simulation and laboratory of control system for wind turbine

7/29/2019 Simulation and Laboratory of Control System for Wind Turbine

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Francesco Marra

Simulation and laboratory

implementation of a wind turbinecontrol system with short-term

grid faults management

MSc Thesis

22 May 2008 31 October 2008


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Francesco Marra

Simulation and laboratory

implementation of a wind turbinecontrol system with short-term

grid faults management

MSc Thesis


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2

MSc ThesisSimulation and laboratory implementation of a wind turbine control system withshort-term grid faults management

This report was drawn up by:

Francesco Marra

Supervisors:prof. Franco Maddalenoprof. Marcello Chiaberge

External supervisor:prof. Tonny W. Rasmussen

rstedDTUDepartment of Electrical EngineeringTechnical University of DenmarkElektrovejBuilding 3252800 Kgs. LyngbyDenmark

www.oersted.dtu.dk/cetTel: (+45) 45 25 35 00

Fax: (+45) 45 88 61 11E-mail: [email protected]

Release date: 31 October 2008

Category: Master Thesis

Edition: 1st edition

Comments: The thesis is part of the requirements to achieve the MasterDegree in Mechatronic Engineering at Polytechnic of Turin -Italy. This work represents 20 ECTS points at Polytechnic ofTurin, 30 ECTS points at DTU.

Rights: Francesco Marra, 2008


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3

ABSTRACT

The purpose of the thesis is the development of a wind turbine control system capable to

handle short-term grid faults. The work has been performed in the department of

Electrical Engineering of Danmarks Tekniske Universitet.

The present thesis aims to contribute to a growing body of literature concerning with

wind turbine control system design. First important know-how on wind technology is

analyzed, considering the different topologies of system in the wind market, and thenthe work conducts to the development strategy that better fits to the aim of project.

The thesis is developed in two steps: 1. Simulation of the designed control system, by

the use of Matlab/Simulink software. 2. Laboratory implementation, with HiL, and

software design by using the digital signal processor, ADSP-21020. Simulation and

experimental results will be depicted and commented.

Field Oriented Control for operation in normal condition and during grid faults will be

considered as control method. In software development for laboratory implementation,

Assembler language is used for DSP programming.

Thesis organization

The thesis is organized in 9 chapters. Notation, list of tables, list of figures and

abbreviations are shown after the table of Contents. Literature references are mentioned

in square brackets by number. Detailed information about literature is presented in

Bibliography. Appendices are assigned with letters and are arranged in alphabetical

order. Equations are numbered in format (x.y) and figures are numbered in format

Figure x-y, where x is the chapter number and y is the number of the item. The enclosed

CD/ROM contains the project report in Word and PDF formats, source code of the

designed software, Simulink models and documentation used throughout the project.

Author would like to thank the supervisor, prof. Tonny W. Rasmussen and the

Department of Electrical Engineering of DTU for the important support provided

throughout the period of the work.


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CONTENTS

Abstract .............................................................................................................3

List of figures ....................................................................................................7

List of tables....................................................................................................11

Notation ...........................................................................................................12

Abbreviations..................................................................................................14

1 Preface ..........................................................................................................15

1.1 Problem formulation ............................................................................................. 15

2WIND SYSTEM TECHNOLOGY ...................................................................17

2.1 Power control capability ....................................................................................... 17

2.2 Speed control capability ....................................................................................... 18

2.3 Control objectives in Wind technology ................................................................ 20

2.4 Project Development Strategy .............................................................................. 22

3 MODELING....................................................................................................25

3.1 Wind turbine model .............................................................................................. 25

3.2 Drive-train model.................................................................................................. 27

3.3 Induction machine model...................................................................................... 29

3.4 Back-to-back converter model.............................................................................. 31

4 CONTROL SYSTEM DESIGN.......................................................................34

4.1 Control of generator in different operation regions.............................................. 34

4.2 Current model ....................................................................................................... 35

4.3 Indirect Field Oriented Control ............................................................................ 36

4.4 Speed loop design ................................................................................................. 40

4.5 Flux loop design ................................................................................................... 44

4.6 Space vector PWM design.................................................................................... 48

5SIMULATIONS ..............................................................................................53

5.1 Blocks of system................................................................................................... 54

5.2 Implementation of blocks in Simulink ................................................................. 56

5.3 Simulation settings................................................................................................ 59

5.4 Simulation results ................................................................................................. 60

6SOFTWARE DESIGN....................................................................................66

6.1 Process time-schedule........................................................................................... 67

6.2 Flow-chart ............................................................................................................. 70

6.3 Data structures ...................................................................................................... 72


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Contents

6

7CODE IMPLEMENTATION ...........................................................................76

7.1 Timer management................................................................................................76

7.2 PI realization..........................................................................................................81

7.3 First order filter realization....................................................................................81

7.4 Signal conditioning................................................................................................828LABORATORY IMPLEMENTATION ............................................................84

8.1 Test bench setup ....................................................................................................84

8.2 Speed measurement method ..................................................................................85

8.3 Open loop tests and results ....................................................................................87

8.4 Closed loop tests and results .................................................................................89

9 Conclusion ...................................................................................................94

9.1 Designed control strategy......................................................................................94

9.2 Simulation tool ......................................................................................................94

9.3 Digital Signal Processor in Wind Energy..............................................................959.4 Software development...........................................................................................95

9.5 Simulation and experimental results .....................................................................95

9.6 Further work..........................................................................................................96

References ......................................................................................................97

A Reference frame theory ..............................................................................99

B Laboratory equipment ..............................................................................103


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7

LIST OF FIGURES

Figure 2-1: Wind turbine concepts ................................................................................ 19

Figure 2-2: Ideal power regulation for a wind turbine .................................................. 20

Figure 2-3: Wind turbine system................................................................................... 22

Figure 2-4: Reference system for laboratory implementation....................................... 23

Figure 2-5: Torque characteristic of the induction machine.......................................... 24

Figure 3-1: Power as a function of rotor speed for different wind speeds. ................... 26

Figure 3-2: Power as a function of rotor speed for different pitch angle at Vn............. 26

