be as in Fig.3. 2 :

Ctrl(s).Mod(s).F(s)Vref(s)V(s)

-

+Ctrl(s).Mod(s).F(s)Vref(s)

V(s)

-

+

Fig.3. 2 Block diagram simplified.

F(s) in the figure is a first order function where the pole is not close to the origin. Otherwise, this method cannot be used, as it will give unstable responses. The method of dominant pole is to place the zero of the PI controller in the dominant pole, which will be in the case of Chapter 6 s=-Rtrans/Ltrans, where Rtrans is the transformer onshore resistance and Ltrans is the transformer onshore inductance. This will give:

24

trans

trans

p

i

LR

KK

=

. (3.1)

With one equation and two parameters to compute there are two strategies to determine the parameters.

3.1.1. Setting

The close looped system will be a second order system. The of the system will be 0.707 for the optimum transient in overshoot and rise time, and with this Kp and Ki are computed.

3.1.2. Setting the bandwidth of the system

The other method is to neglect the pole from the modulator dynamics, and thus consider the system to be a first order system. However this can only be done if the poles are not to far away from the real axis. The cut off frequency of the system in close loop shall be chosen, usually 7 to 10 times longer than the frequency of the system. In this way Kp will be computed. From the equation above, Ki will be computed.

3.2. Symmetry criterion method

More in-depth information about this method in the applications of electric motor control can be found in [4]. In this thesis it is not motors which are being controlled, but power electronic converters. However, the block diagram of both will be the same, so the same method can be used. For example, the speed control of the PMSG with ATR in Chapter 5 will be used, and the voltage control of the voltage in the submarine cable in the Chapter 6 will be used as well. Generally, the block diagram of the system to control will be as presented in Fig.3. 3 :

Fig.3. 3 Block diagram using the symmetry criterion.

Mod(s) in Section 4.1.3. is the modulator dynamics, in Chapter 6 and in Chapter 5 will be the current control dynamics. F(s) will be 1/ (sLboost) in Section 4.1.3. 1/(sJeq) in Chapter 5 and 1/(sConshore) in Chapter 6, but it will be similar mathematically. Only when P(s) can be considered to vary too slowly in the time scale of the dynamics of the system, P(s) can be considered to be zero. In this case the method of dominant pole can be used.

Ctrl(s) Mod(s)

F(s)P(s)

Vref(s)+

-

-

+F(s)Ctrl(s) Mod(s)

F(s)F(s)P(s)

Vref(s)+

-

-

+F(s)F(s)

25

However, if large perturbations arise, P(s) needs to be accounted for (for example in Chapter 6). In these cases the method of symmetric criterion should be used instead. The function transfer of the close looped system will be:

( ) ( ) ( )( ) ( ) ( )( )

( ) ( ) ( )sPsFsModsCtrlsF

sVsFsModsCtrl

sFsModsCtrlsV

ref )(1)(1)(

+

= (3.2)

Because the minus sign is in the action loop in Fig.3.3. Kp and Ki should be negative for the system to be stable (only in the speed control this does not happen and so the parameters will be positive). Renaming:

( ) ( )sHsFsModsCtrl =)()( .(3.3) Then:

( ) ( )( ) ( )( )

( ) ( )sPsHsF

sVsH

sHsV

ref+

++

=

11 (3.4)

( )( )

( ) ( )( ) ( )sPsHsF

sV

sH

sVref +

++

=

111

1. (3.5)

As -H(s) has already a pole in the origin, a P controller was used [4] to guarantee steady state error equal to zero, so Ki=0. In this case the zero of the PI regulator will cancel the pole of G(s). Doing the calculations the function transfer between V(s) and Vref(s) will be a second order system:

( ) ( ) ( )sVsssV refnnn

sP 22

2

0 2

++=

=

(3.6)

Doing the calculations with =0.707, the following equation will be derived:

ZK p 2

1= . (3.7)

Where is the time constant of Mod(s) and Z is the gain of the cascaded Mod(s) and F(s). It will be the inductance in the boost converter in Section 4.1.3., the inertia seen from the PMSG in Chapter 5, the Capacitance of the capacitor between the submarine cable and the VSC on-shore in Chapter 6.

