Improvement of a fixed-speed wind turbine soft-starter based on a

University of SevilleDepartment of Electrical Engineering

Improvement of a fixed-speed windturbine soft-starter based on a

sliding-mode controller

Doctoral Thesis

by

Angel Gaspar Gonzalez Rodrıguez

Seville, March 2006

Improvement of a fixed-speed wind turbinesoft-starter based on a sliding-mode controller

Angel Gaspar Gonzalez Rodrıguez

Departamento de Ingenierıa Electronica, de Telecomunicacion y Au-tomatica de la Universidad de Jaen.

Para la obtencion del Grado de Doctor por la Universidad de Sevillacon Mencion de Doctorado Europeo.

Directores:

• Dr. D. Manuel Burgos Payan.Universidad de Sevilla.

• Dr. D. Juan Gomez Ortega.Universidad de Jaen.

A mi familia

Abstract

This work tackles the problem arising when the induction generator of afixed-speed or two-speed wind turbine is connected to the grid. A weakgrid where a local customer and a wind turbine are supplied by the networkby means of a long overhead line has been defined and simulated usingPSCAD/EMTDC and MATLAB. This situation particularly evidences theimpact of switching operations, mainly the start-up or the change betweengenerator windings.

Since the mechanical parameters defining the performance of the rotorspeed are rarely given by manufacturers, a simplified structural analysis ofa blade has been made in order to estimate the inertia time constant as afunction of the blade length and weight.

The performance and the logic control of the soft-starter gradually con-necting the induction generator of the wind turbine to the rotor is alsostudied. During this transient, the third order model has been establishedas the best model to explain the performance of the induction generator.Expressions for the real and reactive power has been derived which showthe strong influence of the voltage derivative on the reactive power.

Finally, two closed-loop controllers have been designed that improve theopen-loop linear control of the soft-starter. The former and more basicstructure presents a PI characteristic whose control signals are the suppliedvoltage and its derivative. The latter, based on sliding-mode techniques, isthe proposed one and is able to maintain the voltage dropout in a specifiedvalue. For fast connection conditions, the voltage dropout constrain mustbe relaxed in order to avoid excessive shaft torques and speed overshoots.

Acknowledgements

Quisiera agradecer a mis directores de tesis, Manolo Burgos y Juan Gomez,su guıa y el apoyo incondicional que me han mostrado, ası como por lamezcla de paciencia e insistencia que me ha permitido concluir este trabajo.

A Carlos Izquierdo, al que recuerdo con mucho carino, y a todos miscompaneros del Departamento de Ingenierıa Electrica de Sevilla: AntonioGomez, Manolo, Jose Marıa, Pedro, Jesus, Jose Luis, Jose Luis, Paco, Es-ther, Jose Antonio, Alicia, Antonio, Reme, Luis y Pilar. Con todos ellos hevivido momentos muy entranables.

A mis ya no tan nuevos companeros de Jaen: Javier Gamez, Silvia, Jesus,Alejandro y demas companeros de planta y fatiga.

A Juan, Jose Juan, Nacho y a los demas amigos de futbol, valvula deescape en los muchos momentos de stress.

A mis padres Antonio y Marıa y a mi hermano Toni, por todo.

Y a mi mujer Marıa Jesus, y a mis hijos Marıa Jesus y Gaspar, por eltiempo que esta tesis les ha robado y por los muchos y buenos momentosque he pasado y me esperan con ellos. Y porque sı.

Jaen Angel Gaspar Gonzalez Rodrıguez24 de Enero de 2006

Table of Contents

Table of Contents

List of Tables

List of Figures

Index

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Start-up transients 112.1 Wind generator starting process . . . . . . . . . . . . . . . . . 112.2 Voltage fluctuation . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Description of the system 173.1 Turbine-generator mechanical system . . . . . . . . . . . . . . 183.2 Generator electrical model . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Induction generators in wind turbines . . . . . . . . . 223.2.2 Two-speed induction generators . . . . . . . . . . . . . 233.2.3 PSCAD/EMTDC squirrel cage model . . . . . . . . . 243.2.4 Electrical parameters . . . . . . . . . . . . . . . . . . . 25

3.2.5 PSCAD/EMTDC and MATLAB for simulating in-duction generators . . . . . . . . . . . . . . . . . . . . 26

3.3 Soft-starter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.4 Additional components . . . . . . . . . . . . . . . . . . . . . . 28

3.4.1 Power Transformer and line to the PCC . . . . . . . . 283.4.2 Local load . . . . . . . . . . . . . . . . . . . . . . . . . 303.4.3 Electrical network and distribution line . . . . . . . . 30

4 Estimation of mechanical constants 334.1 Estimation of the inertia time constant . . . . . . . . . . . . . 34

4.1.1 Values used for the analysis . . . . . . . . . . . . . . . 37Blade fatigue stresses . . . . . . . . . . . . . . . . . . 37

4.1.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 394.1.3 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . 414.1.4 Blade weight . . . . . . . . . . . . . . . . . . . . . . . 414.1.5 Static analysis . . . . . . . . . . . . . . . . . . . . . . 424.1.6 Inertia Time Constant H . . . . . . . . . . . . . . . . 49

Comparison of cumulated mass distributions . . . . . 494.1.7 Estimating a wind turbine inertia constant . . . . . . 504.1.8 Estimating H for different wind turbine capacities . . 514.1.9 Estimating the remaining inertia time constants . . . 55

4.2 Other mechanical constants . . . . . . . . . . . . . . . . . . . 594.2.1 Self damping . . . . . . . . . . . . . . . . . . . . . . . 594.2.2 Torsional stiffness . . . . . . . . . . . . . . . . . . . . 614.2.3 Mutual damping . . . . . . . . . . . . . . . . . . . . . 62

5 Soft-starter 655.1 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Thyristor triggering . . . . . . . . . . . . . . . . . . . . . . . 695.3 Operation modes . . . . . . . . . . . . . . . . . . . . . . . . . 705.4 Wind turbine soft-starter . . . . . . . . . . . . . . . . . . . . 735.5 Asymmetrical soft-starter . . . . . . . . . . . . . . . . . . . . 745.6 Firing angle control system . . . . . . . . . . . . . . . . . . . 74

6 Induction machine dynamic models 776.1 Fifth order model . . . . . . . . . . . . . . . . . . . . . . . . . 786.2 Reduced models for the induction machine . . . . . . . . . . . 81

6.2.1 First approach: third order model . . . . . . . . . . . 816.2.2 Second approach: first order model . . . . . . . . . . . 81

6.3 Third order model main equations . . . . . . . . . . . . . . . 826.3.1 Validity conditions . . . . . . . . . . . . . . . . . . . . 82

6.3.2 Reduced electrical system . . . . . . . . . . . . . . . . 856.4 P and Q in the third order model . . . . . . . . . . . . . . . 87

7 Sliding-mode control to limit voltage dropout 917.1 Voltage dropout in a weak grid . . . . . . . . . . . . . . . . . 947.2 Definition of the sliding trajectory . . . . . . . . . . . . . . . 977.3 Sliding mode controller with integral compensation . . . . . . 1027.4 Control law parameters . . . . . . . . . . . . . . . . . . . . . 1077.5 Implementation of the proposed controller . . . . . . . . . . . 1117.6 Simulation using the proposed controller . . . . . . . . . . . . 1147.7 Comparison to other control schemes . . . . . . . . . . . . . . 1177.8 Sensitivity to speed and voltage measurements . . . . . . . . 1237.9 Influence of the line impedance . . . . . . . . . . . . . . . . . 126

8 Conclusions 1298.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1298.2 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . 132

A Weight and size for different blades 135

B Extended power-diameter table 139

References 143

List of Tables

3.1 Electrical parameters of wind turbine induction generators. . 253.2 Characteristics of different conductors. . . . . . . . . . . . . . 29

4.1 Data for the estimation of H . . . . . . . . . . . . . . . . . . 564.2 Data for the estimation of M and H . . . . . . . . . . . . . . 574.3 References including H. . . . . . . . . . . . . . . . . . . . . . 58

6.1 Electrical parameters for the induction machine. . . . . . . . 82

6.2 Transfer function Gr =−δTr

δωr. . . . . . . . . . . . . . . . . . . 83

6.3 Transfer function Gv =δTv

δVs. . . . . . . . . . . . . . . . . . . . 84

7.1 Electrical constants for stability study I. . . . . . . . . . . . . 1077.2 Electrical constants for stability study II. . . . . . . . . . . . 108

A.1 Weight, size and corresponding power for several blades I. . . 135A.2 Weight, size and corresponding power for several blades II. . 136A.3 Weight, size and corresponding power for several blades III. . 137

B.1 Diameter and power for several wind turbines I. . . . . . . . . 139B.2 Diameter and power for several wind turbines II. . . . . . . . 140B.3 Diameter and power for several wind turbines III. . . . . . . . 141B.4 Diameter and power for several wind turbines IV. . . . . . . . 142

List of Figures

1.1 Market share of wind turbine concepts. . . . . . . . . . . . . . 2

2.1 Flicker curve according to IEC 868. . . . . . . . . . . . . . . . 15

3.1 Wind turbine in a weak grid. . . . . . . . . . . . . . . . . . . 183.2 PSCAD diagram of the system components. . . . . . . . . . . 193.3 Mechanical components in a wind turbine. . . . . . . . . . . . 203.4 Multimass and induction machine components. . . . . . . . . 213.5 Graphical model for the multimass mechanical dynamics. . . 223.6 Two-cage induction machine model. . . . . . . . . . . . . . . 243.7 Transient simulations of an induction machine using PSCAD

and MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . 263.8 Real and reactive power dependance on the voltage and its

derivative. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.9 Soft-starter power circuit . . . . . . . . . . . . . . . . . . . . 283.10 Normalized voltage evolution for different line impedances. . 303.1 Voltage change vs. line impedance. . . . . . . . . . . . . . . . 31

4.1 Graphical model for the multimass mechanical dynamics. . . 344.2 Wind turbine blade. . . . . . . . . . . . . . . . . . . . . . . . 354.3 Definitions for a wind turbine blade. . . . . . . . . . . . . . . 354.4 Composition of the blade. . . . . . . . . . . . . . . . . . . . . 364.5 Chord along the span. . . . . . . . . . . . . . . . . . . . . . . 364.6 Relative thickness. . . . . . . . . . . . . . . . . . . . . . . . . 374.7 Fatigue cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . 384.8 Cycle to failure for R = -1, R = 0.1 and R = 10. . . . . . . . 40

4.9 Lift and drag coefficients. . . . . . . . . . . . . . . . . . . . . 414.10 Relationship between weight and length. . . . . . . . . . . . . 434.11 Load-carrying main spar from a wind turbine blade. . . . . . 444.12 Components of the aerodynamic forces. . . . . . . . . . . . . 444.13 Thickness, skin and chord. . . . . . . . . . . . . . . . . . . . . 454.14 Distribution of forces acting at the blade. . . . . . . . . . . . 464.15 Shear web width along the blade span. . . . . . . . . . . . . . 494.16 Typical and calculated cumulated mass. . . . . . . . . . . . . 514.17 Comparison of different weight-length relationships. . . . . . 524.18 Relationship Capacity-Diameter. . . . . . . . . . . . . . . . . 544.19 Inertias for different turbine capacities. . . . . . . . . . . . . . 554.20 Composition of forces exerted on the blade. . . . . . . . . . . 60

5.1 Soft-starter power circuit. . . . . . . . . . . . . . . . . . . . . 665.2 Soft starter control circuit and control signal time evolution. 675.3 Variation in the supplied voltage by means of a soft-starter. . 695.4 Pulses at gates. Separation between forward thyristor trig-

gering pulses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.5 Gate triggering sequence and line currents. . . . . . . . . . . 715.6 Conduction periods of the thyristors. Operation with current

interruptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.7 Conduction periods of the thyristors. Operation without cur-

rent interruptions. . . . . . . . . . . . . . . . . . . . . . . . . 735.8 Asymmetrical pulse sequence at the thyristor gates and phase

current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.1 Arbitrary reference frame. . . . . . . . . . . . . . . . . . . . . 786.2 Small signal block diagram representation of the induction

generator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.3 Root loci for the mechanical closed-loop function transfer . . 846.4 Real and Reactive Power. Comparison of steady state, third

and fifth order models. . . . . . . . . . . . . . . . . . . . . . . 89

7.1 Single wind turbine feeding a consumer in a weak grid. . . . . 947.2 Voltage in the PCC during the connection process. . . . . . . 967.3 Sliding trajectories for different αP + βP . . . . . . . . . . . . 997.4 σ and ∇σ in the phase plane. . . . . . . . . . . . . . . . . . . 1007.5 Example of ~x = (x1, x2) that might not reach σ = 0. . . . . . 1007.6 Simplified performance of the soft-starter. . . . . . . . . . . . 103

7.71

kssat different generator voltages and slips. . . . . . . . . . . 109

7.8 Sliding-mode controller with integral compensation. . . . . . 1127.9 Calculation of σ. . . . . . . . . . . . . . . . . . . . . . . . . . 1137.10 Sliding-mode controller simplified control law. . . . . . . . . . 1147.11 Overall scheme of the wind turbine feeding a local load. . . . 1157.12 Performance of the system connected through a soft-starter

fired in accordance with a sliding-mode controller action . . . 1167.13 Three firing angle control techniques . . . . . . . . . . . . . . 1187.14 Firing angle controllers used as references. . . . . . . . . . . . 1197.15 Voltage dropout for different control schemes . . . . . . . . . 1217.16 Voltage change and shaft torque for different control schemes 1227.17 Performance of tested control schemes for another generator . 1237.18 New PSCAD component designed to simulate the presence

of noise in the speed and voltage measurements and the dis-cretization process. . . . . . . . . . . . . . . . . . . . . . . . . 124

7.19 Performance of the sliding-mode controller when noise anddiscretization are added to the speed signal. . . . . . . . . . 125

7.20 Controllers’ performance when a random noise in voltage andspeed signals are considered. . . . . . . . . . . . . . . . . . . . 126

7.21 Comparison of tested controllers for different line impedances. 1277.22 Voltage dropout and voltage change vs. line impedance. . . . 128

Index

E′, 86Enw, 94H, inertia time constant, 4, 33, 51,

54, 80I, momentum of inertia, 43Ib, base current, 88J , inertia constant, 34, 50, 51, 54K, torsional stiffness, 61L, blade length, 35Lr, rotor self-inductance, 85Ls, stator self-inductance, 85Llr, rotor leakage inductance, 79Lls, stator leakage inductance, 79Lms, magnetizing inductance, 79M , 79MD, mutual damping, 62My, flapwise momentum, 43, 45, 46Mz, chordwise momentum, 43N c, number of load cycles, 38Nr, turns of the rotor winding, 79Ns, turns of the stator winding, 79Nx, axil force, 43PCC, point of common coupling, 18,