Figure 3-3: Power as a function of rotor speed for different wind speeds. ................... 26

Figure 3-4: Two-mass model of the wind turbine drive train........................................ 27

Figure 3-5: Bode diagram of Wg/Tg transfer function.................................................. 28

Figure 3-6: Stator and dq equivalent windings........................................................ 29

Figure 3-7: Back-to back converter ............................................................................... 31

Figure 3-8: Star connected generator and generator side converter .............................. 32

Figure 4-1: Ideal power regulation for a WT................................................................. 34

Figure 4-2: Current model: rotor flux estimation block diagram .................................. 35

Figure 4-3: Indirect field oriented control system with IG and VSI.............................. 38

Figure 4-4: Torque in terms of rotor flux and q-axis stator current............................... 39

Figure 4-5: Speed loop .................................................................................................. 40

Figure 4-6: sqi loop....................................................................................................... 41

Figure 4-7: */sq sqi i Bode diagram ................................................................................... 42

Figure 4-8: */sq sqi i step response..................................................................................... 42

Figure 4-9: r loop....................................................................................................... 42

Figure 4-10: Speed loop Bode diagram......................................................................... 44

Figure 4-11: Speed loop step response.......................................................................... 44

Figure 4-12:sdi loop...................................................................................................... 44


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List of figures

8

Figure 4-13: */sd sdi i Bode diagram.................................................................................46

Figure 4-14: */sd sdi i step response...................................................................................46

Figure 4-15:si

loop ......................................................................................................46

Figure 4-16:*/

s si i

Bode diagram..................................................................................47

Figure 4-17: */s si i

step response...................................................................................47

Figure 4-18: refV in SVM...............................................................................................48

Figure 4-19: State sequence for symmetric SVM..........................................................49

Figure 4-20: Switching sequence in symmetric SVM ...................................................51

Figure 4-21: Switching sequence in asymmetric SVM..................................................51

Figure 5-1: Wind turbine control system .......................................................................53Figure 5-2: F.O.C. block ................................................................................................56

Figure 5-3: Speed controller block.................................................................................57

Figure 5-4: Fault manager block ....................................................................................58

Figure 5-5: SV-PWM block ...........................................................................................59

Figure 5-6: SV-PWM calculation in sector 1.................................................................59

Figure 5-7: View to solver options of Simulink model..................................................59

Figure 5-8: Simulation time used in simulations ...........................................................60

Figure 5-9: Rotor speed profile as result of simulation in r.p.m. ...................................61

Figure 5-10: Zoom on rotor speed profile ......................................................................61

Figure 5-11: Average electric power generated by the IG.............................................62

Figure 5-12: Average current on the DC side ................................................................62

Figure 5-13: Current on the DC side ..............................................................................63

Figure 5-14: Phase-to-phase voltage of SVM ................................................................63

Figure 5-15: Rotor speed profile during grid fault.........................................................64

Figure 5-16: Electric power under grid fault..................................................................64

Figure 5-17: Average current on the DC side under grid fault ......................................65

Figure 6-1: Sample time Ts............................................................................................68

Figure 6-2: Software time chart .....................................................................................69

Figure 6-3: Flow chart....................................................................................................70

Figure 6-4: Data structures of the in-use timing table....................................................73

Figure 6-5: Data structures of the temporary timing-table.............................................74

Figure 6-6: Loading of the new timing-sequence ..........................................................75


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List of figures

9

Figure 6-7: Slide process of linear buffer ...................................................................... 75

Figure 7-1: First order digital filter................................................................................ 82

Figure 7-2: Conditioning procedure .............................................................................. 83

Figure 8-1: Laboratory test bench ................................................................................. 84

Figure 8-2: Control Panel of Frequency Converter ABB ACS600 ............................... 85

Figure 8-3: Phase-to-phase SVM voltage and VDC ..................................................... 87

Figure 8-4: Phase voltage and line current .................................................................... 87

Figure 8-5: Phase voltage and line current at rated speed ............................................. 88

Figure 8-6: Phase-to-phase voltage of SVM and line current at speed of

100rpm .................................................................................................................. 89

Figure 8-7: Rotor speed measure with * 100r rpm = , fc = 50Hz................................. 90

Figure 8-8: Rotor speed measure with * 100r

rpm = , fc = 10Hz................................. 90

Figure 8-9: Rotor speed measure under grid fault, with * 100r

rpm = , fc =

50Hz ...................................................................................................................... 91

Figure 8-10: Rotor speed measures with * 100r

rpm = and different torque

commands.............................................................................................................. 92


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11

LIST OF TABLES

Table 1: Open loop transfer functions of sqi loop ........................................................ 41

Table 2: Closed loop transfer functions ofsqv loop ..................................................... 42

Table 3: Open loop transfer functions of speed loop ................................................... 43

Table 4: Closed loop transfer functions of speed loop ................................................. 43

Table 5: Open loop transfer functions of*

sdi loop ........................................................ 45

Table 6: Closed loop transfer functions of*

sdi loop...................................................... 45

Table 7: Open loop transfer functions of si loop ........................................................ 46

Table 8: Closed loop transfer functions of *si

loop...................................................... 47

Table 9: SV-PWM duty cycles ....................................................................................... 52

Table 10. Sample time of the subsystems ...................................................................... 60

Table 11: Signal conditioning....................................................................................... 86

Table 12: Closed loop settings ....................................................................................... 89

Table 13: Closed loop settings ....................................................................................... 91


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Notation

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NOTATION

Symbol Unit Definition

Rs Stator resistance

s rad/s IG synchronous speed

,g r rad/s Generator rotor speed

fs Hz Line frequency

Vmin m/s Cut-in wind speed

Vmax m/s Cut-out wind speed

Vn m/s Rated wind speed

degree Pitch angle of the wind turbine blades

v m/s wind speed

V m/s Mean wind speed

Tref Nm Reference torque

WT rad/s WT speed

'

WTT Nm WT torque referred to the high speed shaft

'