When s=0, V(s) follows the reference but it will have a error from the disturbance, because F(s)/(H(s)+1) doesnt lead to zero when s=0. A PI controller is needed to solve this matter [2]. In this case, it can be seen doing the computations that V(s) will follow the reference and the perturbation wont have influence on it (it will appear a zero in the origin in F(s)/(H(s)+1), which is the goal. Doing various simulations with many values of Ki, the best value that will give fast response to the perturbation is with Tz/ =4, where Tz is the time

26

constant of the zero from the PI controller. However this parameter will give an overshoot of 43%. A first order filter in the reference with time constant equal to Tz will reduce the overshoot to acceptable values while maintaining good responses. With this value doing the calculations, Ki will be:

281Z

K i = (3.8)

3.3. Method of Ziegler Nichols

For this method the information was taken from [5]. The method of Ziegler Nichols is a set of rules for obtaining the values of the regulators, obtained empirically from simulation studies. In this thesis it was used only for the current control of the full bridge converter. From the two possible Ziegler Nichols methods the method of stability margin was selected.

The first step is to consider the regulator to be a P controller, and continuously increasing the gain until the response is unstable. The gain where the response will become unstable will be called KPcrit. Then the period of the oscillations when the gain is KPcrit will be measured, and it will be called TCcrit.

With these two values, depending on if the regulator will be a PI or PID, or the method used is the Ziegler Nichols or the Tyreus-Luyben, the parameters Kp, Ti and Td will be computed using Table3. 1:

Table3. 1 Ziegler-Nichols and Tyreus-Luyben tuning rules.

Controller parameters (Ziegler-Nichols) Controller parameters (Tyreus-Luyben) Type of controller Kp Ti Td Kp Ti Td

PI 0.45KCcrit 0.85TCcrit - KCcrit/3.2 2.2TCcrit -

PID 0.6KCcrit 0.5TCcrit 0.12TCcrit KCcrit/2.2 2.2TCcrit TCcrit/6.3

Ki and Kd can be computed from Kp, Ti and Td:

=

=

dpd

i

pi

TKKTK

K (3.9)

Its important to know that the response obtained by the Ziegler Nichols Method is acceptable, but not optimal. It means that there can be other responses that are even faster and with less overshoot than the one obtained in the Ziegler Nichols Method.

27

Chapter 4 Torque control solutions

In this chapter the sizing, control, simulation and efficiency analysis of several solutions for torque control of the PMSG are presented. The techniques for the determination of the control parameters were announced in Chapter 3. The calculation of losses will be presented to determine the efficiency of each converter.

The three DC/DC converters analysed here are in order of appearance: the boost converter, the full bridge converter, and the ATR (Active Three-Phase Rectifier) with IEGTs.

These converters were chosen to raise the voltage from the low level in the PMSG to a high level suitable for transmission. Because of this, all the following converters will have an output voltage higher than the input voltage. Also, in this thesis the electrical grid will be as a constant voltage grid.

The rated voltage in the PMSG can be 690V or 5kV, but the level of the output voltage in the three converters is always the same: 60kV. This value will be used later in Chapter 6 for the determination of losses in the whole park in option 2. The output voltage in the simulations for the three converters will be considered constant, because it is controlled by the DC/DC converter that will raise the voltage from 60kV to 200kV, a voltage level suitable to transport the whole power from the park (200MW) across 300 km until the shore.

The IEGTs are chosen to be used as switches because they can withstand high voltage (4.5kV) and high currents (750A) when the converter doesnt need a lot of current it is assumed the IEGT with the same voltage but lower current, has shorter switching times. The data sheet is in [18]. For the diodes the data sheet is in [21].

The first converter described in this section is the simplest of the kind of voltage source converter, for the purpose to raise the voltage. It is called boost converter (step-up converter).