23, 29, 94, 95, 117R′

r, rotor resistance, 23Rr, rotor resistance, 107

Rs, stator resistance, 107RFe, equiv. resistance iron losses, 26Rlin, line resistance, 30, 31, 108, 127S, complex power, 87, 88SD, self damping, 59Sb, base power, 88Te, mechanical torque, 79Tr, rotor time constant, 86Ub, base voltage, 88UPCC , 94X, 86X ′, transient reactance, 86Xm, magnetizing reactance, 107Xr, rotor reactance, 107Xs, stator reactance, 107Xcg, center of gravity, 50Xlin, line reactance, 30, 31, 108, 127Z, 87Z ′, transient impedance, 86, 88Zb, base impedance, 88Ω, rotational speed, 45, 62α, firing angle, 69, 70, 73, 102, 114,

118α, angle of attack, 41, 59αP , 98αQ, 98

βP , 98βQ, 98δ, relative wind speed angle, 46εcap, spar cap width, 35, 43, 50εskin, skin width, 35, 50εweb, shear web width, 35, 43, 47, 49,

50εweb, 45λ, flux linkage, 78λ, tip speed ratio, 35, 39ωr, generator rotor speed, 78σ, leakage parameter, 82σ, stress, 38, 39σxx, span-wise strength, 43θ, stator voltage angle, 87, 97, 994UL, permitted voltage dropout, 98,

102, 112cd, aerodynamical drag coefficient, 41,

46, 59cl, aerodynamical lift coefficient, 35,

41, 46ch, chord, 35, 59d, d-axis component, 79g, gravity acceleration, 45kperim, perimeter factor, 45kss, 103lv, low voltage side of the transf., 95ngb, gearbox ratio, 52npp, number of pole pairs, 53, 61, 80p, derivative operator, 78q, q-axis component, 79r, rotor magnitude, 78s, slip, 68, 82, 85, 111, 116, 120, 123s, stator magnitude, 78t, referred to stator, 79th, thickness, 35usl, control law, 102vr, relative wind speed, 46, 59vtip, tip speed, 53, 59z, number of blades, 35, 52

aerodynamical drag coefficient, 41, 46,59

aerodynamical lift coefficient, 35, 41,46

angle of attack, 41, 59asymmetrical soft-starter, 74, 120axil force, 43axil strength, 42

base current, 88base impedance, 88base power, 88base voltage, 88blade geometry, 34blade length, 35box spar structure, 36brake, 19by-pass contactor, 74

cable, 29capacitor bank, 12, 74, 123center of gravity, 50chattering, 117chord, 35, 45, 59chordwise momentum, 43complex power, 87, 88, 92, 97compressive strength, 39connection sequence, 11consumer, 2, 13, 18, 94, 95, 115, 116contactor, 12control law, 102, 114, 125cut-in, 114cut-in speed, 11, 23

Danish concept, 1, 23deenergization, 27deep wound effect, 22, 24derivative of voltage, 27derivative operator, 78discretization, 123double cage model, 24

drag, 20

efficiency, 23equiv. resistance iron losses, 26

fatigue, 19, 37firing angle, 68–71, 73, 102, 114, 118,

126fixed-speed wind turbine, 14flapwise momentum, 38, 43, 45, 46flexible coupling, 19, 21flicker, 12flux linkage, 78

gearbox, 18, 20, 33gearbox ratio, 52generator rotor speed, 78glass reinforced epoxy skin, 36gravity acceleration, 45

hub, 55

in-rush current, 68inertia constant, 19, 34, 50, 51, 54inertia time constant, 4, 33, 51, 54,

80inrush current, 4interconnection, 4, 8, 14, 92iron losses, 23

leakage parameter, 82leakage reactance, 24line reactance, 30, 31, 108, 127line resistance, 30, 31, 108, 127load cycles, 38local load, 18, 30, 94, 115, 130

magnetizing inductance, 79magnetizing reactance, 107mass distribution, 50MATLAB, 4, 26, 112mechanical torque, 79

momentum of inertia, 43multimass, 19mutual damping, 21, 34, 62

noise, 123number of blades, 35, 52number of load cycles, 38number of pole pairs, 53, 61, 80nw, network, 94

overhead line, 29, 30

per unit system, 33perimeter factor, 45permitted voltage dropout, 98, 102,

112PI-controller, 117, 125pitch-controlled, 14point of common coupling, 18, 23, 29,

31, 94–96, 117power fluctuation, 13power transformer, 12, 18, 28PSCAD/EMTDC, 4, 18, 24, 26, 89,

120pulse sequence, 70pulse train sequence, 69, 120

R-value, 38, 39reference frame, 78referred to stator, 79relative thickness, 35relative wind speed, 46, 59relative wind speed angle, 46relative wind velocity, 20resolution, 123rotational speed, 45, 62rotor leakage inductance, 79rotor reactance, 107rotor resistance, 23, 107, 121rotor self-inductance, 85rotor time constant, 86

rotor, wind turbine, 18

self damping, 20, 33, 59shaft spring constant, 21shaft torque, 121, 122shear web, 36shear web width, 35, 43, 47, 49, 50short circuit power, 30skin width, 35, 50sliding mode, 92slip, 24, 27, 68, 82, 85, 111, 116, 120,

123slip overshot, 121soft-starter, 12, 18, 27, 65span-wise strength, 43spar cap, 36spar cap width, 35, 43, 50speed overshot, 117squirrel cage induction generator, 24stall-controlled, 14start-up sequence, 11stator leakage inductance, 79stator reactance, 107stator resistance, 107stator self-inductance, 85stator voltage angle, 87, 97, 99steady state model, 81, 89stress, 38, 39

tensile strenghts, 39thickness, 35, 47thyristor, 28thyristor triggering, 69tip speed, 53, 59tip speed ratio, 35, 39torsional stiffness, 21, 33, 61transient impedance, 86, 88transient reactance, 86turns of the rotor winding, 79turns of the stator winding, 79twist angle, 21, 61

two-speed induction generator, 12, 23

ultimate strength, 39

voltage change, 31, 96, 121, 122, 125–127

voltage controller, 66, 67voltage dropout, 94–96, 120, 121, 125–

127

weak grid, 4, 14, 17, 30, 31, 94, 114,127, 130

weight, 41wind farms, 17wind torque, 19winding, 12, 23, 114

X/R ratio, 31

Chapter 1

Introduction

1.1 Motivation

Wind turbines for the production of electrical energy have spread all aroundthe world and have shaped up, together with minihydraulic energy, to be themain source of renewable energy contributing to the reduction of greenhouseeffect gases.

The declining power electronic device production costs, as well as economiesof scale have introduced two new designs between most accepted wind tur-bine models: variable-speed and variable-slip turbines. The former typ-ically consist of direct-drive synchronous generators connected to the net-work through frequency converters. In the latter, one can also find frequencyconverters, but connected to the wound rotor of doubly-fed induction genera-tors. In fact these are not novel configurations, and even large variable-speedwind turbines came prior to fixed (or two) speed Danish concept based onsquirrel cage induction machines. But price reduction of power electron-ics based on IGBTs and its higher reliability, have lead variable-speed andvariable-slip models to overtake squirrel cage for wind turbines over 1.5 MWin capacity (see Fig. 1.1 extracted from [1]).

However, for a long time, and mainly for turbines up to 1.5 MW, therewill exist an important quota of constant-speed or two-speed wind turbines.

2 Chap. 1: Introduction

Figure 1.1: Market share of wind turbine concepts.

One of the drawbacks of the induction generators used in these turbines,derived from its inability to vary the speed except within a narrow range, isits stiffer performance that can cause disturbances in the electrical grid thatthe wind turbine is connected to. In general, two issues greatly determinethe impact of fixed-speed wind turbines:

• Wind speed changes cause fluctuations in the real power delivered tothe distribution network.

• Wind turbine electrical connection gives place to voltage dropout thatcould deteriorate the power quality of the nearby consumers.

Both of them cause a decline in the power quality that utilities are re-sponsible for supplying.

Present study addresses the latter issue, the impact of the constant-speedor two-speed wind turbine start-up on the voltage at the point of commoncoupling within the medium voltage electrical distribution network. As aresult of this analysis, a closed-loop controller will be designed in order tomitigate the undesirable side effect of the resulting transient.

1.2 Survey 3

1.2 Survey

Improvement of the impact of fixed-speed wind turbine.

In comparison to other electrical issues concerning wind turbines, suchas transient stability, self-excited operation or delivered power fluctu-ations, the impact of electrical connection of wind turbines to the gridhas not been received the same attention. In fact this problem onlyarises with constant-speed or two-speed generators (hereafter referredto as fixed-speed generators), and theoretically, for stall-controlledwind turbines only. This configuration is not being considered fornew multi-megawatt wind turbines, although it is still used by mostof the main manufacturers (Neg Micon, Bonus, MADE, Ecotecnia) intheir medium-size designs.

A limiting factor for the fixed-speed stall-controlled wind turbines isthe voltage dropout caused by switching operations, mainly duringthe start-up. This negative side impact is more marked the weakerthe grid the wind turbine is connected to.

Closed-loop control for soft-starters.

Information about soft-starters can be found in a dispersed and im-plicit way. Furthermore, this information is basically related to themotor operation of induction machines, starting from standstill. Thisis not the situation in wind turbines, where the induction machinespeed hardly varies during the soft-starter performance, but involvesa shift between motor and generator operation. Since the inductiongenerator connection must be accomplished for rotational speed veryclose to the synchronous speed, applied voltage vs. firing angle char-acteristics as shown in [2] or [3] are not applicable here.

In order to mitigate this drawback of the fixed-speed wind turbines, anovel closed-loop control of the soft-starter used to gradually connectthe generator to the distribution network will be presented in thiswork. The analysis will be focused on stall-controlled wind turbinesbut it can also be applied to pitch-controlled turbines, in the case ofwind gusts suddenly exerting an uncontrolled accelerating torque onthe rotor speed.

Third order model to explain the start-up evolution.

The third order induction machine model has been used to explain thestart-up dynamic process. The steady state model is not suitable as it


is not able to explain the reactive power evolution. The value of thereal power also differs from the actual one mainly when its contributionis of more influence. The fifth order model is the most accurate but it isdifficult to use in order to provide analytical expressions or qualitativeideas.

As the soft-starter is an electronic device whose performance duringthe wind turbine start-up is very poorly modeled, an open-loop con-trol appears as a simple but far from optimum strategy to smooth theelectrical connection of the induction generator. Two closed-loop con-trols have been simulated: a PI controller and a sliding-mode basedcontroller. Both of them are based on the qualitative study of theinduction machine performance.

Controlling real and reactive power.

The third order model equations show that reactive power and thederivative of the generator voltage are closely related. Therefore, theobjective of both closed-loop controllers will not be to limit the inrushcurrent, as has traditionally been the most important feature of soft-starters, but to regulate the reactive power or at least, avoid highpeaks in its value with the aim of decreasing the voltage dropout at theinterconnection. The interconnection is defined in [4] as the electricalconnection between a wind turbine generator system and a network, inwhich energy can be transferred from the wind turbine to the networkand vice versa.

Realistic estimation for inertia time constant.

Wind turbine performance during the start-up as well as in transientstability studies is strongly influenced by the mechanical parametersof the turbine dynamics: inertia constant, self and mutual dampingor torsional stiffness. These parameters are rarely given by the manu-facturer/supplier, and wind turbine modeling is usually forced to usevague estimated values. Therefore, a discussion about how to obtainrealistic values of the inertia time constant as a function of the blademass and length, or the rated wind turbine power will be introducedin this work. The dependence of the remaining values on the ratedpower will be also provided.

PSCAD/EMTDC for electromechanical transients simulations.

A scenario including a weak electrical network using two simulationtransient programmes: MATLAB and PSCAD/EMTDC. The former

1.3 State of the art 5

allows an easier design of new components and it is a more refined anddepurated general purpose program. It also provides a more directinterface for data management: identification, error analysis, plots...The latter is quite faster when the system includes a relatively largenumber of nodes. One of the reasons is the use of interpolation withPSCAD/EMTDC in determining the exact switching times that al-lows the simulation to run at high speed and does not introduce in-accurate results [5]. Another valuable feature of PSCAD/EMTDC isthe accurate model provided for the wind turbine rotors, transformers,underground cables and other electrical and electronic devices.

1.3 State of the art

Start-up process The electrical connection of wind turbine generators tothe distribution network is a process that has not been well docu-mented in wind energy literature. Furthermore, most of the worksprovide data and conclusions regardless of whether the wind turbineis stall-controlled or pitch-controlled.

Differentiated data for both kind of controls for the start-up and theshutting down can be found in [6, Larsson]. For the case of stall-controlled wind turbines, the author vaguely indicates that the gen-erator is connected to the grid when its rotor speed is close to thesynchronous one.

[1, Ackermann], [2, Hansen et al] and [7, Hansen et al] state thatthe connection must be initiated when the generator speed reaches orexceed the synchronous speed. Simulations performed for the case ofstall-controlled wind turbines disagree with this assert, and thereforethe referenced report and article could be referred to pitch-controlledwind turbines where a control of the applied torque allows to avoidthe over-speed.

In the extreme case of a direct connection without soft-starter [8, Ham-mons and Lai], the electrical connection is also initiated at a oversyn-chronous speed.

Soft-Starter Existing information about soft-starters is mainly focused toinduction motors starting from standstill. The objective in this caseis usually to control the firing angle of the soft-starter thyristors inorder to limit the start-up current and to minimize torque pulsations


[9, Deleroi et al], [10, Zenginobuz et al], [11, Cadirci et al], [12, Kayet al] and [13, Prasad and Sastry]. A soft-starter is employed in [14,Ginart et al] as a discrete frequency inverter to provide a high startingtorque. [15, Gastly and Ahmed] proposes an artificial neural networkto control the speed of induction motor drive systems.

Besides this capability of limiting the current and, in some cases, min-imizing the torque pulsations, existing soft-starting for motor applica-tions also include another kind of starting [16, McElveen and Toney],that is the voltage ramp starting. In this scheme, the voltage is pro-gressively increasing, according to a predetermined evolution of thefiring angle. This second method is the only included by wind turbinesoft-starters. Furthermore, no references to closed-loop strategies, su-pervising and limiting the current or the voltage dropout, have beenfound. In this sense, the uncontrollability of the induction machine atspeeds close to the synchronous one makes no feasible to adapt controlschemes from motor drives to the case of wind turbines.

However, interesting information about the sequence of firing pulsesof the tyristor gates can be found in [9, Deleroi et al], [10, Zenginobuzet al] or [15, Gastly and Ahmed].