WT rad/s WT speed referred to the high speed shaft

WTJ 2Kg m Moment of inertia of WT referred to the generator side

genJ 2Kg m Moment of inertia of generator

shaftT Nm Shaft torque on generator side

gearK - Gearbox gain

refV V Reference line-to-starpoint space vector voltage


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Notation

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Tpwm s Switching period

Ts s Sample time

Teta rad Electric angle

PWT W WT mechanical power

Rr Rotor resistance

dq rad/s Speed of dq reference frame

Ls H Stator winding inductance

LM H Mutual inductance

Lr H Rotor winding inductance

rdq Wb Rotor flux linkage space vector in dq coordinates

Tr s Rotor time constant

S - IG slip speed

Ra Equivalent resistance

Ta s Equivalent time constant

p - Pole pairs

Te Nm Electromagnetic torque


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Abbreviations

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ABBREVIATIONS

Acronym Definition

WECS Wind energy conversion system

WT Wind turbine

IG Induction generator

SCIG Squirrel cage induction generator

WRIG Wound rotor induction generator

FSPCWT Full-scale power converter for wind turbine

DFIGWT Doubly-fed induction generator for wind turbine

PWM-VSI Pulse width modulation for Voltage Source Inverter

VSC Voltage source converter

DFOC Direct field oriented control

IFOC Indirect field oriented control

PI Proportional-integral controller

MAIN Subroutine where control algorithm is implemented


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1PREFACE

The progress of wind power technology in recent years has exceeded all expectations,

with Europe leading the global market of MW wind-farm. Such a progress has led to

cost reduction to levels comparable, in many cases, with conventional methods of

electricity generation. Anyway, the increased penetration of wind power in the grid has

entailed important technical barriers that limit the development, as stability is a key

issue. The Grid Operators in different countries are issuing new grid requirements,

called also grid codes that impose more restrictions for the wind turbines behavior

especially under grid faults. These new requirements are challenging the control of the

wind turbines and new control strategies are needed to meet the target.

When a short-term grid fault occurs in a Megawatt wind farm, grid companies with

large amounts of wind power presently are starting to require wind turbines to remain

connected to the grid during a fault, to avoid the time of reconnection process, which

need 4-5 minutes. Furthermore it is economically convenient to handle the fault, without

disconnecting the wind turbine from the grid, this permit to store the incoming energy

from the wind and to recover it, at the end of fault.

In order to be able to stay connected under grid faults special control strategy has to be

employed. This strategy should ensure that current and voltage protections are not

tripped and no electric power is delivered to the grid. The project aims to simulate a

new technical solution in terms of control under grid faults and to test the real system on

a laboratory test-bench for experimental measurements, by means of a Digital Signal

Processor.

1.1 Problem formulation

The main goal of this project is the design of a wind turbine control system capable to

handle short-term grid faults.

Grid faults can be divided by type of event as follow:

Blackout: total absence of electrical current, due to excessive demand or grid damage;

Sag: short grid under voltage, due to a peak of demand;

Harmonic: variation on the wave shape produced by inductive loads;

Surge: short grid over voltage, typically due to the switching off of a big electrical

process;


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Preface

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Spike: sudden grid voltage pulse, due to a lightning or to a voltage recovery after a

blackout;

Since most of grid fault events are short-term, in the order of 100-300ms of duration it

is convenient that control system is able to handle the fault condition withoutdisconnecting the wind turbine from the grid. In fact, in case of disconnection, it would

need some minutes to the wind turbine to reach again the steady state condition.

The idea is to increase the generator rotor speed during the fault, in order to store the

incoming energy from the wind, in form of kinetic energy in the wind turbine inertia.

The stored kinetic energy, transformed in electric energy, can flow through the grid at

the end of fault. Anyway, by this method, only short-term grid faults, in the order of

100-300ms time-duration, can be handled, since generator speed can increase till

allowed values.


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WIND SYSTEM TECHNOLOGY

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2WIND SYSTEM TECHNOLOGY

In this chapter the main points of wind system technology are presented as background

know-how, in order to conduct to the better development strategy for the WT control

system.

2.1 Power control capabilityWind technology has to cope with the intermittent and seasonal variability of the wind

as well as with grid-fault events.

During normal condition the control begins to work when wind speed is above the cut-

in speed so that power is injected into the utility grid; moreover they include some

mechanisms to limit the captured power at high wind speeds to prevent overloading.

Three control strategies can be used for captured power control:

stall control;

pitch control;

active stall control.

Thestall controlis based on a specific design of the blades so that stall occurs when

the wind speed exceeds a certain level; it means that the captured power is automatically

limited in the rated power range. This method is simple, robust and cheap but it has low

efficiency at low wind speed.

In case ofpitch control, blades can be tuned away from or into the wind as the

captured power becomes too high or too low; this is performed by rotating the blades, or

part of them, with respect to their longitudinal axes. Below rated wind speed, blades are

pitched for optimum power extraction whereas above the rated wind speed blades are

pitched to small angle of attack for limiting the power. Advantages of this type of

control are good power control performance, assisted start-up and emergency power

reduction; the biggest disadvantage is the extra complexity due to the pitch mechanism.

In case ofactive stall control, stall is actively controlled by pitching blades to larger

angle of attack with wind speed above the rated value.


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Underfault conditions the control should be able to freeze out the electric power

generation without disconnecting the wind turbine from the grid. This is possible by

using Direct Field Oriented Control and power electronics as well.

2.2 Speed control capability

Beyond the captured power controllability, another important feature is the speed

controllability. Based on this, WTs are classified into two main categories:

Fixed speed WTs;

Variable speed WTs.

Fixed speed WTs are equipped with induction generator (squirrel cage induction

generator SCIG or wound rotor induction generator WRIG) directly connected to thegrid and a capacitor bank for reactive power compensation. This is a very reliable

configuration because of the robust construction of the standard IG. The IG

synchronous speed is fixed and determined by the grid frequency regardless of the wind

speed; this implies that such WTs can obtain maximum efficiency at one wind speed.