4.1. Boost converter connected to PMSG

The first application is to use a PMSG of 690V, followed by a three phase diode rectifier, and a boost converter that raises the voltage from 931V to 60kV. The schematic of this system is shown in Fig. 4.1.:

wrotor

rated speed

Continuous

pow ergui

A

B

C

+

-

Universal BridgeRload

Tm

mA

B

CPermanent Magnet

Synchronous Machine

L

Iref

g CE

IEGT

Diode

Idc

IrefOut

Current_Control

i+

-

Current Measurement1

Cout

iL

Fig 4.1 Diagram with the first implementation using the boost converter.

28

However is not possible to raise the voltage from 690V to 60kV because the duty cycle of the converter will be very close to 1. This will lead to very low efficiency, close to 3.5%. This is unacceptable.

4.1.1. Description

The maximum ratio for the voltage raise in the boost converter is 4 times approximately [7], therefore a three phase transformer next to the PMSG to raise the voltage must be used.

In all configurations the speed in the PMSG is considered to be constant (and equal to the rated speed) because in the time scale of the dynamics of the system, the speed is constant due to the fact the mechanical time constants are much higher than the electric ones.

4.1.2. Sizing

The PMSG can have a nominal voltage of 5kV or 690V. The transformer, depending of the case, raises it from 5kV or 690V (the values used in this thesis, in Section 2.2.3.) to 35kV. It has 0.002pu of resistance and 0.05pu of inductance on the primary and secondary side. In this case, the boost converter will raise the voltage from 35kV*1.35=47kV (due to the diode rectifier) to 60kV.

The dimensioning of the inductor Lboost must be done in order to guarantee that the current ripple will be less than 10% of the nominal current. From [7] the following formula can be extracted:

( ) ( )H

MWfUUUU

ifUUUU

Lcomo

inoin

Lcomo

inoinboost 3.221.0

2

=

=

= . (4.1)

Where Uin=47kV, Uo =60kV, fcom=1000Hz.

4.1.3. Control

Usually it is desired to control the current in the inductor, or the input voltage of the converter. In this case it is necessary to control the input current to control the torque of the generator as they are proportional (as large and sudden variations in the torque can provoke too much mechanical stresses in the shaft of the PMSG) and to protect the semiconductors in case of short-circuits.

The output of the regulator, the control voltage Uc determines the right duty cycle in order for the inductor current to achieve the desired result. Uc is compared with a carrier wave having a much higher frequency. It can be triangular, or saw-tooth type. This comparison can be done digitally in a microprocessor or analogically by an AMPOP.

A saw-tooth signal from 0 to 10V with frequency 1 kHz will be used as a carrier. The frequency could be higher, but that would lead to too high switching losses. The current control block is presented in Fig 4.2. :

29

1Out

Modulator

PI

DiscretePI Control ler

2Iref

1Idc

Fig 4.2 Current control block used in the simulation of the boost converter.

Writing the equation for the inductor gives:

dtdi

LiRUU LboostLLpin += . (4.2)

Where Uin is the voltage after the diode rectifier bridge, Up is the voltage across the IEGT, RL is the resistance of the inductor, Lboost the inductance, iL is the current in the inductor. Using the Laplace transformation it is found:

sLRUU

IboostL

pinL

+

= . (4.3)

Uc enters the modulator. It has a statistic delay, which normally is considered to be half of the switching period. It has also a gain. This gain can be computed in [7] and for the boost converter it is equal to:

600010

6000010max

====

=

VV

VU

u

Uu

UK o

c

o

c

pavv . (4.4)

With the modulator dynamics together with (4.3) the complete block diagram representing the dynamics of the system is presented in Fig 4.3. Block diagram representing the dynamics of the system. :

Fig 4.3. Block diagram representing the dynamics of the system.