A very interesting and detailed description of the soft-starter conduc-tion modes and patterns for the current and voltage waveforms, canbe found in [9, Deleroi et al], [17, Le and Berg], [18, Barton] or [19,Murthy and Berg].

Another capability of soft-starters is addressed in [20, Blaabjerg], thatis the performance as a voltage controller reducing the supplied voltageat low loads, thus reducing the iron losses. The study concludes thatthe energy saving is not enough to advise the installation of the soft-starter to an ac drive since the payback time will be long.

Calculation of the voltage dropout The voltage dropout experiencedby a local load at the interconnection node has been calculated inthe literature in different ways. For continuous operation it is estab-lished that the voltage dropout caused by the wind turbine can bedetermined from the components of the complex power and the com-ponents of the impedance linking the consumer with the distributionnetwork. The simplified expression

4U =P R + QX

U2(1.3.1)

is usually preferred [21, Thiringer], [22, Saad-Saoud and Jenkins], [23,

1.4 Objectives 7

Brauner and Haidvogl] although a more accurate one is provided [24,25, Larsson] or [26, Bossanyi, Saad-Saoud and Jenkins].

However, when switching operations are being studied, the voltagedropout is obtained multiplying the inrush current by the short cir-cuit impedance or the line reactance [6, Larsson], [27, Demoulias andDokopoulos], [28, Nevelsteen and Aragon], [12, Kay et al]. Due tothe high value of the derivative of the voltage during the start-up, thereactive power will be quite higher than the real power during mostof the start-up transient. Nevertheless, in order to more accurate es-timate the voltage dropout, both components of power must be takeninto account and the expression 1.3.1 used. A different conclusionis reached in [8, Hammons and Lai] where induction generators em-ployed in low head hydro schemes are connected without soft-starters,obtaining that the voltage dip is proportional to inrush current and toimpedance of the supply for the case where impedance of the supplyis predominantly resistive.

Voltage dropout or voltage change Another concern to be taken intoaccount is that most of papers dealing with the switching operations ofwind turbines, quantifies the start-up impact by means of the voltagedip or voltage dropout, that is the difference between the voltage priorthe process and the lower voltage during the connection transient.However, the maximum voltage change during the electrical connectionshould be considered [29, Standard CEI 61400-21], which may involvethe final voltage once the electrical connection has been accomplished.

1.4 Objectives

As a result of the literature survey, the following main conclusion can bederived:

• Most of the technical literature about soft-starters deals with inductionmotor performance where the main objective is to reduce the inrushcurrent following the motor start-up process in order to fulfil technicaland normative regulations. However, regulations and conditions forthe induction generators in wind turbines are quite different.


– While induction motors start from standstill, induction genera-tors are connected to the distribution network when the rotorspeed reaches a value close to the synchronism.

– While induction motors regulations limit the inrush current dur-ing the start-up process, induction generators regulations limitthe voltage variations at the interconnection to the distributionnetwork.

In this thesis, the performance of soft-starting devices with wind turbineinduction generators will be addressed in order to cover the lack of work inthis area. Differences between the performance of soft-starters working withmotors and generators will be analyzed.

As a result, a new induction generator soft-starting approach will be pro-posed, focused on the voltage at the interconnection rather than in the cur-rent, as in the previous motor approach. To reach this goal the controllerwill limit the reactive power flow and will try to compensate the associatedvoltage dropout with the real power injection.

Previously, a simplified structural analysis of a wind turbine blade will beperformed in order to analyze the relationship that links the inertia timeconstant of a wind turbine rotor with the blade length and weight. Startingfrom this expressions and data extracted from manufacturers catalogues,approximate laws relating the inertia time constant and the self-damping tothe wind turbine rated capacity will be estimated.

1.5 Content

After the introduction, Chapter 2 describes the electrical connection process,its impact at the interconnection, and sets the convenience of limiting thedropout within acceptable values.

Chapter 3 presents the scenario designed to test the proposed solutions tomitigate the electrical connection impact during the start-up.

Chapter 4 analyzes in depth the mechanical component that models thewind turbine rotor, as well as its coupling to the generator shaft. A discus-sion will be introduced to question how to calculate realistic values for thewind turbine inertia as a function of the mass and length of the blades.

1.5 Content 9

In Chapter 5, an electronic device called soft-starter will be studied. Thiscomponent is used to gradually connect the induction machine to the elec-trical grid where eventually the produced real power will be delivered.

Chapter 6 reviews the main approaches that are used to model inductionmachine performance, specially those used for the description of transientsituations. The complete system of differential equations will be simplifiedto yield a reduced order model that appears as the most suitable one toexplain the induction machine performance during the start-up.

Chapter 7 will present two improvements to the currently used method tocontrol the soft-starter, with the aim of alleviating the impact of the windturbine connection to the grid.

Finally, in Chapter 8 the main conclusions and the relevant contributionsof this work will be summarized. To conclude, some guidelines and sugges-tions for future work will be provided.

Chapter 2

Start-up transients

2.1 Wind generator starting process

With regard to wind turbines without frequency converters, the electricalconnection of the generator to the network is one of their starting sequencestages. This sequence begins when a wind speed higher than the cut-inspeed 1 is detected and consists of the following steps:

• The nacelle is positioned for the rotor plane to be perpendicular towind direction.

• Slow shaft and/or fast shaft brakes are released.

• Aerodynamical tip brakes are drawn in (fixed-pitch turbines) or bladesare turned to 45o angle (variable pitch turbines). Following that, rotorwill accelerate due to the incoming wind energy.

1Cut-in wind speed is the lowest wind speed at hub height at which the wind turbinestarts to produce useable power [30]

12 Chap. 2: Start-up transients

• When induction machine rotor speed, equal to the fast shaft speed,is close to the induction machine synchronous speed, about 0.96-0.98times this speed, the generator electrical connection to the networkbegins [31]. Some reports and research papers state that the soft-starter should begin its performance when the generator speed exceedsthe synchronous speed [1][2][7], although simulations show an excessivevoltage dropout and torque overshot in the case of stall-controlled windturbines, where the incoming torque exerted by the wind cannot becontrolled.

To accomplish the electrical connection, the network voltage will begradually supplied to the machine terminals through an electronic de-vice called soft-starter. It consists in six thyristors whose gates areexcited by trains of pulses initiated at certain firing angles. Con-trolling these firing angles, the generator voltage can theoretically beregulated.

• Electrical connection can be considered to be completed when voltageat the generator terminals presents the same rms value as that of thenetwork at the low voltage side of the power transformer.

• At this point a contactor will close its poles by-passing the thyris-tors and the capacitor bank is connected according to compensationrequirements.

Two-speed induction generators possess two stator windings: the former,used at low wind speed, is the low power one (about five times less) and theslower as it is generally a three pole-pair winding; the latter is used in the restof the wind speed operating range, giving place to the rated real power, andit is generally a two pole-pair winding. Thus, for normal situations where thewind speed increases to a high enough value, the connection process mustbe repeated for each winding, since the synchronous speed will be differentfor each case.

2.2 Voltage fluctuation

The term flicker is derived from the impact of the voltage fluctuation onlamps such that they are perceived to flicker by the human eye. Flickeris defined as “an impression of unsteadiness of visual sensation induced by

2.2 Voltage fluctuation 13

a light stimulus, whose luminance or spectral distribution fluctuates withtime”. It can be measured with a flicker meter, where the physiologicalprocess of visual perception is simulated based on voltage measurements[32]. To be technically correct, voltage fluctuation is an electromagneticphenomenon while flicker is an undesirable result of the voltage fluctuationin some loads. However, the two terms are often linked together in standards[33], and thus from an electrical point of view, flicker is usually referred to asa measure of voltage variations which may cause disturbances to consumers.

Voltage variations is one of the main concerns related to the connectionof wind turbines to the network and many investigations have been maderegarding flicker produced by continuous operation [32, 26, 21, 7, 34], byswitching operations [6], or both [35, 36].

Voltage fluctuations under continuous operations is caused by active powerfluctuations which in turn are produced by tower shadow, yaw errors, windshear, wind eddies or fluctuations in the control system. Power fluctua-tions due to wind-speed fluctuations have lower frequencies and thus areless critical for flicker [1].

On the other hand, switching operations, mainly the start-up, produceshigh reactive power transients that cause voltage dropouts.

In some areas where wind farms are being installed, utilities are takingthe issue of flicker induced by operating fixed speed wind turbines seriously,due to their responsibility to supply a minimum level of quality power totheir customers. They insist on type test results being provided for turbinesproposed for connection to their networks, from which they decide on themaximum generation capacity which can be connected at the proposed pointof connection.

Therefore voltage fluctuation may be a limiting factor on the size of thewind farm to be connected. This constraint has been a contributing factortowards leading some wind turbine manufacturers and wind farm develop-ers to adopt variable-speed turbines, that produce lower voltage fluctuationthan fixed-speed turbines. This lower impact is achieved due to the factthat power fluctuations and switching operation are smoothed because thenetwork-side converter of variable-speed turbines can be used to control theactive and reactive flow and hence also the voltage [26].

Indeed, Bossanyi [26] and Fiss [35] state that flicker emissions from fixedspeed wind turbines may prove to be a limiting factor on the capacity of


wind turbine plants that can be installed in certain areas, particularly withweak networks.

The problem will tend to be more severe as the unit size of wind turbinesincreases, since the magnitude of rotational sampling effects increases asthe rotor size becomes more comparable with the size of turbulent eddiesthrough which the blades are slicing, and also because the number of turbineson a wind farm of a given ratio will be smaller, resulting in a smaller degreeof cancelation between uncorrelated fluctuations. Variable speed turbinesgenerate much lower levels of flicker and are therefore preferred by someutilities.

This work is mainly focused on the voltage variations due to the start-up transient, providing some general and specific ideas of how to improvethe voltage dropout occurring during the electrical connection between theinduction generator and the network. In this case, the term voltage changeis preferred to voltage fluctuation.

If a small number of fixed-speed stall-regulated wind turbines were clus-tered in a wind park, due to uncontrollable torque during start-up, it willproduce higher voltage dropout, compared to pitch-controlled turbines [6]where the wind torque can be controlled and the connection to the grid canbe performed in a smoother way (it takes about 1-2 seconds for the con-nection to be accomplished). In the case of stall-regulated wind turbines,the accelerating torque cannot be controlled and the generator must be con-nected quickly, to avoid an excessive over-speed (connection takes 0.3-0.7seconds) [25]. This gives place to an undesirable high reactive power flowtowards the induction machine.

On the other hand voltage dropout at the interconnection during startand stop of generators is normally less significant if the wind farm is large,due to the smoothing effect of the superposition of uncorrelated fluctuations[37].

Because of these two issues, it is worth investigating how to mitigate theimpact of constant-speed stall-regulated wind turbines during the connectiontransient in order to produce less voltage changes in small wind farms orisolated wind turbines connected to weak grids. Reducing this disturbancecan make the voltage changes caused by switching operations not to be alimiting factor for constant-speed stall-regulated wind turbine in these smallwind stations, and could decrease the impact of the connection transientsfor these kind of turbines in larger wind farms.

2.2 Voltage fluctuation 15

Figure 2.1: Flicker curve according to IEC 868.

According to the IEC 61400-21, measurements have to be taken of theswitching operation during wind turbine cut-in and when switching betweengenerators, although the latter is more serious as it involves higher valuesfor the reactive power flow.

The simplest interpretation of the flicker emission caused by switchingoperations of wind turbines is the one presented in Standard IEC 868 [38]used by A. Larsson [25, 24] and E. Bossanyi et al. [26]. In compliancewith this Standard the magnitude of maximum permissible voltage changesagainst the number of voltage changes per second is plotted (Fig. 2.1).According to this, voltage variations occurring every two minutes or moreare allowed to be as large as 3%.

The study of the impact alleviation of the start-up operation must bedone for the whole range of wind speed conditions. At low wind speeds,the single impact of the connection is expected to be less serious, but windturbines may start and stop several times in a few minutes. For high windconditions, the connection transient is faster and also the reactive power ishigher, thus increasing the voltage dropout.

Chapter 3

Description of the system

This chapter will describe the mechanical and electrical components thattake part in the wind turbine electrical connection to the network. Subse-quently, the specific values that define the components will be derived inorder to make a realistic simulation.

Standards like IEC 868 indicate the permitted values for the voltagedropout, and at the same time current regulations (for instance [31] in Spain)force the manufacturer to introduce devices in order to avoid current surgesduring the wind turbine start-up.

Voltage dropout effect due to the wind generator connection to the net-work is more marked when the generator is connected to a low short-circuitpower network, what is called a weak grid. This is also the case of a reducednumber of wind turbines feeding small centers of population that are con-nected to the network through long medium voltage (typically 11 or 20 kV)overhead lines. This case is not usual in many countries like Spain wherewind turbines are mostly grouped in wind farms connected through a 66 kVline. In this case the effect of uncontrolled and unbalanced consumption ofreactive power can also be felt although but with different characteristics:voltage dropouts are less severe but more frequent.

The present work mainly analyzes the first case because the different testedcontrollers can be more easily compared as the controllers’ effect on the

18 Chap. 3: Description of the system

voltage dropout is more pronounced.

Figure 3.1 shows the main blocks and devices involved in the system tobe studied. From left to right, one can observe the wind turbine rotor, thegearbox, the induction generator, the soft-starter, the power transformer,the line linking the transformer to a local load, and another line from thelocal load to the utility electrical network. The connection point to theelectrical bus of the site power collection system is called point of commoncoupling (PCC ), although in some papers it appears referenced as point ofcommon connection. PCC is defined in [39] as the point of the public supplynetwork, electrically nearest to a particular load’s installation, and at whichother loads installations are, or may be, connected.1

Figure 3.1: Wind turbine in a weak grid.

As a part of the study, the system has been simulated by means of anelectromagnetic transient simulator called PSCAD/EMTDCTM , takingadvantage of some components included in the library and creating someothers in Fortran code. Fig. 3.2 shows the main components correspondingto the electrical and mechanical systems, such as they appear in the program.

Following sections describe each of the components.

3.1 Turbine-generator mechanical system

A three-bladed horizontal axis rotor has been considered, as it is the mostcommon configuration. Fig. 3.3 shows one of the possible compositions forthe mechanical elements from the blades to the induction generator.

1The terms consumer, customer or local load will be either used regarding to theimpedance at the PCC

3.1 Turbine-generator mechanical system 19

Figure 3.2: PSCAD diagram of the system components.

There is a flexible coupling to allow for possible misalignments between theturbine shaft and the generator, and to absorb torque variations, reducingin this way material fatigue.