As power electronics is not involved in this configuration, it is not possible to control

neither reactive power consumption nor power quality; in fact due to its fixed speed,

wind fluctuations are converted into torque fluctuations, slightly reduced by small

changes in the generator slip, and transmitted as power fluctuations into the utility grid

yielding voltage variations especially in weak grids.Variable speed WTs are equipped with an induction or synchronous generator

connected to the grid through a power converter. The variable speed operation, made

possible by means of power electronics, allows such WTs to work at the maximum

conversion efficiency over a wide range of wind speeds. The most commonly used WT

designs can be categorized into four categories:

fixed speed WTs (FSWT);

partial variable speed WTs with variable rotor resistance (PVSWT);

variable speed WTs with partial-scale frequency converter, known as doubly-fedinduction generator-based concept (DFIGWT);

variable speed WTs with full-scale power converter (FSPCWT).


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Figure 2-1 shows the structure of the above concepts. They differ in the generating

system (electrical generator) and the way used to limit the captured aerodynamic power

above the rated value.

- Fixed speed WTs are characterized by a squirrel cage induction generator (SCIG)

directly connected to the grid by means of a transformer. The rotor speed can be

considered locked to the line frequency fs as very low slip is encountered in normal

operation (typically around 1%).

The reactive power absorbed by the generator is locally compensated by means of acapacitor bank following the production variation. A soft-starter can be used to provide

a smooth grid connection.

This configuration is very reliable because the robust construction of the standard SCIG

and the simplicity of the power electronics.

- Partial variable speed WTs with variable rotor resistance use a WRIG connected to the

grid by means of a transformer. The rotor winding of the generator is connected in

series with a controlled resistance; it is used to change the torque characteristic and the

operating speed in a narrow range (typically 0 10% above the synchronous speed). A

capacitor bank performs the reactive power compensation and smooth grid connection

occurs by means of a soft-starter.

- For a DFIGWT, the stator is directly coupled to the grid while a partial scale power

converter controls the rotor frequency and, thus, the rotor speed. The partial scale power

converter is rated at 20% 30% of the WRIG rating so that the speed can be varied

within 30% of the synchronous speed. The partial scale frequency converter makes

such WTs attractive from the economical point of view. However, slip rings reduce the

reliability and increase the maintenance.

Figure 2-1: Wind turbine concepts


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- Variable speed FSPCWTs are characterized by the generator connected to the grid by

means of the full-scale frequency converter.

2.3 Control objectives in Wind technology

WECSs connected to the grid must be designed to minimize the cost of supplied energy

ensuring safe operation, acoustic emission and grid connection requirements. Control

objectives involved in WECSs are:

energy capture;

mechanical load;

grid connection requirements.

Energy captureVariable-speed variable-pitch WTs are usually controlled according to the curve in

Figure 2-2; it represents the energy capture capability of a WT in the generated power-

wind speed plane.

As shown in Figure 2-2 , the range of operational wind speed is delimited by the cut-in

wind speed Vmin and cut-out wind speed Vmax. The WT remains stopped beyond these

limits. Below Vmin the available energy is too low to compensate the operational cost

whereas above Vmax the WT is shut down to prevent mechanical overload. The

selection of the Vmax speed is a trade-off between the following items:

constructing the WT robust enough to support high mechanical stress would be

economically inconvenient;

Figure 2-2: Ideal power regulation for a wind turbine


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even though strong winds have large energy content, they occur seldom so their

contribution to the annual production is negligible.

A good compromise is often Vmax = 25 m/s. The rated mean wind speed Vn is the speed

at which the electrical generator works at its rated power. Within the interval [Vmin;

Vn], the available power is lower than the rated value and so the WT speed is controlledto maximize the captured energy (variable speed, fixed pitch operation). In this

operational region, the captured power is proportional to3V , where V is the mean wind

speed. In countries where the wind energy is dispatched as traditional energy, the

captured power has to react based on the set-point given by the dispatched center; it

follows that the captured power could be controlled to be less than the available one.

Above Vn, the induction generator is controlled such that the captured power is limited

to the rated value to prevent mechanical overload (fixed-speed variable-pitch operation).

In this region the available power in the wind exceeds the rated power, thus the WT

must be operated with an aerodynamic efficiency lower than in the previous region.

Mechanical loads

Mechanical loads can cause fatigue damage and thereby reduced lifetime of the WT.

Since the overall cost is spread over a shorter period of time, the cost of energy will rise.

Mechanical loads can be divided into static loads, which result from the interaction of

the WT with the mean wind speed, and dynamic loads, which comprise variation of the

aerodynamic torque that propagate down the drive train and the mechanical structure.

The control system of a WT has a very strong impact especially on the dynamic

mechanical loads. The control of the electric generator affects the propagation of drive-train loads whereas the pitch control affects the structural loads.

Grid connection requirements

The injection of large amount of wind power into a network might affect the steady

state voltage especially in presence of weak grid. To ensure electrical system stability,

system operators in many European countries are setting grid connection requirements

for wind generators also known as grid codes (GCs). For MW-size WECSs, very high

technical demands are required, such as:

regulation of active and reactive power (frequency and voltage control);

fast responses under dynamic situation;

power quality;

low voltage ride-through capability.

WECSs must provide the power quality required to ensure the stability and reliability of

the power system they are connected to, and to satisfy the customers connected at the

same grid. Voltage and frequency at the point of common coupling (PCC) must be kept

as stable as possible. In general, frequency is a quite stable variable. Frequency


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variations are always due to power unbalance between generation and consumption (e.g.

generators accelerate when the supplied power exceeds the consumption, hence

increasing the frequency; analogously they slow down when they can not cover the

power demands, thereby frequency decreases). Voltage variations take place as a

consequence of variation of the mean wind speed; the amplitude of these variationsdepends on the impedance of the grid connected at the PCC, on active and reactive

power flows. A way of attenuating voltage variations, without affecting power

extraction, is to control the reactive power flow. Nowadays the most effective way of

reactive power control is based on power electronics.

In the next years, the major research challenge is directed towards the grid integration of

large wind farms to the electrical power grid. It implies that the survival of different WT

concepts is strongly connected by their ability to support the grid, to handle faults on the

grid and to comply with grid requirements of the utility companies.