30

In Fig 4.3. the pole s=-RL/Lboost is very close to the origin, because RL is dimensioned as small as possible in order for the inductor to have as low losses as possible. If the technique to place the zero of the PI controller near this pole is used, this can lead to instabilities problems as mentioned in Chapter 3. For this reason the symmetry criterion will be used. The low-pass filter in the reference is used to decrease the overshoot and

(3.7) and (3.8) are used to compute the parameters of the controller, presented again in (4.7.). is the time constant of the modulator dynamics, in this case half of the switching period. Remembering the minus sign in the action loop in Fig 4.3. the following expressions are found:

==

==

4008

395.02

2v

boosti

v

boostp

KL

K

KL

K

. (4.5)

4.1.4. Simulation Results:

The simulation is shown below. The step time for the current reference is at 0.03s. The result is shown in Fig :

0.02 0.025 0.03 0.035 0.04 0.045 0.0510

15

20

25

30

35

40

45

50

55

60

indu

ctor

cu

rren

t(A)

time(s)

Fig 4.4 Inductor current Response.

Looking at Fig 4. the response takes 8 ms to follow the reference without steady state error, as the current in the inductor in the nominal power should be 2MW/47kV=42A. The overshoot is 10%. The current ripple is 10% as desired in the inductor sizing. The voltage and current for the Diode and IEGT are in Fig 4.5. and Fig 4.6.

31

0.025 0.03 0.035 0.04 0.045 0.05-10

0

10

20

30

4050

dio

de cu

rre

nt(A

)

0.025 0.03 0.035 0.04 0.045 0.05

-60

-40

-20

0

dio

de vol

tage

(kV)

time(s)

Fig 4.5. Voltage and Current in the diode.

0.025 0.03 0.035 0.04 0.045 0.05

0

20

40

60

80

IEGT

c

urre

nt(A

)

0.025 0.03 0.035 0.04 0.045 0.05

0

20

40

60

IEGT

vo

ltage

(kV)

time(s)

Fig 4.6. Voltage and Current in the IEGT.

Looking at Fig 4.5. and Fig 4.6. the IEGTs and diodes have a current of 42A and voltage of 60kV as expected. Fig. 4.7. presents the evolution of the most important generator variables:

32

0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-50

0

50

Ia(A

)

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-60

-40

-20

Iq(A

)

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-40-20

02040

Id(A

)

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-20

-10

0

time(s)

Torq

ue(kN

m)

Fig 4.7. Currents Ia, Iq and Id in the stator in the PMSG and electromagnetic torque.

It is seen that at 30ms, when the current reference has a step, all generator variables change. It means that the current controller is controlling the generator currents and therefore the generator torque. It can be seen that Iq and the torque are proportional as expected. The current is not sinusoidal; Id is not constant and has a small average value that is due to the diode bridge conduction overlap. This will cause additional losses in the PMSG and lowers the power factor, which means that the PMSG will be more expensive.

4.2. Full Bridge Converter connected to the PMSG

4.2.1. Description

In this section the full bridge converter is going to be described for the application of raising the 690V from the PMSG to 60kV, like in the boost converter section.

The full bridge converter can implement voltage or current sources. In the voltage case it should have a capacitor on the input and an inductor on the output. The purpose of the inductor is to smooth the current in the output and consequently in the transformer and in the IEGTs. In the current source case, it is the opposite: an inductor is placed in series with the input and a capacitor in the output. In this thesis the first case was investigated. The schematic of the full bridge in this application is given in Fig 4.8. :

33

wrotor

rated speed

Uo=60kV1 2

Single Phase Transformer

A

B

+

-

Rectifier2

A

B

C

+

-

Rectifier1

Tm

mA

B

CPermanent Magnet

Synchronous Machine

Lload

Iref

g

A

B

+

-

Inverter

Idc

IrefOut

Current_Control

i+

-

Current Measurement

Cin

current

Fig 4.8. Full bridge converter used in this application.

The full bridge converter is connected at the input capacitor Ci. The inverter converts DC to AC and controls the current and speed of the PMSG. The inverter output connects to a single phase transformer that will raise the voltage. This transformer usually is made of a special type of iron giving to acceptable iron losses so that it can operate at higher frequencies, like 400 Hz or even 1 kHz. In this thesis the frequency used is 400 Hz. Adopting 400 Hz leads to small transformers that are cheaper and lighter than the usual grid transformers of 50Hz. The transformer will isolate the load galvanically from the generator that will protect it against short-circuits from the grid, which is an advantage for the full bridge converter [9].