In this configuration, there is a brake on the fast shaft, where the brakingtorque is lower, but with the drawback of idleness in case of gearbox orcoupling breakage.

For the turbine modeling, a complex PSCAD/EMTDC library componentcalled Multimass has been used. Fig. 3.4 depicts this component. TheMultimass component simulates the dynamics of up to six masses connectedto a single rotating shaft. In the present work only the two main masseswill be simulated. One mass, as usual, represents the generator rotor. Theother one refers to the wind turbine.2

The mechanical input TL is the wind torque exerted over the wind turbinedue to the lift force component over the rotating plane. This torque isspecified as an external input, and together with the stator voltage system,the electrical generator and the mechanical turbine-generator parameterswill define the electrical torque and rotor speed evolutions.

Figure 3.5 shows a dynamic model for this component [40][41]. The mostsignificant components in the dynamics are the generator inertia constantand above all the turbine inertia, due to the blade length and weight. It ismore useful and usual to translate the inertia into a unit system relatively

2As the component does not include a gearbox, all slow shaft mechanical values mustbe referred to the fast shaft


Figure 3.3: Mechanical components in a wind turbine.

independent of the rated power or speed, and hence inertia values from dif-ferent turbines can be compared regardless of the rotor size. The expressionused for the system unit change is:

H = nblades · J(rpmgen

2π60

)2

2 · Pwatt · n2gb

(3.1.1)

where nblades is the number of blades, rpmgen is the generator rotationalspeed, Pwatt is the wind turbine capacity (rated power) expressed in wattsand ngb is the gearbox ratio.

Another important parameter is the self damping of every mass. For theturbine (SD2 in Fig. 3.5), this parameter accounts for the aerodynamicaldrag producing a torque which opposes the wind motor torque. It dependson the blade length, chord, cleanliness and material, as well as the relativewind velocity in relation to the blade velocity, specially regarding to thespeed regime (turbulent or laminar).

Torque produced by the aerodynamical drag is proportional to the squareof the speed, although the PSCAD model uses a linear approximation. This

3.1 Turbine-generator mechanical system 21

Figure 3.4: Multimass and induction machine components.

will not lead to significant errors if simulations are performed at almostconstant speeds, as is the case.

Regarding the generator self damping SD1, it is caused by the friction ofthe rotor shaft and to the ventilation losses.

In a simplified way, torque transmission is enabled by the torsion in thefast and slow shafts. As previously mentioned, a flexible coupling is usuallyintroduced to allow for misalignments. In this case, torque transmissiontakes place due to the coupling twist angle that is inversely proportionalto the Shaft spring constant or Torsional stiffness K12 and directly propor-tional to the transmitted torque.

When transients in the transmitted torque occur, variations will appear inthe twist angle that are damped by a torque proportional to the differenceof speeds between both rotating masses. The proportionality coefficient isthe mutual damping parameter MD.

Therefore, shaft spring constant and mutual damping values are deter-mined by the coupling between turbine rotor and the gearbox (as appearsin Fig. 3.3), or between gearbox and generator.


Figure 3.5: Graphical model for the multimass mechanical dynamics.

3.2 Generator electrical model

3.2.1 Induction generators in wind turbines

Except for very specific applications, the biggest induction machines arefound as generator units for wind turbines. There are some distinctive fea-tures for the induction generators being designed to be part of a wind tur-bine:

• Since they operate as generators and the rotor is accelerated by thewind torque, the deep wound effect is not a concern. This effect isvery desirable in the start-up of induction machines acting as motors,but this is not the case.

3.2 Generator electrical model 23

• For squirrel cage generators, a rotor resistance (referred to stator)slightly higher than for the case of motors is preferred. This allows amore flexible performance against changes in the wind torque, and itsoftens the start-up. The drawback is an efficiency decrease since it isrelated to 1−R′

r.

• Iron losses are in general lower than for generators used in other appli-cations [42]. This can be achieved by decreasing the saturation of themagnetic core. This way, magnetizing current decreases, and hence sodoes the no-load stator current, thus allowing a lower cut-in speed.

3.2.2 Two-speed induction generators

Disturbances due to the induction generator connection to the networkare more marked in the case of Danish concept wind turbines (fixed-speedpassive stall-controlled) and recently introduced active stall wind turbines,equipped with squirrel cage induction machines. Most of these generatorsare comprised of two stator windings, with different rated power and num-ber of poles (four and six poles for standard generators). The small six-polestator winding is connected when the wind speed is low, and therefore, thewind torque. As the synchronous speed is lower, this issue allows to dimin-ish the noise at low wind speed (precisely when it is more perceptible). Thepower losses also decrease at this wind condition. For higher wind speed,the generator is switched to the four-pole operation, connecting the statorwinding having the same rated power as the wind turbine capacity.

However, the small six-pole stator winding will not be taken into accountin the connection study, since it gives place to lower disturbances in relationto the main stator winding. Three facts support this idea:

• Current flowing through the line impedance between the high voltagenetwork and the PCC is lower for the secondary winding and hencevoltage dropout will be less serious.

• From (3.1.1) it is clear that the inertia time constant H is higher forthe secondary winding, even when it is slower, since the rated poweris quite lower.

• Rotor resistance is usually higher for the secondary winding.


Figure 3.6: Two-cage induction machine model.

Two last facts give place to a slower connection process, thus alleviating theimpact of the start-up.

3.2.3 PSCAD/EMTDC squirrel cage model

The squirrel cage induction generator model included in the PSCAD/EMTDClibrary is a double cage model, that considers the deep wound effect in therotor circuit. This configuration assumes two short-circuited bar layers: theupper bars, having high resistance and low leakage reactance, and the lowerones, with reduced resistance and higher leakage reactance [40].

At low mechanical speeds, rotor current frequency is high and the currentsflow through the low inductance rotor circuit. In normal operation, the rotorcurrent frequency is low, and the currents flow through the low resistancecircuit. Therefore, the effective rotor resistance is high for low speed (betterperformance for an industry motor start) and low in normal operation (lowerrotor power losses). This effect can be modeled in steady state operation astwo bar sets in parallel as shown in Fig. 3.6.

In any case, the EMTDC routine that simulates the induction machinedoes not use a steady state model, but a fifth order dynamic one, whoseparameters can be derived from the double cage induction machine model.

In the case of a wind turbine generator’s electrical connection to the net-work, slip values are small (in the order of 0.04 or lower) and the rotorcurrents frequencies make the lower bars the only ones involved in the ma-chine performance. Since it is not a significant parameter, and, on the other

3.2 Generator electrical model 25

hand it is usually difficult to obtain, the deep wound effect will not be con-sidered [43] and thus, high values to the second cage resistance and reactancewill be introduced.

3.2.4 Electrical parameters

Electrical parameters defining the induction generator whose transient isto be studied, have been chosen in accordance to values extracted fromseveral wind turbine catalogues in the range of 350 kW to 1.65 MW. Table3.1 gathers values for resistances and reactances obtained from differentmanufacturers, including some values extracted from some dynamic stabilitystudies.

Finally, values similar to [44] have been chosen although with a not sohigh rotor resistance.

Table 3.1: Electrical parameters of wind turbine induction generators.

Model P (MW) rs(p.u.) xs(p.u.) rr(p.u.) xr(p.u.) xm(p.u.)

Nordex 1 0.0062 0.0787 0.0092 0.0547 3.642

NegMicon 1.5 0.0227 0.0795 0.0156 0.0597 3.755

NegMicon 1 0.0225 0.173 0.008 0.13 3.428

WinWorld 0.6 0.0197 0.1271 0.0089 0.0956 4.667

Bonus 0.6 0.0065 0.0894 0.0093 0.1106 3.887

Bonus 1 0.0062 0.1362 0.0074 0.1123 3.911

Vestas 1.66 0.0077 0.0697 0.0062 0.0834 3.454

Ref. [45] 0.35 0.0064 0.0689 0.0071 0.2105 3.118

Ref. [46] 0.35 0.0063 0.064 0.0066 0.0934 3.306

Ref. [22] 1 0.0076 0.1248 0.0073 0.0884 1.836

Ref. [44] 0.6 0.0059 0.0087 0.019 0.143 4.76

Chosen values 1 0.0059 0.0087 0.01 0.143 4.76


Values for the resistance of equivalent iron losses RFe have not been in-cluded since PSCAD/EMTDC, following the American tradition, does notincorporate this parameter in the induction machine model but in the ro-tational losses. In order to avoid the deep bar effect, very high values (inthe order of 10 p.u.) have been taken for the second cage resistance andinductance.

3.2.5 PSCAD/EMTDC and MATLAB for simulating induc-tion generators

Figure 3.7: Transient simulations of an induction machine using PSCAD and MAT-LAB for s = −0.005: a) voltage at the generator terminals, b) current, c) real power,d) reactive power.

Figure 3.7 compares simulations made with PSCAD/EMTDC and MAT-LAB for an induction machine fed by a three-phase voltage system, whoserms value is the indicated in the upper left box. Some discrepancies can beappreciated regarding the voltage and current due to the rms values, with ahigher delay and ripple in the case of the PSCAD simulation. An unusuallyhigh value for the inertia has been introduced in order to maintain the slipconstant, specifically in a generator operation where s = −0.005. This helps

3.3 Soft-starter 27

to observe how the current and the real and reactive power depend, not onlyon the voltage, but also, and mainly in the case of the reactive power, on itsderivative.

The influence of the derivative of voltage on the system performance willbe explained later on, although Fig. 3.8 already illustrates this fact.

Figure 3.8: Real and reactive power dependance on the voltage and its derivative.

The first graph shows the voltage and real power evolutions, while in thesecond one, the derivative of voltage and the reactive power are represented.The voltage and its derivative are shown with a solid line. Real and reactivepower are shown with dashed line. Powers are considered positive whenflowing towards the induction machine.

Since the slip is negative enough (s = −0.005), real power will alwaysbe negative, although in the graph it appears multiplied by −1. Reactivepower, if the induction machine is analyzed in steady state, should alwaysbe positive. However, negative derivatives of voltage will give place to adeenergization in the asynchronous machine inductances that can lead toreactive supplies. This negative reactive power state is difficult to achieveand will not be pursued, although a control in the voltage derivative will beintroduced in order to avoid excessively high values for the reactive power.

3.3 Soft-starter

The soft-starter is a power converter, which has been introduced as ancil-lary equipment in fixed speed wind turbines to reduce the transient currentduring connection or disconnection of the generator to the grid [2]. The


Figure 3.9: Soft-starter power circuit

soft-starter is a general purpose controller with six thyristors, a back toback connected pair in each line [3] as shown in Fig. 3.9.

Using firing angle control of the thyristors in the soft-starter, the generatoris smoothly connected to the grid.

The soft starter and the structures to control its performance will bestudied in Chapter 5.

3.4 Additional components

The remaining components being part of the studied system will be pre-sented below.

3.4.1 Power Transformer and line to the PCC

A three-phase power transformer adapts the voltage levels between the in-duction generator, typically 690 V, and the local network, typically 20 kV.Most regulations dictate that the transformer must be star-delta configured(grounded star on the generator side and delta on the network side). The

3.4 Additional components 29

Table 3.2: Characteristics of different conductors.

Conductor R20oC(Ω/km) X(Ω/km) Imax(A)

LA 30 1.075 130LA 56 0.614 185LA 78 0.426 246LA 110 0.307 ∼ 0.39 314LA 145 0.242 330LA 180 0.190 400

delta winding avoids modifying the zero sequence impedance on the networkside. The grounded star decreases the harmonic distortion.

Cable impedance from the generator to the transformer can be disre-garded, even for small or medium size turbines where the transformer isoutside the wind turbine.

The line from the transformer to the point of common coupling can bean overhead line or underground cable. Characteristics for several overheadlines obtained from [47] and [48] are presented in Table 3.2. Capacitanceof underground cables is higher, which can help the connection transientproviding reactive power and decreasing the voltage dropout. Instead ofthat, a more restrictive situation will be analyzed by including a LA-30overhead line. The impedance line is:

RLA30 = 1.075Ω

km

XLA30 = 0.39Ω

km

As expected, simulations show that this impedance will hardly produce anyeffect on the voltage on the customer side. If an underground cable is in-cluded in the design, an increase in the voltage level at the interconnectionwill be expected at the load node, although from the point of view of thevoltage dropout, almost no difference can be appreciated from the simula-tions.


Figure 3.10: Normalized voltage evolution for different line impedances.

3.4.2 Local load

It will be considered a situation where a local load exists at the point ofcommon coupling at the medium voltage level. Simulations will be carriedout for the following values, although as for the previous impedance, thesedata are of no influence on the results.

Pcons = 500kW cosϕ = 0.85

3.4.3 Electrical network and distribution line

The local load will be connected at an intermediate point of a weak electricaldistribution network modeled as a 500 MVA short circuit power source withan impedance corresponding to an overhead line 15 km in length. A highercapacity line (LA-56) is chosen to comply with local regulations [49]. At20oC, specific line resistance and impedance are

RLA56 = 0.614Ω

km

XLA56 = 0.39Ω

km

Short circuit reactance of a 500 MVA short circuit power source must beadded to this impedance although its contribution is negligible.

3.4 Additional components 31

If the voltage dropout is defined as the maximum drop in the rms valueof the voltage at the point of common coupling with respect to the voltageprior to the connection, its value is determined mainly by the line reactance.

If, instead of it, the term voltage change, defined as the maximum dif-ference in voltage during the connection transient (see Fig. 3.10), is to beused, then its value is influenced by both the line resistance and reactance.

Fig. 3.1 plots the maximum voltage change, taken as a representativemagnitude of the impact of the start-up process, for different conditions ofthe weak grid given by its short circuit power and the Xlin/Rlin ratio. Firingangles are regulated by means of the open-loop linear controller. In the situ-ations when the voltage before the start-up is higher than the voltage whenthe connection transient has finished, dashed lines refers to the differencebetween this final voltage and the lowest voltage during this transient.

Figure 3.1: Voltage change vs. line impedance.

The left hand graph is similar to other ones found in [21] or [24], butthe right hand one is more interesting, where the voltage change is plot-ted against the line resistance and reactance. As can be seen, the impact,referred to as the maximum voltage change during the connection, is propor-tional to the line resistance for a fixed reactance. That is because the higherthe Rlin, the higher the difference between the voltage before and after theconnection, which can be translated to a higher voltage change assuming anapproximately constant voltage dropout (Fig. 3.10). This difference can beobtained from the generated (negative) real power Pwt and the consumed


(positive) reactive power Qwt according to

4U ' PwtRlin + QwtXlin

U2. (3.4.1)

Table 3.2 shows specific resistance and reactance for several conductors ofthe same series. As the overhead line capacity increases, specific resistancedecreases with the power of approximately 0.6, and the specific reactancehardly varies. Thus it is expected that as the number of wind turbinesincreases, along with the capacity of the evacuation line, the voltage changewill decrease, although on the other hand the number of switching operationswill increase.