2.4 Project Development Strategy

The Full-scale Power Converter WT concept is used to develop the project because it

matches with the laboratory equipment. We cant use the doubly-fed power converter

strategy because we have not a doubly-fed induction generator, but both the strategies

are suitable to fulfill the goal.

As generating system, an induction machine is selected. Induction machines are cheaper

and easily controllable respect to synchronous machine; this is the reason why they are

preferred in the wind market. The reference system is reported in Figure 2-3.

Figure 2-3: Wind turbine system

The real reference system is represented in Figure 2-3 whereshaft

T andgen

are

respectively the mechanical torque and the rotational speed of the induction generator.

The IG is controlled by Indirect Field Oriented Control method, which uses the current

model of the machine that is the most used concept on induction machine control for

industrial applications. Furthermore Indirect Filed Oriented Control makes use of the 3-


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phase currents and rotor speed measurements to perform the algorithm, and current and

speed sensors are available on the laboratory test bench.

The IG is connected to the ac grid through a power converter, the so-called back-to-

back PWM-Voltage Source Inverter; it is a bi-directional power converter consisting of

two conventional VSC (generator and grid side converters). The pitched-controlled WTand the gearbox are not available for laboratory implementation therefore they are

implemented by means of a torque-controlled asynchronous machine (master). The

grid-side converter is not used, as it would require its own control system; since its

control is not included in this project, the grid side converter is substituted by a dc

power supply directly connected at the dc link. The electric power produced, flowing

through the generator side converter, is dissipated by a braking resistor whose current is

controlled by a chopper circuit, included in the test bench. According to the above

considerations, the layout of the system is modified as presented in Figure 2-4. The

reference torque refT is produced according to the models of the WT and the wind.

Figure 2-4: Reference system for laboratory implementation

Induction machine principle

As shown in torque characteristic ofFigure 2-5, an induction machine can operate in

different regions. In order the induction machine to operate as generator the following

work conditions must be ensured:

negative sleep speed (typically less than 1% for large wind farm): the rotorspeed is higher than rated speed; of the overall generator region of torque

characteristic, only the stable interval can be considered for project

development.

reactive power supply: in order to produce the magnetization current, and so therotational magnetic field, reactive power must be supplied to the machine. For

grid connected case, the reactive power is supplied from a capacitor bank for the

80% and from the grid for the remaining 20%. While in isolated case reactive

power is produced directly by the power converter (generator-side converter).


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The wind turbine moves the induction generator rotor in real case, while a driver motor

is used for laboratory implementation. The driver motor is powered by a frequency

converter commanded in torque operation.

Figure 2-5: Torque characteristic of the induction machine


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3MODELING

In this chapter the modelling of the system is done. The considered models are used on

next step for simulations on Simulink platform.

3.1 Wind turbine model

The WT converts wind energy to mechanical energy by means of a torque applied to a

drive train. A model of the WT is necessary to evaluate the torque and power production

for a given wind speed and the effect of wind speed variations on the produced torque.

The torque TWT and power PWT produced by the WT within the interval [Vmin, Vmax],

where V is the mean wind speed, are functions of the WT blade radius R, air pressure,

wind speed and of coefficients CQ and CP.

( )

( )

3 2

2 3

1,

2

1( , ) ,2

WT Q

WT P V P

T R C V

P C P R C V

=

= =

( 3.1)

CP is known as the power coefficient and characterizes the ability of the WT to extract

energy from the wind. CQ is the torque coefficient and is related to CP according to:

P

Q

CC

= ( 3.2)

Here, is the tip-speed-ratio,

WT

R

V = ( 3.3)

whereWT

is the WT rotor speed.

As seen from previous equations, TWT and PWT depend both on the coefficient CP that is

normally provided by manufacturer in the form of a lookup table. An alternative way to

calculate CP is based on the following approximation:

12.5

116( , ) 0.22 ( 0.4 5 ) i

P

i

C e

= ( 3.4)


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MODELING

26

where is the pitch angle andi

is described by the equation:

3

1 1 0.035

0.08 1i

=

+ + ( 3.5)

Figure 3-1 shows how PWT varies with rotor speed for different wind speeds. Theoptimum tip speed ratio curve gives the highest efficiency points for PWT. As seen from

figure, for a 2.2KW wind turbine, with rated wind speed of 8m/s, the maximum power

is at Vn. Figure 3-2 shows how PWT varies for different at the rated mean wind speed

Vn. Maximum PWT is reached for =0 but as is increased, PWT decreases. This is

useful to prevent mechanical overloading of the WT when wind speed exceeds Vn.

Figure 3-1: Power as a function of rotor

speed for different wind speeds.

Figure 3-2: Power as a function of rotor

speed for different pitch angle at Vn.

Similar curves as the above-mentioned figures are valid for TWT as well. As for power,

torque varies similarly with WT and .

For the simulation case the Simulink wind model has been used. It differs from the

analyzed one, essentially for the use of normalized unit (p.u).

Figure 3-3: Power as a function of rotor speed for different wind speeds.

As we can see from Figure 3-3, the Wind model block receives the wind speed and

generator rotor speed as inputs and puts out the mechanical torque Tm for the IG.


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MODELING

27

3.2 Drive-train model

The rotating shaft system in a wind turbine is divided in sections: the turbine itself is

quite heavy and the machine rotor is light. The shaft, connecting the generator and the

turbine cannot be assumed to be of infinite stiffness: the gearbox reduces the stiffness,

therefore the shaft will twist as it transits torque from one end to the other. Typicalvalue of resonance frequency of such systems is in the range of 1-2Hz, and for a

specific Danish windmill the resonance frequency is known to be 1.67 Hz.

Thus a model of the drive train is required as it has influence on grid interconnection by

producing power fluctuations. Other mechanical dynamics, such as tower and flap

bending modes, are negligible from this point of view.

A two mass model on the generator side is considered; the model is represented in

Figure 3-4 where'

WTJ and

genJ are respectively the inertia of the wind turbine referred

to the generator side, and the inertia of the induction generator.