The output of the single-phase transformer is connected to a diode rectifier bridge to convert to DC. The output inductor filter Lload is displayed and at the end there is a voltage source of 60kV that represents the DC grid, since as usual this voltage is controlled to be constant.

4.2.2. PMSG, transformer and full bridge converter

The usual value for the voltage of the PMSG is 690V. However this will lead to very high ratios for the single phase transformer. For this a 10kV PSMG was used instead.

The first parameter of the converter to be dimensioned is the minimum duty cycle (at rated conditions). It will be set to 30%. Knowing [9]:

in

o

nUU

= . (4.6)

It is known Uo is 60kV and Uin 13.5kV, so n will be 14.5. The minimum duty cycle cannot be higher than 30% because the transformer ratio would be too small and the duty cycle at lower wind speeds would be higher than 1.

The flux of the PMSG was computed in order to obtain the rated voltage at rated conditions. The current in the IEGTs is [9]:

34

AUMWI

inIEGT 478

2== . (4.7)

4.2.3. Sizing the output inductor and input capacitor

Applying the inductor equation in the interval when the voltage in the output of Rectifier2 is zero, and setting the current ripple to 10% the output inductor will be:

( )H

IfU

Lloadcom

o

load 77.152.01

=

=

(4.8)

fcom is the switching frequency, equal to 400Hz. The current in the load will be 2MW/60kV=33A, and =30%. From [9] it is known that the input capacitor needed for 10% of voltage ripple will be:

( ) ( ) FkVkVInI

nUfUC inload

incom

o

in 961485.14335.145.134006055 22 =

== (4.9)

Iin is the current in the input, equal to P/Uin.

4.2.4. Control and determination of the controller parameters

The current in the inductor and the input voltage can be controlled in the full bridge converter. In this approach only the current needs to be controlled, in order to prevent uncontrolled currents that can destroy the semiconductors, and also to control the current in the generator, this way controlling the torque. Usually the speed and current control of the generator are cascaded; the output of the PI controller of the speed is the current reference. In this study of the full bridge, only the current control is studied, the speed control will be explained in the next section.

The current is always compared with the reference, the error passes through a PI controller, and the output will be a control voltage Uc. This control voltage is approximately equal to the duty cycle of the converter (the ratio between the active period1 and the switching period). From this control voltage to the gate signals of the switches there are some alternatives: unipolar and bipolar switching, phase shift, duty cycle control [10]. For the beginning of the study the phase shift control was chosen, because it seems to be the best option for this application [9]. The schematic of the inverter with the input and output voltage and currents is depicted in Fig 4.9:

1 Active period The period when power flows from the source to the load. The voltage in the transformer is not

zero.

35

S1

S2

S3

S4

Vi

It

Ii

Vp

Fig 4.9 Schematic of the inverter.

The phase shift control is based on two square waves with 50% pulse width; one square wave commands switches 1 and 2 in Fig 4.9 and the other commands switches 3 and 4. Switch 2 is instructed to be the logical negative of switch 1 and switch 4 to be the logical negative of switch 3 in order to prevent short circuits of the capacitor Ci. The command voltage Uc that leaves the regulator is multiplied by half the switching period. This value is the delay between these 2 square waves. Uc varies between 0 and 1; this means the delay will vary between 0 and T/2. For a better understanding of this control, the simulink model used for simulation is shown in Fig 4.10 :

1/(2Fcommutation)

1Pulses

t

PulseGenerator1

PulseGenerator1/800

boolean

boolean

double

Clock

NOT

NOT

Add

1Uc

Fig 4.10 Phase shift control block.

The square waves Pulse Generator and Pulse Generator1 in Fig 4.10 and the voltage Up in Fig 4.9 are shown in Fig 4.11 :

Fig 4.11 Waveforms for the control of switch 1 and switch 3 (switches 2 and 4 are the negative).