Chapter 4

Estimation of mechanicalconstants

Performance of the wind turbine during the start-up as well as in transientstability studies is strongly influenced by a broad set of mechanical param-eters (Fig. 4.1) involved in the turbine dynamics. These parameters arerarely given by the manufacturer/supplier, and hence only an estimation ofthem is usually found in the bibliography.

In this chapter the structure of a wind turbine to estimate its mechanicalparameters is analyzed. Also, an expression that provide a first approach toa realistic inertia value to be used in transient simulations will be derived.

The parameters to be studied are depicted in Fig. 4.1. As can be seenthe gearbox does not explicitly appear. In fact, simulation programs do notinclude this component in their libraries, not even as an ideal torque/speedtransformation. Therefore, it is necessary to refer all values to the fastspeed side (generator side) or rather to directly translate the values of themechanical parameters into a per unit system. Expressions to accomplishthis change of unit systems will be provided.

The parameters to be estimated or, at least, bounded are the turbine andgenerator inertia time constants H, turbine and generator self damping SD,torsional stiffness K of the flexible coupling between rotor and generator,

34 Chap. 4: Estimation of mechanical constants

Figure 4.1: Graphical model for the multimass mechanical dynamics.

and mutual damping MD of the changes in the twist angle of this coupling(Fig.4.1).

4.1 Estimation of the inertia time constant

The inertia constant has a great and direct impact on the transient stabilityof wind farms and the start-up of wind turbines, and thereby this value isreferenced continuously in wind farm dynamic performance studies. How-ever, most of these papers only offer an estimation of inertia as suppliers donot use to facilitate this information [50]. Thus, disregarding papers aboutvertical axe wind turbines [51], two-bladed rotors [52, 53] or small size ma-chines [54, 55], very few works indicate numerical values for this constant[56, 57, 41, 44, 46, 58, 45, 59, 60, 61, 62, 63] most of them being estimatedvalues, as in [63], which obtains Hturb and Hgen from an experiment whereturbine is abruptly disconnected from the grid, or refer to multi-megawattwind turbines. With regard to simulations it is common to find the sameexperiment for several inertia values [50, 64, 65, 63].

An estimation of the inertia constant can be obtained starting from theblade geometry and cross-section, and calculating an approximated massdistribution along the blade span. A possible blade geometry and somenecessary definitions appear in Fig. 4.2, 4.3 and 4.4. They also show theblade section perimeter at an intermediate spanwise distance and a possibleinner structure [66, 67].

4.1 Estimation of the inertia time constant 35

Figure 4.2: Wind turbine blade.

Figure 4.3: Definitions for a wind turbine blade.

Chord distribution along the blade span is shown in an approximate wayin figure 4.5, and compared to optimal distribution according to expression[42]:

chb(r) =16 π R

9 · cl λ z

1√(λ

Lr

)2

+49

(4.1.1)

where λ is the tip speed ratio, L is the blade length, cl is the liftcoefficient and z is the number of blades.

Defining thickness as the maximum length in the direction transversalto the chord line, and relative thickness as this magnitude divided by thechord (th/chb in Fig. 4.3), the spanwise distribution of this value offers theapproximated distribution of Fig. 4.6 [68][62].

Next to the junction with the hub there is a cylindrical constant-chordpart. The longer and more important part is the farther from the rootand it has an aerodynamical shape as in Fig. 4.3 or 4.4, more elongatedtowards the tip and wider towards the root. Between both parts there is acomplicated variable geometry link that fits both kinds of sections.

Starting from the blade geometry, an estimation of the mass distribution,which in turn determines inertia time constant, can be obtained. A moreformal study of the blade design can be found for example in [67] but in this


Figure 4.4: Composition of the blade.

Figure 4.5: Chord along the span.

work some approximations will be done with the sole aim of establishing anqualitative idea of the mass distribution:

• As previously indicated, the blade will be divided into three partsalong the span. There is a first cylindrical zone, close to the hub; theaerodynamical zone, which is the longest, with decreasing chord; andfitting them the third with more complicated geometry.

• It will be assumed that the mass is due to the glass reinforced epoxyskin and to the box-spar structure acting as the structural reinforce-ment for the blade to be more efficient at resisting out-of-plane shearloads and bending momenta (see Fig.4.4).

• At a certain distance r from the root, skin and shear web widths areconstants.


Figure 4.6: Relative thickness.

• The only action to be considered will be the out-of-plane bending mo-mentum and the inertia tensor will be considered as a diagonal matrix(symmetrical cross-section from the point of view of stress distribu-tion). The most exerted points will be assigned a distance from theflection axes equal to half the thickness.

4.1.1 Values used for the analysis

Blade fatigue stresses

There are two scenarios to be taken into account in the wind turbine bladedesign [69]:

• The first one analyzes the extreme loads that a wind turbine can suffer,which can be estimated using two simplified methods: parked underextreme winds and an operating gust condition

[70]. The first method calculates the extreme loads with the turbine inthe parked condition in accordance with IEC and Germanisher LloydClass I design recommendations. In the second method the turbine isconsidered to be operating at constant speed during a 55 m/s gust.Both load estimation approaches provide similar results.

• The second scenario refers to the analysis of the cycling loads in nor-mal operation over the blade during the complete life of the windturbine which diminishes the maximum strength the material is ableto withstand.

A further knowledge of the methodology for blade design can be found in[67], but here only a simplification of the second scenario will be taken into


account assuming an amplitude variation of 18% around the mean ratedvalue. Fatigue load spectra for different numbers of cycles, as explainedin [71] or [72], will not be considered. These variations are due to thewind shear, to the tower shadow, to gravitational forces, or, with lowerfrequencies, to weak wind gusts. Mean value is due to the out-of-planeflapwise momentum and to the centrifugal forces.

A common parameter in the fatigue behavior is the R-value which for thisfatigue cycle yields (see Fig. 4.7)

R =σmin

σmax=

σm − σa

σm + σa=

σm − 0.18σm

σm + 0.18σm= 0.7 (4.1.2)

where σmin and σmax represent the minimum and maximum stress in a fa-tigue stress cycle (tension is considered positive and compression is negative)and σm and σa are the mean value and the amplitude of the fatigue stresscycle.

Figure 4.7: Fatigue cycles.

The number of load cycles is very high in wind turbines. Assuming aneffective disposability of 80% for a rotational speed of 25 rpm, the numberof load cycles for each blade is:

N c = 0.8 · 20 years 8766hours

year

60min

1hour25 rpm = 2.1 · 108cycles (4.1.3)


Starting from typical data [73] about a composite of glass reinforced epoxy,typical fatigue characteristic properties can be the ones represented in Fig.4.8.

It can be noticed from these figures that for always positive tensilestrengths (R = 0.1), the mean permissable tensile strength is in the orderof σm = 100MPa. If compressive strengths are considered at the extradosor downwind side with R = 10, although the value for static compressivestrength is lower than the static tensile one, at 2.1 · 108 cycles the com-pressive strength limit is higher (see Fig. 4.8). Furthermore, centrifugalforces decrease, in absolute value, the compressive strength, and hence thisstrength can be considered a less restrictive condition.

For other R-values, [74] proposes the following equation

σu − σmax = a σmax

(σmax

σu

)b

(N c − 1) (4.1.4)

where σmax is the maximum applied stress, σu is the ultimate tensileor compressive strength (obtained at a strain rate similar to the 10 Hzfatigue tests), N c is the number of load cycles and a, b, and c are the fittingparameters. For an R-value of the fatigue cycle equal to 0.7 the related valuesare a = 0.04, b = 2.5, c = 0.45, σu = 360MPa and N c = 2.1 · 108cycles.

The value of σmax which satisfies (4.1.4) is 124MPa whose correspondingσmean is

σmean =σmax

1.18= 106 MPa (4.1.5)

similar, although a bit lower, to 120− 140MPa appearing in [67].

4.1.2 Geometry

Data regarding to the blade geometry analyzed as an example has beenderived from tables and graphs included in [68] and correspond to a 26 mblade from an 850 kW wind turbine.

For a 26 meter blade, having a 1.8 meter hub radius, assuming a rated tipspeed ratio of λ = 7 and a nominal wind speed equal to vwind = 12 m

s , therotational speed yields

Ω =λ · vwind

Rhub + L= 3.02

rad

sec= 28.83 rpm (4.1.6)


Figure 4.8: Cycle to failure for R = -1, R = 0.1 and R = 10.


4.1.3 Aerodynamics

The lift and drag coefficients have been extracted from Fig.4.9 [42] consid-ering a smooth surface, a Reynolds number of 3 · 106 and an angle of attackequal to 4o.

cl = 0.7cd = 0.006

Figure 4.9: Lift and drag coefficients.

According to the line of considered approximations, Reynolds numbervariations along the span will not be taken into account. Therefore if bladetwist gives place to a constant angle of attack α, then coefficients cl and cd

are constants along the blade span.

4.1.4 Blade weight

In order to test the validity of the analysis and to fix security factors, theactual mass of the analyzed blade needs to be obtained.

In the case where blade weight data are not available, an estimation ofthe relationship between weight and blade length can be extracted. Hence,starting from the table at Appendix A obtained from manufacturers’ cata-logues and [75], an expression relating both parameters can be derived.


Searching for an expression relating weight and length blade of the type

Mpala = kM · Lαpala (4.1.7)

the function sum of quadratic errors is minimized

f(kM , α) =n∑

i=0

(Mi − kM · Lα)2 (4.1.8)

giving

kM = 2.95α = 2.13 (4.1.9)

These values are quite similar to that of [76] (kM = 1.6 and α = 2.3), andto that of [77] (kM = 1.50 y α = 2.34). The estimated values provided by[68] are slightly different (kM = 0.619 and α = 2.63).

Figure 4.10 shows the estimation according to previous parameters anda representation of some values extracted from manufacturers and otherpapers (kM = 2.95, α = 2.13 and diamonds). A close agreement can be seenfor low rotor diameters. The higher dispersion at greater diameters can beexplained by the scarce data available for these turbine sizes.

The α value so close to 2 could suggest to think that skin and structurereinforcement width does not vary linearly with the blade length.

In accordance to these functions, the weight for a 26 m blade is typicallybetween 2870 kg and 3260 kg, for example M = 3075 kg.

Another necessary datum is the density of glass reinforced plastic thatdepends on the composition of the material. The value of ρgrp = 1700 kg

m3

will be chosen.

4.1.5 Static analysis

This analysis starts from expressions [78] to calculate axil strengths at acertain distance r from the rotation axis at a point defined through itscoordinates y and z

σxx(r, y, z) =Nx(r)A(r)

+Mz(r)Iz(r)

y +My(r)Iy(r)

z (4.1.10)


Figure 4.10: Relationship between weight and length.

where σxx is the span-wise strength, Nx(r) is the force in the same directiondue to centrifugal loads, A(r) is the spar cap and shear web areas, , Mz(r)and My(r) are the chordwise and flapwise momenta due to the resultantforce component, and finally Iy(r) and Iz(r) are the momenta of inertia ofthe spar caps and shear webs structure with respect to the chord line andto the axis perpendicular to it.

As indicated in [79] and the figure 4.11 extracted from it, the main sparcarries most of the flapwise bending loads whereas the shell carries most ofthe edgewise bending loads.

This can be derived by observing Fig. 4.12 which makes evident the highervalue of the z-axis force component in relation to the y-axis one, giving placeto higher values of My in relation to Mz. As a result, the second addendwill not be taken into account in the spar cap thickness analysis.

With regard to the structural reinforcement area, it is obtained by mul-tiplying the section perimeter by the spar width. In fact, this width is notconstant along the box-spar. In [70] the structural shear web was taken tobe 5/3 the thickness of the blade skins, and the spar caps reinforcement is2/3 of this outer skin. Thus, taking the thickness of the structural shear webas the base, the area of the main spar can be expressed as the product of the


Figure 4.11: Load-carrying main spar from a wind turbine blade.

Figure 4.12: Components of the aerodynamic forces.


parameter ksparperim, the chord ch(x) and the structural shear web thickness

(Fig. 4.13).

Figure 4.13: Thickness, skin and chord.

S(x) = ksparperim(x) · ch(x) · εweb(x) (4.1.11)

Hence the expression for the axil force yields

Nwebx (x) = ρGRP Ω2

∫ L+Rhub

xkspar

perim(r) · ch(r) εweb (r) r dr (4.1.12)

where ρGRP is the reinforced plastic density, Ω is the rotational speed atrad/s, Rhub is the hub radius, L is the blade length , εweb (x) and ch (x)are the expressions for the lumped box spar width and the blade chord as afunction of the distance to the rotation axis and g is the gravity acceleration.

Bending flapwise momentum My(r) can be calculated by integrating theforce differentials shown in Fig. 4.14 whose expression appears in (4.1.14).

dFL =ρ

2ch(x) · vr(x)2 · cl(δ) · dx (4.1.13)

dFD =ρ

2ch(x) · vr(x)2 · cd(δ) · dx (4.1.14)

where ρ is the air density, ch(x) is the distribution of chord along the blade


Figure 4.14: Distribution of forces acting at the blade.

span, cl and cd are the aerodynamical drag and lift coefficients, and vr(x)is the resultant relative velocity defined through its direction δ and itsmodulus |vr|

δ = atan(vwind

Ω · x)

(4.1.15)

|vr|2 ' Ω2

(v2wind

Ω2+ x2

)(4.1.16)

Thus, flapwise momentum My(x) yields

My(x) =Ω2

2ρ (cd sin(δ)+cl cos(δ))

∫ Rhub+L

xch(x) (r−x)

(v2wind

Ω+ r2

)dr

(4.1.17)


for x > lim aerod (see Fig. 4.5) and

My(x) =Ω2

2ρ (cd sin(δ)+cl cos(δ))

∫ Rhub+L

lim aerodch(x) (r−x)

(v2wind

Ω+ r2

)dr

(4.1.18)

for x ≤ lim aerod.

The momentum of inertia of the box-spar with regard to the chord lineat distance x, Iy(x), is obtained from normalized expressions of the aerody-namical section.

Ispary (x) =

∮εz2 · ch(x)

√1 +

(ddy

profile(x, y))2

dy (4.1.19)

which for the sake of clarity, will be expressed as the parameter kIy(x)multiplied by the shear web thickness and the cube of the chord.

Ispary (x) = kIy(x) · εweb(x) · ch(x)3 (4.1.20)

In order to take into account the worst scenario, the value of z in (4.1.10)corresponds to the most stressed point due to the flapwise momentum whichis the farthest point from the median line. A value equal to the half thethickness is to be considered.