Figure 3-4: Two-mass model of the wind turbine drive train

The moment of inertia for the low speed shaft, high-speed shaft and gearbox wheels can

be neglected because they are small compared with'

WTJ and

genJ . Therefore the

resultant model is essentially a two-mass model connected by a shaft characterized by

an equivalent torsional stiffness 'eK and damping factor'

eD .

The drive-train converts the aerodynamic torque produced by the WT, TWT, into a

torque at the high-speed shaft Tshaft. This conversion is mathematically described by the

following differential equations:

'

'

'

' ' '

'

( )

k g WT gear

kk

WT shaft

WT

WT

shaft e g WT gear e k

K

T T

J

T D K K

=

=

=

= +

( 3.6)


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MODELING

28

wheregear

K is the proportional gain of the gearbox,k

is the torsional shaft speed,

'

WTT is the WT torque referred at the high-speed shaft, '

WT is the WT rotor speed, Tshaft

is the torque applied at the rotor of the generator and g is the generator mechanical

speed.The torque Tshaft available to be transmitted by the shaft is:

'' '

WT

WTshaft WT

dT T J

dt

= + ( 3.7)

The torque at the generator end, seen from the shaft is:

g

shaft g gen

dT T J

dt

= ( 3.8)

The twisting of the shaft depends on the shaft torsional stiffness Kshaft:

( )shaft

g WT

shaft

T

K = ( 3.9)

The transfer function between the generator speed and the torque at generator side is

shown in (3.10). The constants Kt and Kg are 1/'

WTJ and 1/

genJ respectively.

2

3

( )( )

( ) ( )

g g t shaft

g t shaft g shaft

K s K KsH s

T s s K K K K s

+ = =

+ + ( 3.10)

The Bode diagram reported in Figure 3-5 represents the typical frequency response of

such a system. By the way, since the WT and the gearbox are not included in the

laboratory equipment, both simulations and experimental tests are conducted without

considering the drive-train model.

Figure 3-5: Bode diagram of Wg/Tg transfer function


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MODELING

29

3.3 Induction machine model

In this section the model of the induction machine in the rotating dq reference frame is

derived. First, equations in the stationary reference frame are obtained. The -axis isaligned with the stator a-axis, as shown in Figure 3-6.

Figure 3-6: Stator and dq equivalent windings

In such reference frame the induction machine can be represented by means of space

vector as follows:

s

s ss

dv R i

dt

= + ( 3.11)

The current si , voltage sv and stator flux linkage s space vectors with respect

to the -axis are represented in the rotating dq reference frame as follows:dq

j

s sdqv v e= ( 3.12)dq

j

s sdqi i e= ( 3.13)dq

j

s sdq e = ( 3.14)

where dq is the angle between the stator-axis and the d-axis.

Substituting (3.12), (3.13) and (3.14) into (3.11)

dq dq dq sdqj j jsdq sdqs

dv e R i e e

dt

= + ( 3.15)

Hence

sdq

sdq sdq sdqs dq

dv R i j

dt

= + + ( 3.16)

Using a similar approach, the rotor voltage equations in the reference frame, rotating

at r, can be obtained:


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MODELING

30

r

r r0 rd

v R idt

= = + ( 3.17)

Since the rotor is short circuited, rv = 0. In order to obtain a model of the induction

machine, both stator and rotor variables must be represented in the same reference

frame. Beingr the angle between the rotor-axis and the stator-axis, it yields:

rr

js e

= ( 3.18)

rr s

ji i e= ( 3.19)

Substituting (3.18) and (3.19) in (3.17) and multiplying by rje the rotor voltage

equation in the reference frame is obtained:

r

r r0rr r

dv R i j

dt

= = + ( 3.20)

The current, voltage and flux linkage rotor space vectors with respect to the -axis arerepresented in the rotating dq reference frame as follows:

dqr

jrdqv v e= ( 3.21)

dqr

jrdqi i e= ( 3.22)

dqr

jrdq e = ( 3.23)

Wheredq

is the angle between the stator -axis and the d-axis. Substituting (3.21),

(3.22), (3.23) into (3.20)

dq dq dq dq rdqj j j jrdq rdq rdqr r

dv e R i e e j e

dt

= + ( 3.24)

Hence

0 ( )rdq

rdq rdq rdqr r dq

dv R i j

dt

= = + ( 3.25)

3.16 and 3.25 can be written as function of the stator current space vector sdqi and the

rotor linkage flux space vector rdq . After mathematical manipulation:

sdq M Msdq sdq sdq rdq rdqs s dq s dq

r r

di L d Lv R i L j L i j

dt L dt L = + + + + ( 3.26)

0 ( )sdq rdq rdq rdqr M r dq r d

L i jdt

= + + + ( 3.27)

where

rdq rdq sdqr ML i L i = + ( 3.28)

is the rotor flux linkage referred to the stator side:


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MODELING

31

2

1 M

r s

L

L L = ( 3.29)

is the dispersion factor and

1r

r

r r

R

L T = = ( 3.30)

is the inverse of the rotor time constant Tr.

3.4 Back-to-back converter model

The back-to-back converter consists of two voltage source converters (VSC) and a

capacitor bank as shown in Figure 3-7. In generator mode operation, the generator side

converter absolves, at the same time, the following functions:

inverter for reactive power supply through the IG rectifier for the generated current from the IG

Therefore, due to the bi-directional flow of current, the grid side converter is considered

an active power converter.

On the other hand the grid-side converter operates as inverter, since it receives the DC

voltage on the DC link and produces the 3-phase voltages for the grid. The grid-side

converter need of its own control system, anyway its design beyond from the aim of

project, thus the grid-side converter will not be considered later on.

Figure 3-7: Back-to back converter

The model of the back-to-back converter is necessary in simulation to feed the generator

model. But since only the generator side converter is considered, the model of the whole

back-to-back converter is not needed. Consequently, the model of the generator side

VSC is sufficient to carry out the simulations. The model of the VSC is an average

model as the system includes a mechanical system making the time frame of interest

much longer than the switching time of the converter. Therefore, there is no need to

have a switching model where the effect of switching adds little significance to the

result.