36

This way, there are four intervals in one period: 1. Switches 1&4 ON 2. Switches 1&3 ON 3. Switches 2&3 ON 4. Switches 2&4 ON

It can be seen that when Uc=0 there is no intervals 1 and 3, which means the voltage at the primary of the transformer (Up) will always be zero. This gives the lowest Up RMS (0). If Uc=1 intervals 2 and 4 dont exist, it means Up will never be zero, it will be a square wave with pulse width 50% between Uin and Uin. This gives the highest Up RMS (Uin).

The parameters for the current control regulator of the converter will be computed using the tuning rules of Ziegler Nichols explained in Chapter 3. The goal as was said before is to control the torque of the PMSG. The output current was controlled. In the simulation it can be seen that the input and output current steady state values are proportional, so controlling the output current is the same as controlling the torque of the PMSG.

KPcrit was found to be 0.1 and TPcrit to be 15 ms. The response of the output current was simulated for PI and PID controllers. The reference changed from 5 to 15A. The responses are presented in Fig 4.12:

0.03 0.035 0.04 0.045 0.05 0.055 0.060

2

4

6

8

10

12

14

16

18

Iout

(A)

time(s)

PI ZieglerPID ZieglerPI TyreusPID Tyreus

Fig 4.12 Step response of the full bridge with different controllers.

By comparing in Fig 4.12. the four responses it can be seen that the red and blue curves have steady state error, and the black curve doesnt start in 5A. For this it was concluded that the best curve is the green one, which represents the PI controller using the Ziegler-Nichols tuning rules.

4.2.5. Simulation results

The controller presented above was used in simulations. The speed is constant and equal to its rated value, and the reference current changes from 5 to 33A at 35ms. The voltage in the capacitor Ci, the control voltage Uc and the input and output currents are in Fig 4.13 :

37

0.03 0.035 0.04 0.045 0.05 0.055 0.0610

15

Uin

(kV)

0.03 0.035 0.04 0.045 0.05 0.055 0.06

200

400

Iin(A

)

0.03 0.035 0.04 0.045 0.05 0.055 0.060

20

40Io

ut(A

)

0.03 0.035 0.04 0.045 0.05 0.055 0.060

0.5

1

Uc(V

)

time(s)

Fig 4.13 Input voltage, control voltage Uc and input and output currents of the full bridge converter.

When the reference current changes the control voltage increases immediately for the current to increase faster. The ripple in the output current and in the input voltage is 10% as expected. The input and output currents are proportional apart from the transient state which means controlling the output current will control

the torque of the PMSG. It takes approximately 20 ms to stabilize.

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06-400-200

0200400

Ia(A

)

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06-400

-200

0

Iq(A

)

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06-300

-200

-100

0

Id(A

)

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-30

-20

-10

0

time(s)

Torq

ue(kN

m)

Fig 4.14 Stator Ia, Iq, Id and electromagnetic torque of the PMSG.

38

Fig. 4.14. shows the variables in the PMSG. The current is not sinusoidal, because of the Rectifier1. For this the current Id is not zero as in the boost converter. Iq and the torque are proportional. The input speed value is erated/np=628rad/s/4=157rad/s. The torque is 2MW/157rad/s=13 kNm as expected. It doesnt have oscillations, which is essential for a good speed control of the PMSG. In Fig 4.15 the variables in the transformer, the current and the voltage in the primary side are displayed:

0.03 0.032 0.034 0.036 0.038 0.04 0.042 0.044 0.046 0.048 0.05-600

-400

-200

0

200

400600

Curr

ent i

n th

e Pr

imar

y(A)

0.03 0.032 0.034 0.036 0.038 0.04 0.042 0.044 0.046 0.048 0.05-15

-10

-5

0

5

1015

Volta

ge in

th

e Pr

imar

y(kV)

Fig 4.15 Voltage Vp and the current in the primary side of the transformer.

The current is approximately constant. The voltage is controlled by the phase shift control. The current in the IEGTs is displayed in Fig. 4.16. :

0.03 0.032 0.034 0.036 0.038 0.04 0.042 0.044 0.046 0.048 0.05-600

-400

-200

0

200

400

600

Curr

ent I

EGT(

A)

time(s)

Fig 4.16 Current in the Rectifier1 and in the IEGTs.