Hence, from (4.1.10), (4.1.12) and (4.1.17) the width of the shear webyields

σ =ρGRP Ω2

∫ L+Rhub

xr kspar

perim εweb (r) ch(r) dr+

th(x) εweb(x)+ (4.1.21)

+Ω2ρ (cw sinδ + ca cos δ) th(x)

4 kIy(x) εweb(x) ch3(x)

∫ Rhub+L

min(x,lim aeord)

ch(r)(r − x)(

v2wind

Ω2+ r2

)dr

A variable change will be introduced where S(x) is the new unknown, and


an auxiliary constant will be also defined.

S(x) = ksparperimεweb(x) · ch(x) (4.1.22)

KAcent =ρGRP Ω2

ks · σ (4.1.23)

KB(x) =Ω2 ρ th(x) (cd sin(δ) + cl cos(δ))kspar

perim

4 kIy(x) ch(x)2 σ(4.1.24)

Thus, expression (4.1.22) yields

S(x) = KAcent

∫ L+Rhub

xr S(r) dr

+ KB

∫ Rhub+L

min(x,lim aeord)(r − x)

(v2wind

Ω2+ r2

)ch(r) dr (4.1.25)

Deriving (4.1.25), it gives

dSd x

= −KAcent xS(x)−KB(x)∫ Rhub+L

min(x,lim aeord)

(v2wind

Ω2+ r2

)ch(r) dr

+d KB(x)

dx

∫ Rhub+L

min(x,lim aeord)(r − x)

(v2wind

Ω2+ r2

)ch(r) dr +

(4.1.26)

Multiplying both terms by eKAcent

2x2

and integrating the resulting expres-sion, the equation for the area S(x) along the blade span (the integrationconstant has been canceled as derived from (4.1.25)) yields

S(x) = −e−KAcent

2x2−KAgrav x ·

∫ Rhub+L

xe

KAcent2

p2+KAgrav p ·(

d KB(p)d p

∫ Rhub+L

min(p,lim aeord)(r − p)

(v2wind

Ω2+ r2

)ch(r) dr (4.1.27)

+ · KB(p)∫ Rhub+L

min(p,lim aeord)ch(r)

(v2wind

Ω2+ r2

)dr

)dp


Once derived the area S(x), the web width can be obtained.

εweb(x) =S(x)

ksparperim(x) ch(x)

(4.1.28)

The shear web width obtained from (4.1.28) follows the distribution repre-sented in 4.15. It can be seen that, due to the low value for the thicknessat the tip, the width of the shear web is considerably larger than the widthcloser to the blade root.

Figure 4.15: Shear web width along the blade span.

4.1.6 Inertia Time Constant H

Comparison of cumulated mass distributions

However, difficulties arising during the manufacturing process make thata constant value for the shear web and the spar cap thickness is usuallypreferred. In order to provide for other materials which are also part of theblade (mainly the balsa core) the value obtained previously is multiplied bya factor which is greater near the root [80]. In this sense, and in order to


improve the reliability against extreme winds, a 50% increase of the sparthickness is also applied.

The same analysis can be made for the blade skin. This shell bears mostof the edgewise bending loads which are due to the aerodynamical forces,but mainly to the weight force when the blade is in a horizontal position.It also bears the centrifugal forces as tensile ones. Instead of considering acalculated evolution of the skin width, a constant value for this value willbe applied as well.

As mentioned before, [70] gives values for the approximated ratios betweenshear web skin and the outer skin, and also between shear web skin and thespar caps thickness. Taking into account these relationships, the total masswill depend on the shear web width. For a 1.9 cm skin (35% over themaximum calculated in 4.15), a total mass of 3090 kg is obtained.

The cumulated mass distribution along the span is shown in Fig. 4.16 incomparison to two typical cumulated mass distributions [62, 67]. It showsthat making the value of the skins constant and reinforcing the cylindricalpart of the blade, the cumulated mass distributions fit typical ones. Startingfrom calculated skin and spar cap areas along the span and the density ofthe glass reinforced plastic, the inertia constant J expressed in kg ·m2 andthe center of gravity from the blade root have been calculated

J = 417255 kg ·m2 (4.1.29)Xcg = 7.81m

The center of gravity is similar to the one given by [68] or [81] for thesame length blade.

Applying the same analysis to different lengths, the values α = 0.552 andβ = 2.645 have been found for the relationship M = α · Lβ. In figure 4.17this relationship is compared to the other graphics presented previously.

4.1.7 Estimating a wind turbine inertia constant

For geometrically similar blades having a length similar to the previouslyanalyzed, the inertia constant can be approached from the following ex-pression

J = kJ ·mass · L2 (4.1.30)


Figure 4.16: Typical and calculated cumulated mass.

where kJ is obtained from (4.1.29)

kJ =417255kg m2

3090kg · 262m2= 0.2 (4.1.31)

Similar values are derived by calculating the inertia of the blades whosecumulated mass distributions are depicted in Fig. 4.16, in relation to [62](kJ = 0.184) and [67](kJ = 0.1829).

4.1.8 Estimating H for different wind turbine capacities

Two expressions can be used to relate inertia constants H and J [40]

H = z · J(rpmrotor

2·π60

)2

2 · Pwatt(4.1.32)

H = z · J(rpmgen

2π60

)2

2 · Pwatt · n2gb

(4.1.33)


Figure 4.17: Comparison of different weight-length relationships.

where z is the number of blades, rpmrotor and rpmgen are the rotationalspeeds of the rotor and the generator, Pwatt

1 is the wind turbine capacityexpressed in watts and ngb is the gearbox ratio. These data are necessaryto estimate the H constant for a wind turbine.

In order to observe the trend of the inertia time constant value along withthe increasing capacity, the Power− to− length, the Weight− to− lengthand the ratiogb− to− length relationships should be introduced in (4.1.33).

Data from Appendix B have been correlated (Fig. 4.18) and the followingrelationships estimated.

• Capacity as a function of the rotor diameter

P ' kP ·DαP = 310 ·D2.01 (4.1.34)

similar to that given in [77](124 ·D2.23) , and slightly lower than thatgiven in [82] (195 ·D2.155).

1Some simulation programs such as PSCAD/EMTDC consider the apparent powerMVA as the power base


• Mass of the blade as a function of its length

Mpala ' kM · LαM = 2.95 · L2.13 (4.1.35)

as obtained in (4.1.9).

• Rotor diameter as a function of the blade length

D ' relDL · L ' 2.08 · L (4.1.36)

• And from Tables 4.1 and 4.2, the gearbox ratio as a function of therotor diameter

ngb ' kgb ·D = 1.186 ·D (4.1.37)

being the proportionality constant in the form of

1.186 =

50Hz

npp2π · L

vtipms

(4.1.38)

assuming a two pair poled machine npp = 2 and a constant tip speedof vtip = 63.5 m

s .

In fact, an slightly increasing dependance with power can be foundin the tip speed but is mainly due to the appearance in the statisticsof high power offshore wind turbines, faster as they do not comply astrict noise constraint.

Starting from (4.1.31), (4.1.8), (4.1.35) and (4.1.8) the expression for theinertia time constant (4.1.33) turns into

H = nblades · kJ ·M · L2

(f(1+sG)nppoles

2π)2

2 · P · n2gb

(4.1.39)

=nblades

2· kJ · kM ·

(D

relDL

)αM

·(

D

relDL

)2

(f(1+SG)nppoles

· 2π)2

kP ·DαP · k2gb ·D2


Figure 4.18: Relationship Capacity-Diameter.

which can be expressed as

H(sec) = kH ·D(m)αH being (4.1.40)

kH = nblades · kJ · kM

(D

relDL

)αM+2

(f(1+SG)nppoles

· 2π)2

kP · k2gb

= 2.175

αH = αM + 2− αP − 2 = 0.12

The value for the exponent αH = 0.12 means that the inertia time con-stant increases slightly as the diameter does. A similar expression can beestimated for the H − P relationship

H(sec) = 1.544 · P (W )0.0597. (4.1.41)

Fig. 4.19 shows this trend in solid blue line according to previous relation-ship. Green triangles show inertia time constants directly extracted fromthe literature, being most of them estimated or assumed values, and notexcessively reliable (Table 4.3). The few red triangles are related to actualvalues of J where the inertia time constant can be obtained once the polepairs, capacity and gearbox ratio are known. Data regarded to violet dia-monds are obtained in the same latter way (from Table 4.1) but estimatingthe inertia J from the weight and the blade length as in (4.1.31)2.

2Data for Nordex N80 and N90 and DeWind D62 and D64 have been excluded due totheir significatively higher values, over 8.5 sec


As can be seen, actual or estimated data are mainly in the range of 3 - 5s, as indicated in [83].

Figure 4.19: Inertias for different turbine capacities.

In accordance with the relationship shown in Fig. 4.19, a value ofHturb = 3.5 s will be used as a base for the simulations.

4.1.9 Estimating the remaining inertia time constants

With regard to the hub inertia, this device weighs around one third of therotor mass (without including shaft nor gearbox), or analogously half theweight of the three blades. Assuming a maximum radius of 2 meters for amedium size wind turbine, the hub inertia can be estimated from (4.1.33),yielding a constant H lower than 0.05 s. The other components of the torquetransmission system (gearbox, brake, fast shaft or slow shaft) have neithersignificant inertias, and hence they will be omitted unless direct data areavailable.

By comparison, it is easier to find reliable values for the generator inertia.They show the great influence of the kind of generator on its inertia. Forexample, for a generator in the region of 1500 kW, the inertia can varyfrom around 75 kg · m2 (generator Weier from Vestas V66-1.65MW, rotorwinding weight 1950 kg, total weight 6473 kg) for a wound rotor and around


Table 4.1: Data for estimating H: rated capacity (kW), blade length (m), gear boxratio, blade weight (kg) and estimated inertia time constant H (sec).

Turbine Capacity Bladelength

Gearbox

BladeWeight

Inertiatime

Bazan Bonus MkIV 600 19 55 1800 2,70Dewind Iberica D46 600 22,15 45,5 1800 5,37Dewind Iberica D48 600 23,15 45,5 1800 5,86Ecotecnia 600 600 19,1 55,76 2900 4,28MADE AE 46/I 660 21 59,53 2500 3,56Gamesa V47-660kW 660 23 52,63 1500 3,28Gamesa G47 Ingecon 660 23 52,65 1600 3,49Nordex N 50 800 23,3 63,6 3000 3,80MADE AE 52 800 25,1 58,34 3200 5,59Gamesa G52 850 850 25,3 61,74 1900 2,83Gamesa G58 850 850 28,3 61,74 2500 4,67DeWind D62 1000 29,1 53,5 4300 9,61Dewind Iberica D64 1250 31,1 48,9 4800 11,7Nordex N62/1.3MW 1300 29 79 4300 3,37Nordex N60 1300 29 78,3 4900 3,90Nordex N62 1300 29 78,3 4900 3,90Ecotecnia 62 1300 1300 29 81,8 5800 4,23Neg Micon NM1500/64 1500 31,2 87,74 6900 4,39Sudwinds70/1500 1500 34 95 5200 3,35Nordex S70 1615 34 94,7 5600 3,38Nordex S77 1615 37,5 104,2 6500 3,94Vestas V66-1.65 1650 32,15 78,8 3800 2,89Ecotecnia 74 1670 1670 34 94,63 5800 3,39Ecotecnia 80 1670 1670 37,3 94,63 6035 4,24Gamesa G80 2000 2000 39 100,5 6500 3,70Gamesa G87 2000 2000 42,3 100,5 6500 4,35Gamesa G90 2000 2000 44 100,5 7000 5,07Gamesa G83 2000 2000 40,5 100,5 9400 5,76Nordex N90 2300 43,8 77 10200 10,8Nordex N80 2500 38,8 68 8600 8,46


Table 4.2: Data for estimating M and H: rated capacity (kW), rotor diameter (m),gear box ratio, and estimated inertia time constant H (sec).

Turbine Capacity Rotordiameter

Gear boxratio

Inertiatime

Gamesa G42 600 42 44 3,66Neg Micon 600/43 600 43 55,6 3,69Gamesa G44 600 44 45 3,72Neg Micon 600/48 600 48 71,4 3,81Neg Micon 750/44 750 44 55,6 3,72Neg Micon 750/48 750 48 68,2 3,81FuhrLander 800 48 66 3,81MADE AE 56 800 56 63,02 3,99MADE AE 59 800 59 66,37 4,06Suzlon 950 950 64 89,2 4,16FuhrLander 1000 54 69 3,95Bonus 1MW 1000 54,2 69 3,96Neg Micon 1000/60 1000 60 83,3 4,08Suzlon S60 1MW 1000 60 67,31 4,08Suzlon S62 1MW 1000 62 67,31 4,12Suzlon S64 1MW 1000 64 82,29 4,16DeWind D60 1250 60 46,9 4,08Suzlon S60 1.25MW 1250 60 74,92 4,08DeWind D62 1250 62 50,2 4,12DeWind D64 1250 64 53,1 4,16Suzlon S64 1.25MW 1250 64 74,92 4,16Suzlon S66 1.25MW 1250 66 74,92 4,20Bonus 1,3MW 1300 62 78 4,12MADE AE 61 1320 61 80,8 4,10FuhrLander 1500 70 94,7 4,27FuhrLander 1500 77 104 4,39Bonus 2MW 2000 76 89 4,38DeWind D80 2000 80 94 4,45Suzlon 2MW 2000 88 118,1 4,57MADE AE90 2000 90 101 4,61Bonus 2,3MW 2300 82,4 91 4,49Ecotecnia 100 3MW 3000 100 126,3 4,75


Table 4.3: References including H.Reference Capacity (kW) H (sec)

[54] 180 3,13[41] 200 1,93[84] 225 2,94[55] 225 2,94[57] 300 5,3[45] 350 3,13[85] 400 5[56] 600 4,19[60] 600 3,2[86] 2000 3,71[65] 2000 3,5[1] 2000 4,5[58] 2000 3,52[63] 2000 2,5[63] 2000 4,5[50] 2000 3,5[50] 2000 4,5[50] 2000 5,5[50] 2000 6,5[64] 2000 2,5[87] 6000 4,93

35−50 kg ·m2 for a squirrel cage generator. The expression for the generatorinertia time constant H in seconds is

Hgen(s) = Jgen(kg ·m2)

(f(1+sG)

npp2π

)2

2 · P · n2gb

(4.1.42)

resulting in a value of 0.63 s for the wound rotor and 0.29 − 0.45 s for thesquirrel cage rotor.

These values can be considered to be independent of the rated power [88].Finally, the value Hgen = 0.4 s has been chosen.