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MODELING

32

For a star connected generator, the generator side voltages VA0, VB0 and VC0, shown in

Figure 3-8, can be calculated using (3.31), (3.32) and (3.33) where VAN, VBN and VCN

are the line-to-neutral voltages, between the specified points A, B or C and the neutral

point N.

Figure 3-8: Star connected generator and generator side converter

As the average model is used, VAN, VBN and VCN are the average voltages and SA, SB

and SC are the duty cycles.

0 0 0(2 )

3DC

A AN N A DC N A B C

Vv v v s V v s s s= = = ( 3.31)

0 0 0( 2 )

3

DC

B BN N B DC N A B C

Vv v v s V v s s s= = = + ( 3.32)

0 0 0( 2 )

3DC

C CN N C DC N A B C

Vv v v s V v s s s= = = + ( 3.33)

where V0N is defined as:

0

1( ) ( )3 3

DCN AN BN CN A B C

Vv v v v s s s= + + = + + ( 3.34)

The current IDC can be expressed as:

[ ]A

DC A B C B

C

i

s s s i

i

=

( 3.35)

With matrix notation the average voltages can be expressed as follow:


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MODELING

33

0

0

0Gain

2/3 -1/3 -1/3

-1/3 2/3 -1/3

-1/3 -1/3 2/3

A A

B DC B

CC

v s

v V s

sv

=

( 3.36)


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CONTROL SYSTEM DESIGN

34

4CONTROL SYSTEM DESIGN

4.1 Control of generator in different operation regions

A variable-speed variable-pitch WT is controlled as represented in Fig.4-1 in such a

way that:

when the mean wind speed V < Vmin (region 1), the WT rotates but it is not connected

to the grid because the power production is not enough to cover the operational cost; when minV V Vn (region 2), the WT is operated at variable-speed mode such thatthe captured power is maximized; the pitch angle is kept to the optimum value, ideally

zero;

when maxVn < V V (region 3), the WT works in variable-pitch operation forlimiting the captured power to the rated value; the WT rotor speed is then kept constant;

when the mean wind speed V > Vmax (region 4), the WT is stopped by means of the

pitch control system to avoid mechanical overloading; in this case mechanical breaks

are normally not enough so blades are pitched to very small angle of attack.

Figure 4-1: Ideal power regulation for a WT

Depending on the WT operation region, different control strategies can be used to

perform the desired action. In this project the operation region 2 will be considered,

since a wind turbine is not available for pitch control implementation.

In region 2, the induction generator is controlled to rotate at the speed that corresponds

to the maximum power coefficientMAXP

C . The generator reference speed is obtained


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35

directly from a lookup table that producers provide for installation, and this table

depends on the electrical-mechanical features of such a wind turbine.

4.2 Current model

In order to use the IFOC concept, a current estimation model is needed.

The current estimation model can be either represented in the stationary reference

frame or in the dq rotating reference frame. Considering a d-q rotating reference frame

aligned with the rotor axis can be written as follows:

'

(1 )dqdq

r

S r

M

i s TL

= + ( 4.1)

The following steps can be used for the rotor flux estimation:

transforming the stator current space vector s(a,b,c)i into sdqi by means of the Park

abc(i ) and Clark ( dq) transformations;

calculating rotor flux components 'rq and'

rd using the previous equation;

calculating rotor flux components 'r and'

r using the inverse Park transformation;

calculating the magnitude 'r

calculating' '

r rcos / = and' '

r rsin / =

calculating'

r

M

Lsi =

calculating the rotor flux frequency by means of the slip compensation equation.

The block diagram of the current model in the dq reference frame is shown in Figure

4-2:

Figure 4-2: Current model: rotor flux estimation block diagram

The rotor flux estimation based on the current model requires the measured speed and

thus the encoder, but the advantage is that the estimation is well performed down to zero


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36

speed. The estimation accuracy is affected by the variation of machine parameters

especially at high speed. For this reason this estimation model is not suitable at high

speed as a voltage model.

Since the current model flux estimation is better at low speed and the voltage model is

better at high speed, the best solution for the rotor flux estimation would be a hybridmodel. However in this project, the current model has been selected because it can work

at every speed even though the accuracy decreases as the rotor speed increases.

4.3 Indirect Field Oriented Control

This method consists on controlling stator currents represented by a space vector in a

rotating reference frame whose coordinates are d and q. The electrical model of the

electrical machine, for stator and rotor respectively, are represented by following

equations:

sdq M Msdq sdq sdq rdq rdqs s dq s dq

r r

di L d Lv R i L j L i j

dt L dt L = + + + + ( 4.2)

0 ( )sdq rdq rdq rdqr M r dq r d

L i jdt

= + + + ( 4.3)

where

rdq rdq sdqr ML i L i = + ( 4.4)

is the rotor flux linkage referred to the stator side

1 M

r s

L

L L = ( 4.5)

is the dispersion factor and

1r

r

r r

R

L T = = ( 4.6)

is the inverse of the rotor time constant Tr.

In the FOC the d-axis is aligned with the d-axis of rotor flux linkage space vector

'

rdq .Whit this assumption the rotor flux in the dq reference frame is a scalar

variable' '

rdq r = and dq = .

4.2) and 4.3) can be decomposed into d and q components as follows (d/dt is here

substituted by the Laplace operator)

d component of rotor voltage:

0 sd r rr M rL i s = + + ( 4.7)

q component of rotor voltage


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37

0 sq r rr M rL i = + ( 4.8)

d component of stator voltage

Msd sd rs s sd s sq

r

Lv R i L si L si s

L

= + + ( 4.9)

q component of stator voltage

Msq sq rs s sq s sd

r

Lv R i L si L si

L

= + + + ( 4.10)

where'

r

m

Lsi = is the component of the stator current that generates the rotor linkage

flux 'r .

From 4.7)

1

r M Mr sd sd

r r

L Li i

T s

= =

+ + ( 4.11)

4.11) shows that sdi is the command variable for the rotor linkage flux.