It is seen the maximum current is 470A as in (4.7.). Changing the reference current from 5 to 15A it was seen that the output current took 10ms to stabilize, half of the time to stabilize from 5 to 33A. This is due to the fact that the converter has a maximum duty cycle to increase the output current as fast as possible. That

39

maximum is 1. So if the current only changes from 5 to 15A, it is normal it takes less time to get there. Resuming, for large perturbations it takes 20ms, for small perturbations 10ms.

4.3. PMSG with a ATR

The electric circuit of this implementation is in Fig 4.17 The first step is to determine the line to line voltage in the AC side, and the inductance between the generator and the ATR:

wrotor

rated speed

generator_measurements

Ud

Uq

teta

Ualpha

Ubeta

dq alpha_beta

Uo=60kV

w

mA

B

CPermanent Magnet

Synchronous Machine

Iqref

g

A

B

C

+

-

Inverter

Idref

Ualpha

UbetaPulses

Discrete SV PWMGenerator

IdIdrefIqIqrefwm

Ud

Uq

Current_Control

Fig 4.17 Equivalent electric circuit.

In this converter, IEGTs will be used. A PMSG of 690V could be used in this simulation. But then the problem is that the DC voltage Uo would be very low and couldnt reach 60 kV. Using the formulas below it is concluded that a good value for the line to line voltage in the AC side of the ATR can be 10 kV.

4.3.1. Determination of the LATR and Udc

The control for the ATR is made using PWM (Pulse Width Modulation) modulation. In the next figure, the three phase voltage sources represent the open voltage from the generator, the impedance represents the impedance of the generator plus the impedance introduced between the generator and the ATR in order to reduce the current harmonics. The voltage in the DC link is going to be controlled by the main inverter onshore, so this voltage is assumed to be constant.

In order to determine the voltage harmonics caused by the PWM in the ATR another simulation model was used, which is displayed in Fig 4.18:

40

Ts=1/20000

Discrete,Ts = 1e-006 s.

pow ergui

v+-

Voltage Measurement

Vdc =100V

Vab (av)

Vab

g

A

B

C

+

-

Universal Bridge3 arms

1

0.0001s+1Transfer Fcn

Idc

To Workspace1

Vab

To Workspace

A B C

Three-PhaseSeries RLC Load

Scope

3

Multimeter

Pulses

DiscretePWM Generator

i+

-

Current Measurement

Fig 4.18 Simulation model to determine the maximum percentage of voltage harmonics.

In this model for the PWM modulation the most significant voltage harmonic was for index modulation equal to 0.5, where the largest harmonic is 31% of Udc. The commutation frequency used is 1 kHz. LATR can be found such as the current harmonic will be 10% of the nominal current. Quoting [16] is known:

mHMW

kVIf

UL

nomcom

ATR 256

31000021.010002

6031.02

0=

==

pipi. (4.10)

( )[ ]223 dgridtransmDC iLEU +> . (4.11)

Where Em is the peak line to ground voltage, e the electric speed of the generator and Iq is the nominal current. In [16] instead of iq it is id. However in [16] the d-axis is aligned with the voltage. As in this case we have a synchronous generator the voltage will be aligned with the flux of the machine. So instead of id it will be iq. In this case:

AkV

MWUP

Iqnom

nom

qnom 200102

===

(4.12)

sradfratederated /62810022 === pipi (4.13)

kVEm 1.83210000 == . (4.14)

Inserting these values gives:

kVU o 6.57> . (4.15)

41

This means that the value 60kV can be used. Quoting also [16]:

mHi

EU

Lqe

m

ATR 268200628

81003

600003

22

220

=

=

. (6.6.)

This is smaller than 200kV. This means the inverter can operate with the voltage level 60kV in the primary side of the transformer. The other equation is:

mHi

EU

Ldgrid

m

DC

trans 9.9933333141009.13 10

22

=

=