4.2 Other mechanical constants 59

4.2 Other mechanical constants

4.2.1 Self damping

This parameter, as well as the other mechanical transmission system pa-rameters, does not have the same influence as the inertia. In the case of selfdamping, since a fixed speed wind turbine is simulated, the effect of the selfdamping during the electrical connection to the grid is reduced to an almostconstant antagonistic torque.

In order to estimate how self damping varies with the rated capacity, thefollowing equation is used [42]:

dFL(r) =ρ

2ch(r) vr(r)2 cd(α) dr (4.2.1)

where dFL is the aerodynamical drag force exerted on a blade differentialat a distance r from the rotor axis, ρ is the air density, ch is the bladechord, vr is the relative speed with respect to the blade, and cd is the dragcoefficient, that is dependent on the material surface state, the Reynoldsnumber and mainly the angle of attack α (Fig. 4.9). The componentof this force upon the rotation plane multiplied by the lever arm r givesplace to the differential torque opposing the blade movement (Fig. 4.20).Integration of these differential momenta for the three blades yields the totalaerodynamical drag torque.

Assuming a tip speed independent of the blade length, then differentialdrag force varies with diameter squared, and the upper integration limit alsovaries with diameter; hence torque varies with diameter cubed.

Assuming that the rotational speed Ω is inversely proportional to thediameter and the resistant torque due to the drag can be expressed in thesimplest way as a friction torque (as done by PSCAD/EMTDC) through

Tdrag = SD

(N ·m · s

rad

)· Ω (4.2.2)

then self damping is expected to vary with D4.

Analogously as for the inertia, the resultant value can be transformed fromthe international system MKS to per unit p.u. through the expression3:

3This expression implicitly consider the self damping in the way indicated by (4.2.1)


Figure 4.20: Composition of forces exerted on the blade.

SD(p.u.) = SD

(Nm · s

rad

) (f(1+sG)

npp2π

)2

P · n2gb

' SD

(Nm · s

rad

) (f

npp2π

)2

P · n2gb

(4.2.3)

As indicated in (4.1.8) rated power varies practically as the square of thediameter, and the gear-box ratio varies as diameter does. This can suggest toassume that self damping in p.u. can be considered as a constant regardlessof the turbine capacity.

SD(p.u.) 6= f(P )

It was assumed that this value depended only on the drag. However it canbe established that it also depends upon the friction and ventilation in thegenerator. These effects can be lumped in a single value.


Very few references can be found with estimated or actual values for thisparameter and the range for these values is very wide. For simulation pur-poses, a self damping of SD = 0.05 p.u. will be finally chosen, close to thevalue provided in [41](0.052) or [46] (0.044).

4.2.2 Torsional stiffness

Regarding torsional stiffness, there are some discordances about the expres-sion of this normalized magnitude or in p.u.

PSCAD manuals [40] propose the following equation for the torsional stiff-ness of the low speed shaft

K ls(p.u.) = K ls

(N ·mrad

) (2·π60 rpmr

)2

P= K ls

(N ·mrad

) (2·π60 rpmg

)2

P · n2gb

(4.2.4)

which results in having dimensions of s−1.

In order to be sure of using the right expression to display torsional stiff-ness in p.u., an intrinsic analysis of the phenomenon must be made. Thus,when two magnitudes are linearly related via a proportionality constant K,the value of this constant in p.u. means the variation in one of the magni-tudes when varying the other one. In relation to the torsional stiffness, itis expected that variations in the real power extracted from the wind giveplace to variations in the twist angle of the rotor due to the torque trans-mission. In this case, the torsional stiffness in p.u. is the constant whichconnects both magnitudes

P (p.u.) = K lspu θ(el.rad.) (4.2.5)

having dimensions of p.u./el.rad.

Starting from the torque and twist angle in the low speed shaft and op-erating in electrical radians instead of mechanical ones (related through thenumber of pole pairs as el.rad = mec.rad · npp) the following expression isobtained

PN · npp · ngb

f (1 + sN ) 2 π(

el.rads

) =PN · npp

ΩN

(el.rad

s

) = TN = K ls

(N ·mel.rad

)θel

ngb · npp

(4.2.6)


where PN , sN and TN are rated capacity, slip and torque, and ΩN is therotational speed at rated conditions.

Comparing previous equations and considering rated conditions (PN = 1),numerical value of torsional stiffness can be identified

K lspu

( p.u.

el.rad.

)= K ls f · (1 + sN ) · 2π

P · n2gb · n2

pp

' K ls f · 2π

P · n2gb · n2

pp

. (4.2.7)

For torsional stiffness values related to the high speed shaft

Khspu

( p.u.

el.rad.

)= Khs f · (1 + sN ) · 2π

P · n2pp

' K ls f · 2π

P · n2pp

. (4.2.8)

In any case, in order to be used in the PSCAD Unit System 9 that usesexpression (4.2.2), torsional stiffness in p.u. must be multiplied by f · 2π

K9PSCAD(s−1) = Kp.u./el.rad. · f · 2π (4.2.9)

To consider the torsional stiffness of both shafts, low and high speed, theequivalent constant results

Keq =K ls ·Khs

K ls + Khs. (4.2.10)

Finally a value of

Kpu = 0.3p.u.

el.rad(4.2.11)

was adopted which is similar to those indicated in [63, 64, 54, 44].

Influence of this parameter on the system dynamics begins to be noticeablefor lower values than aforementioned ones and when the motor or resistanttorque is suddenly lost, as in the case of a short-circuit with breaker open-ing. Mechanical parameter evolution is soft enough for the torsional springconstant influence not to be significant, even in the case of very flexiblecouplings (low torsional constant).

4.2.3 Mutual damping

In the same way as for the self damping, in order to translate into per unit,the following expression must be used

MD(p.u.) = MD

(Nm · s

rad

)(

f

nppoles2π

)2

P · n2gb

(4.2.12)


where rpm is the rotation speed in revolutions per minute at the placewhere the flexible coupling is located. According to the scarce bibliography[41, 46] the value MD = 25 has been chosen.

Analogously to the stiffness constant, in the case of two flexible couplingsexisting, equivalent mutual damping will be the inverse of the sum of theinverses of the individual mutual dampings.

Chapter 5

Soft-starter

The core of present work is to improve the performance of the soft-starterconnecting the induction machine to the network supply.

This chapter only deals with the configuration and operation of this powerconverter, gathering the dispersed information existing regarded to the start-up of induction motors, and pointing out the differences for the case windturbines where the soft-starters must adapt the induction generator voltageto that of the network supply.

The improvement in the control structure will be dealt with in next chap-ter.

5.1 Configuration

The soft-starter is a power electronic converter that is not specific for windturbines, but is being introduced more and more frequently in industrialplants where it is necessary to operate with induction motors controllingthe start currents in a more efficient way than the traditional methods.

A soft-starter device is integrated by 6 thyristors, two per phase, in a backto back or anti-parallel configuration as can be seen in Fig. 5.1. A snubber

66 Chap. 5: Soft-starter

Figure 5.1: Soft-starter power circuit.

RC network is usually included in order to limit the rate of change of the

voltage,dv

dt, across the thyristors. Figure 5.2 shows the soft-starter control

circuit and the way to obtain the beginning of the excitation of the gates(firing angle), similar to [89].

With the name of ac voltage controller [90], it can also be found in ap-plications like an electronic breaker, a simple and economic speed controllerfor single-phase and three-phase induction machines, in the under load tapchanging for power transformers, in induction heating or in static-var com-pensators (an analysis of this electronic device, the involved equations andits performance can be found in [91]). In these cases where soft-startersgradually vary the voltage at the terminals of an induction motor, they of-fer many advantages over conventional starters [12, 16], derived from theirability of working according to three different modes [15]:

• As a proper soft-starter, providing a smooth acceleration, which re-duces motor heating and stress on the mechanical drive system due tohigh starting torque hence increasing the life and reliability of belts,

5.1 Configuration 67

Figure 5.2: Soft starter control circuit and control signal time evolution.

gear boxes, chain drives, motor bearings, and shafts [16]. By reduc-ing the voltage when an induction machine starts, it also reduces thehigh starting current, thus alleviating voltage dips and even eliminat-ing brownout conditions. It also reduces the shock on the driven loaddue to high starting torque that can cause a jolt on the conveyor thatdamages products, or pump cavitations and water hammers in pipes.Thus, a fully adjustable acceleration (ramp time) and starting torquefor optimal starting performance, provides enough torque to acceleratethe load while minimizing both mechanical and electrical shock to thesystem [10].

• As a solid state voltage, saving energy under lightly loaded conditionsif the load torque requirement can be met with less than rated flux.This way, core loss and stator copper losses can be reduced [20].

• As a discrete frequency inverter that increases the frequency until thefrequency of the line is reached (50/60 Hz). The discrete frequen-cies produced are sub-multiples of line-frequency and are generated byomission or inclusion of line frequency half cycles. [14]

For the two first modes, the ones corresponding to the operation as avoltage controller, the control of the current or the torque is based on the


assumption that the terminal voltage is regulated by appropriate adjust-ment of the firing angles triggering the thyristors. However, the relationshipbetween voltage and firing angle is highly nonlinear and is also a functionof the power factor and operating conditions of the induction machine. Thepower factor depends on the rotor speed, or rather the rotor slip, and as willbe seen in the Chapter 6 describing the third order model, it also dependson the derivative of voltage. This makes it quite difficult to find the exactvalue of the firing angle for any motor speed and torque.

Some methods of optimal soft starting have been presented, as in [15]that proposes an open loop controller based on artificial neural networksfor the thyristor firing angles or in [13] which detects the phase current andthe voltage across the non conducting thyristor as inputs for a fuzzy logicbased controller. As in other references, the soft-starters’ objective has beento accelerate induction motors from rest condition with minimized currentsand torque.

In the case of wind turbines, the soft-starter has been introduced to fixedspeed ones to reduce in-rush currents and voltage dropouts. [8] analyzesphenomena which affect voltage dip and inrush current due to the directconnection of induction generators running close to synchronous speed toelectrical distribution in low head hydro electric schemes. This is a differentcase to that studied in the starting of induction motors, since now slip varieswithin a narrow interval around zero, but comprising motor and generatoroperation.

This qualitative change in the operation mode gives place to importantnumerical changes in the relationship between the firing angle and the volt-age at the induction machine terminals. Even if there is not a shift betweenmotor and generator operation modes, this relationship is also affected bythe power factor of the induction machine which in turn depends on thevoltage derivative as will be shown in Chapter 6.

There is no relevant bibliography related to optimum control of a soft-starter for the softened connection of induction machines working as gener-ators.

Fig. 5.3 shows a simplified soft-starter performance for a wind turbinegenerator. Basically, its function is to feed the induction machine witha variable voltage, whose evolution pattern is specified according to someconstraint. This constraint has traditionally been to limit the start-up over-current. In the present work, the soft-starter will be controlled in order to

5.2 Thyristor triggering 69

Figure 5.3: Variation in the supplied voltage by means of a soft-starter.

limit the voltage dropout.

In fact thyristor gates are not triggered by means of continuous pulses norisolated impulses, but by supplying pulse trains beginning at the desiredfiring angle α.

The length of these trains can be shortened [10, 9], to avoid unnecessarytriggering. This last paper shows that adequate operation at each thyristorcan be accomplished with two short trains of triggering pulses separated byan angle of 60o. Designs where the trains are enlarged for a semi-period canalso be found [11]. This solution is easier to implement, but care must betaken in not enlarging the trains of pulses beyond a semi-period, in order toavoid both forward and reverse thyristors being simultaneously triggered.

In general, if the train is not divided, the length of the trains of triggeringpulses must be between 60o and 180o, as indicated in Fig. 5.4.

5.2 Thyristor triggering

Signal Ead in Fig. 5.1 refers to the a phase voltage. Its zero crossing isthe reference taken for the beginning of the pulse train that will excite thegate of the forward thyristor in phase a. It is more suitable using anglesinstead of time instants to refer to the point at which pulse trains begin.


Figure 5.4: Pulses at gates. Separation between forward thyristor triggering pulses.

In this sense, pulse trains are repeated in the remaining thyristors every60o. Therefore the firing angle α refers to the angle between the zerocrossing of any voltage phase and the beginning of the train pulses excitingthe corresponding forward thyristor. It determines the voltage supplied tothe connected device.

The triggering pulse sequence is depicted in Fig. 5.5. Arrows indicate thebeginning of the overlapped train of pulses at the corresponding thyristors.Thus, the first vertical arrow represents the point at which forward thyristorin phase a and reverse thyristor in phase b are both triggered. Firing angle ordelay angle α is the distance between this point and the rising zero-crossingof Ua. In order that the thyristors conduct, this first arrow must be at theleft of the intersection of curves Ua and Ub. In Fig. 5.4 the separation anglebetween forward thyristor triggering pulses is shown to be 120o. Triggersignals for forward thyristor gates and the corresponding reverse one areseparated 180o.

5.3 Operation modes

2-0 Mode. If the triggering begins slightly before the voltage curves cross,it is probable that the current will fade before another thyristor will betriggered again. This is the case of the interrupted currents shown inFig. 5.6, where the conduction intervals appear divided in two. Thisis also reflected in the lower graph where it can be seen how the stored

5.3 Operation modes 71

Figure 5.5: Gate triggering sequence and line currents.

energy is not enough to keep the current in phase a and it fades beforeanother thyristor is fired. There are either two thyristors conductingor none, thus calling this situation the 2-0 mode. In this mode, thevoltage waveforms fed to the connected device are truncated short.

According to [9] triggering pulses must exist 60o after the firing anglein the case of operation with current interruptions to allow the secondconduction interval.

3-2 Mode. If the firing angle decreases, a higher voltage difference betweenvoltage curves exists when the thyristors are triggered, and a higherenergy is supplied to the connected device. This increases the conduc-tion interval until the current in a thyristor (for instance AF) is stillpositive when another opposite thyristor is triggered (CR in this case).

This limit in the operation modes also depends on the power factorof the connected device. Lower firing angle values give place to oper-ation in the 3-2 mode, where there are either three or two thyristorsconducting.

Fig. 5.7 shows the conduction intervals for each thyristor and thecurrent through phase a. As in the 2-0 mode, the lower firing angle,the more complete voltage waveforms and the higher rms voltage isexpected at the connected device.


Figure 5.6: Conduction periods of the thyristors. Operation with currentinterruptions.

Uncontrolled Mode. As long as the firing angle is decreased, conductionintervals extend. Depending on the device’s power factor, there is avalue for the firing angle at which current in one phase fades just beforeit begins to flow in the opposite direction. Firing angles lower thanthis limit will not produce any change in the supplied voltage. Thesoft-starter gets into an uncontrolled operation equivalent to a directconnection to the grid.