From 4.8 the angular speed of the rotor flux linkage 'r is obtained:

r M

r sqr

Li

= + ( 4.12)

4.12) shows that the rotor flux speed is obtained by adding to the electrical rotor

speedr the slip speed '

r

r mr sq

LS i = . This is the main characteristic of the Indirect

Field Oriented Control (IFOC). Substituting 4.11) into 4.9)

(1 (1 ) )1

sd s sq s s s sd

r

sv L i T s T R i

T s

+ = + + +

( 4.13)

where Ts = Ls/Rs is the stator time constant. From the transfer function along the d-axis

is obtained:

2

1 1( )

( ) 1

rsdsd s sq

s s r s r

T si v L i

R T T s T T s

+= +

+ + +

( 4.14)

Substituting 4.12) in 4.10):

( )( ) (1 )s s s r s rsq rs sd s r sq

M r s r

L R T T T T sv L i i i

L T T T

+

= ++

( 4.15)

Defining the equivalent time constant

s r

a

s r

T TT

T T=

+ ( 4.16)

and equivalent resistance


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38

( )s s r

a

s r

R T TR

T T=

+ ( 4.17)

4.15) can be rewritten as follows

( ) (1 )s

sq rs sd s r a a sq

M

Lv L i i R T s iL

= + ( 4.18)

Hence the transfer function along the q-axis is obtained:

'1 ( ( ) )(1 )

s

sq sq s sd s r r

a a M

Li v L i i

R T s L

= +

( 4.19)

The reference scheme of IFOC is depicted in Figure 4-3

IFOC

Figure 4-3: Indirect field oriented control system with IG and VSI

Electromagnetic torque in the dq reference frame

Stator and rotor linkage fluxes can be expressed as functions of the stator and rotor

currents as follows:

s r

r r s

ss M

r M

L i L i

L i L i

= +

= + ( 4.20)

substituting

'

ri from second equation in the first:

s rM

ss

r

LL i

L = + ( 4.21)

Substituting 4.21) into 3.11)

r

s

s Mss s

r

di L div R i L

dt L dt = + + ( 4.22)

Considering the motor operation, the absorbed instantaneous power is:


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39

* * * * r

s s

3 3 3 3( ) Re( ) Re( )

2 2 2 2

s Ms s s ss s

r

di L d t v i R i i L i i

dt L dt

= = + + (4.23)

The mechanical power in 4.23) is only the term that contains the rotor speed r . Hence:

* *r

r

3 3Re( ) Re( )

2 2

M Ms sm r

r r

L d LP i j i

L dt L

= = ( 4.24)

4.24) can be rewritten in the dq reference frame considering dq' ' jr rdq e= and

dq* * js sdqi i e= .

rdq rd rq

rd

3 3Re( ) Re( ( )( )

2 2

32

M M

m r r sd sq

r r

Mr sq

r

L LP j j j i ji

L L

L iL

= = +

=

( 4.25)

where'

rq = 0. The mechanical power can also be expressed as a function of the

electromagnetic torque Te:

r

m eP T

= ( 4.26)

wherep is the number of pole pairs. Equating (4.25) and (4.26)

r32

Me sq

r

LT p iL

= ( 4.27)

4.27) and 4.11) are combined in the block diagram in Figure 4-4. According to Figure

4-4 the rotor flux linkage 'r can be controlled by means of sdi whereas the

electromagnetic torque can be controlled by means ofsqi and

sdi .

Figure 4-4: Torque in terms of rotor flux and q-axis stator current

However, due to the transfer function betweensqi and

r , any step variations on

sqi cannot produce a sudden change in the rotor flux

r , which will build up with time

constant Tr. Thus in the FOC of induction machines, stator currents are controlled in


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40

such a manner thatsqi delivers the desired torque while

sdi maintains the peak rotor flux

at its rated value as far asr rn

. When the induction machine is operated as

generator the rotor flux is reduced proportionally to r1/ in order to avoid overvoltage,

this method is known as weakening operation.

4.4 Speed loop design

The speed loop is represented by the q-axis loop of the system ofFigure 4-3. The loop

is reported in the block diagram ofFigure 4-5.

Figure 4-5: Speed loop

Sincesqi is the torque command variable, the reference value *

sqi depends on the

required torque. In Figure 4-3 the speed loop is the outermost loop and the sqi current

loop the innermost loop. The error between the desired speed *r , and the measured

generator speed r pass through a PI controller (speed controller) in order to generate

the reference signal *sqi . The error between *

sqi and the q component of the stator current

sqi , obtained by means of the rotor flux estimation model, pass through another PI

controller, to generate the reference voltage sqv in the dq reference frame. Anyway'

sqv

is the only component ofsq

v that depends on the q stator currentsqi .

, (1 )sq sq comp a a sqv v R T s i = + ( 4.28)

where

,( ) s

sq comp s sd s r r

M

Lv L i iL

= + ( 4.29)

is considered a disturbance as it does not depend on sqi . In the design, the compensating

term,sq comp

v is neglected, as it has not significant influence on the behavior of the

system.

The PI controllers used for the control design are expressed in the following form:

1( ) iPI p

i

sF s K

s

+ = ( 4.30)


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41

Inner loop design

For the design of thesqi loop, only the proportional term is used. Therefore the inner

loop is composed by a P controller, a delay block and Plant1, as shown in Figure 4-6.

Transfer functions of the open loop are indicated in Table 1.

Figure 4-6: sqi loop

The Delay block represents the delay introduced by the digital calculation which istaken into account by means of a first order function with time constant:

10.333Ts ms

fs= = , where 3fs KHz= is the sampling frequency.

Table 1: Open loop transfer functions ofsqi loop

Open loop transfer functions

Plant11

(1 )a a

R T s+

1

0.02 3.5s +

Delay 11

sampls T+ 413.333 1e s +

G1 1Plant Delay 7 2

1

6.66 0.02117 3.5e s s + +

Open loop poles Pole(G1)1 3000p =

2 175p =

Requirements:

The requirement for the inner loop is to obtain a rising time at a step command

compatible with the management of a 100-200ms grid fault. Therefore the rising time ts

is needed to be much smaller respect to the short-term grid fault period. Furthermore a

proportional gain is chosen in order to meet the following requirements:

10

20%

s

MAX

t ms

s

simulation and laboratory of control system for wind turbine

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