No Conduction Mode. On the other hand, if trains of triggering pulsesbegin at the right of the intersection of curves Ua and Ub, the forwardthyristor in phase a will be inversely polarized and will not conduct.Therefore, the soft-starter will act as an open circuit for firing anglesgreater than 150o and no voltage will be supplied at the load termi-nals. In fact this assertion cannot be made when the connected devicebehaves as a generator.

5.4 Wind turbine soft-starter 73

Figure 5.7: Conduction periods of the thyristors. Operation without currentinterruptions.

A more detailed description of the conduction modes can be found in[18, 19], and its current waveforms in [9, 17].

5.4 Wind turbine soft-starter

For firing angles smaller than 150o the relationship between the firing angleα and the controlled voltage is non-linear and depends additionally on thepower factor of the connected element. The angles that limit operationmodes also depend on the power factor.

The third order induction generator model (Chapter 6) shows that thepower factor depends in turn on the voltage and its derivative, the slip and


the derivative of the generator voltage angle, not making it feasible to obtainthe supplied voltage versus firing angle characteristic.

Another issue regarding wind generator connection is that when voltagesat both sides of the soft-starter are the same (uncontrolled mode), the gen-erator is completely connected to the grid. At this moment, a contactorthat electrically connects the wind turbine and the low voltage transformerside is energized, thus by-passing the soft-starter. Finally a capacitor bankis connected for power factor compensation. The demanded reactive powerwill dictate the number of connected capacitors. From the point of view ofdecreasing the voltage dropout, it could be desirable to connect the capaci-tor bank during the start-up. However, the soft-starter produces harmoniccurrents that can damage the capacitors, and thus the connection of thecapacitors will not be accomplished until the start-up process has finished[68].

5.5 Asymmetrical soft-starter

In the induction machine start-up, an uncontrollability problem arises whenslip is close to zero and voltage is close to that of the grid. In order toincrease the soft-starter controllability, an asymmetry has been introducedin the gate triggering pulses of the thyristors by delaying one of the sixpulses. This gives place to unbalanced voltage and currents systems withlower rms values. The sequence of pulses supplied to the thyristor gates aswell as the waveform for the current Ia are represented in Fig. 5.8.

As will be seen when different controllers are compared, a slightly lowerdropout is obtained for the same controller when including this asymmetryin the soft-starter. The improvement is not so significant as to recommenda modification in the soft-starter hardware.

5.6 Firing angle control system

An adequate control of the firing angle time evolution will decrease overcur-rents, and mainly voltage dropouts during start-up. Present systems linearlydecrease the firing angle as a function of the time, that is the beginning of thetrain of triggering pulses to the thyristors, in an open-loop control. There-fore, firing angle controllers currently installed in wind turbines perform the

5.6 Firing angle control system 75

Figure 5.8: Asymmetrical pulse sequence at the thyristor gates and phase current.

connection in a predefined number of grid periods [2] and do not provideany interaction with the external condition that could alleviate electricalconnection effects.

Throughout this work, the causes of voltage dropout will be analyzedand closed-loop control systems will be introduced in order to improve theperformance of the soft-starter.

Chapter 6

Induction machine dynamicmodels

There are different models to explain the performance of induction machines.The more simplifications are introduced in the modeling process, the less ac-curate is the model, but the lower computational cost. But the main featureof the reduced models is their ability to provide a better understanding ofthe system, and the simplicity to derive analytical expressions.

In this chapter, a survey of the fifth order model and the steady statemodel will be presented as the most popular ones. The third order model,of great applicability in transient stability studies, will be introduced forthe first time as the best approach to explain and understand the real andreactive power evolution during the start-up.

The sufficient conditions for assuring the validity of the third order modelin this process will be presented and checked, and the main equation de-scribing the induction machine performance will be developed.

Finally, additional considerations and simplifications will allow to obtainexpressions for the real and reactive power as a function of the generatorvoltage, its derivative, the derivative of the voltage angle and the slip. Theseexpressions will allow the controller to adjust its performance in order todecrease the voltage dropout.

78 Chap. 6: Induction machine dynamic models

6.1 Fifth order model

An induction machine can be modeled through an equation system relat-ing voltages, currents and flux linkages and including inductances that arefunctions of the rotor speed. A change of variables is often used to reducethe complexity of these time-varying coefficient differential equations [92].There are several changes of variables that are used, but all of them are con-tained in a general transformation that refers machine variables to a frameof reference that rotates at an arbitrary angular speed (Fig. 6.1).

Figure 6.1: Arbitrary reference frame.

The new equations, together with the mechanical ones, give place to afifth order differential equation system. This linear system describes theinduction machine performance with an accuracy that is enough for mostsituations. Many computer programs used for transient studies such asMATLAB and PSCAD/EMTDC have introduced this model in their blocksor subroutines. These equations are [93][94]:

vds = Rs Ids − ωλqs + pλds (6.1.1)vqs = Rs Iqs + ωλds + pλqs

vtdr = Rt

r Itdr − (ω − ωr)λt

qr + pλtdr

vtqr = Rt

r Itqr + (ω − ωr)λt

dr + pλtqr

where λ is the flux linkage, ωr is the rotor speed, ω is the angular speedof the reference frame, p is the derivative operator and the subscripts s, r,

6.1 Fifth order model 79

d and q stand for the stator, rotor and to d− q axis of the reference systemrotating at ω. Electrical variables in the rotor referred to stator, with thesuperscript t, are obtained from the real ones through the ratio of effectivenumber of turns of the stator Ns and rotor winding Nr:

Utdqr =

Ns

NrUdqr (6.1.2)

Itdqr =

Nr

NsIdqr

λλtdqr =

Ns

Nrλλdqr

Rtr =

(Ns

Nr

)2

Rr.

Stator and rotor currents give place to the flux linkages according to:

λds = LlsIds + M(Ids + Itdr) (6.1.3)

λqs = LlsIqs + M(Iqs + Itqr)

λtdr = Lt

lrIdr + M(Ids + Itdr)

λtqr = Lt

lrIqr + M(Iqs + Itqr)

where Lls is the stator leakage inductance,

M =32

Lms (6.1.4)

Lms is the magnetizing inductance and Ltlr is the rotor leakage reactance

Ltlr =

(Ns

Nr

)2

Llr. (6.1.5)

These equations must be completed with the expressions for the mechanicaltorque Te and the drive dynamics.

Te =32npp M (IqsI

tdr − IdsI

tqr) (6.1.6)

Te − Tl = 2Hdωr

d t(6.1.7)


where npp is the number of pole pairs, Tl is the load torque and H is theinertia time constant.

If the electrical frame angular velocity is the one corresponding to thefundamental frequency of the power system the induction machine is con-nected to (ω = ωs)1, the stationary circuit variables are referred to what iscalled the synchronously rotating reference frame. This reference system isparticularly convenient when incorporating the dynamic characteristics ofan induction machine into a digital computer program used to study thetransient and dynamic stability of large power systems [93].

Using the synchronously rotating reference frame avoids sinusoidal com-ponents of the stator state variables that appear when referring to otherreference systems [95][96].

On the other hand, using bold typeface for complex variables and naming

Us = Uds + j Uqs (6.1.8)Ur = Udr + j Uqr

Is = Ids + j Iqs

Ir = Idr + j Iqr

λλs = λds + j λqs

λλtr = λt

dr + j λtqr

equations (6.1.1) and (6.1.3) can be written as:

Us = Rs Is + j ωsλλs + pλλs (6.1.9)Ut

r = Rtr It

r + j (ωs − ωr)λλtr + pλλt

r (6.1.10)λλs = (Lls + M) Is + It

rM (6.1.11)λλt

r = (Ltlr + M) It

r + IsM (6.1.12)

Solving this system results in a significant computational effort and, whatis worse, qualitative ideas about the system performance are difficult toestablish. There are several reduced order models that involve equationsystem simplifications [95], although two approaches are used most: thirdorder model and steady state model.

1Some bibliographies denotes this speed as ωe

6.2 Reduced models for the induction machine 81

6.2 Reduced models for the induction machine

6.2.1 First approach: third order model

This model is derived from the fifth order model by disregarding statortransients. This means canceling the derivatives of stator flux linkages.In a synchronous reference system, this approximation is valid for smallslip values since the high frequency component of the flux linkage can beseparated from the low frequency one and has limited effect on the torqueexpression. However, for high slip values significant differences exist withregard to the fifth order model, since high frequency electrical variables areinduced in the rotor and stator giving place to pulsating torques. Thesehigh frequency components appear when solving the fifth order model butnot in the third order model [97][43].

This model is often used in transient stability studies, as in [98] and [99],that have been taken as a reference in foreseen sections as a first step toderive expressions for the real and reactive power in a wind turbine inductiongenerator.

Other works about transient stability starting from this model are [46, 45]or [61]. In general, third order model will be used in simulations where highfrequency modes are not expected or they are not significant.

6.2.2 Second approach: first order model

This approach is derived neglecting transients in rotor and stator, hencestate variables appear as constant values. This gives place to the steadystate induction machine model. This model has been used in [100] for thesimulation of a fixed speed stall control wind turbine at start-up althoughresults obtained by means of this model show a disagreement with the ob-served performance when rotor speed or stator currents or voltages varyquickly.


6.3 Third order model main equations

6.3.1 Validity conditions

In some transients, as shown in [98], derivatives of stator flux linkage will beneglected, converting the fifth order model in a third order model. Accordingto [97], this reduced order model is said to be accurate if

α =T ′rT ′s

=σ · (Lt

lr + M) /Rr

σ · (Ltlr + M

)/Rs

> 0.8 (6.3.1)

and

RsRr

(Xs + Xr)2 <

2H · sN ·Rr

10 · σ · Ltlr (1− sN )

(6.3.2)

σ being the leakage parameter, Xs and Xtr the stator and rotor (referred to

stator) reactances, and sN the slip speed at operating (rated) conditions.

σ = 1− M2

(M + Ltlr)(M + Lls)

(6.3.3)

Xs = ωs Lls

Xtr = ωs Lt

lr

Xm = ωs M

Drives satisfying the previous conditions can be modeled by third order mod-els having dominant eigenvalues that agree closely with the correspondingeigenvalues of the full model [97].

A new control structure has been tested for the soft-starter synchronizingan induction machine with the parameters shown in Table 6.1. Henceforth

Table 6.1: Electrical parameters for the induction machine.

Rs = 0.0059 p.u. Xs = 0.0087 p.u.

Rr = 0.01 p.u. Xr = 0.143 p.u.

RFe = ∞ Xm = 4.76 p.u.

6.3 Third order model main equations 83

Table 6.2: Transfer function Gr =−δTr

δωr.

Full Model Reduced Model

Zeros: −20.29 -20.23−6.45± j 313.7

Poles: −20.73± j 3.95 −20.68± j 3.94−12.54± j 313.35

and for sake of clarity, rotor magnitudes will not be added the superscriptt.

The induction machine with previous parameters does not comply withcondition (6.3.1). In fact this condition is a sufficient one to ascertain thatdominant eigenvalues for the reduced and fifth order model are similar toeach other. Therefore, according to the small signal transfer functions shownin Fig. 6.2 extracted from [97], the determination of zeros and poles mustbe made for both the reduced and fifth order models.

Figure 6.2: Small signal block diagram representation of the induction generator.

In a general case of the tested induction machine as a part of an ac drivewhere the rotor speed is to be controlled, poles and zeros of Gr must befound for both models (Table 6.2).

If both root loci are drawn starting from these open-loop zeros and poles


Figure 6.3: Root loci for the mechanical closed-loop function transfer for the fifthorder model (in solid line) and the reduced order model (in dashed line).

and taking K =npp TorqueN

2 H ωslipNas the varying closed-loop gain (Fig. 6.3), it

can be seen that both models agree closely for low gain values, which corre-sponds to high inertia time constants. For high gain values, there can appearcomplex conjugated dominant poles converting the system into a subdampedone, and separating the performances for both induction machine models.

However, from the point of view of an induction machine supplied by anincreasing voltage, it is more interesting to analyze the transfer function

Gv =δTv

δVssince the input variable is the voltage. In this case, poles and

zeros for the fifth order model and the reduced one can also be obtainedfrom [97]. Zeros as well as poles corresponding to electrical, not mechanical,equations are represented in Table 6.3.

Table 6.3: Transfer function Gv =δTv

δVs.

Full Model Reduced Model

Zeros: −29.80 -33.78

21.52± j 29.77 34.59

Poles: −20.73± j 3.95 −20.68± j 3.94−12.54± j 313.35

6.3 Third order model main equations 85

If a ramp voltage input is supplied to the transfer function, comparisonof residues indicates that poles at −12.49± j 312.94 can be disregarded, andhence a good agreement between both models is more evident.

Influence of the dynamics of the mechanical system on the feasibility ofreducing to the third order model is given by condition (6.3.2) that is wellsatisfied

0.0059 0.01(0.0087 + 0.143)2

= 0.0025 <2 · 3 · 0.01 · 0.01

10 · σ · Lr (1− sN )= 1.25 (6.3.4)

Therefore, a close agreement between fifth and third order model is expected.

6.3.2 Reduced electrical system

If stator and rotor self-inductances are defined as:

Ls = Lls + M (6.3.5)Lr = Llr + M

and substituting for Ir from (6.1.12) into (6.1.11) and considering a squirrelcage induction machine (Ur = 0) yields:

0 = Rrλλr

Lr−Rr

M

LrIs + p λλr + j (ωs − ωr) λλr (6.3.6)

Multiplying this equation byM

Lrand denoting

λλ′r = λλrM

Lr(6.3.7)

leads to

p λλ′r =M2 Rr

L2r

Is − Rr

Lrλλ′r − j λλ′r sws (6.3.8)

where s = (ωs − ωr)/ωs is the rotor slip.


On the other hand, from (6.1.9) and (6.1.12)

Us = Rs Is + jωs

(Ls Is +

M

Lrλλr − M2

LrIs

)(6.3.9)

= Rs Is + jX ′ Is + jωsM

Lrλλr

where X ′ is the transient reactance.

X ′ =(

Ls − M2

Lr

)ωs =

(Xs + Xm − X2

m

Xr + Xm

)

=(

Xs +Xm ·Xr

Xr + Xm

). (6.3.10)

Denoting

Z′ = Rs + jX ′ (6.3.11)

(6.3.9) reduces to

Us = Z′ Is + j ωs λλ′r = E′ + Z′ Is (6.3.12)

where the voltage behind the transient impedance E′ is defined as

E′ = jωs λλ′r. (6.3.13)

Thus, (6.3.8) can be expressed as

pE′ =1Tr

(j (X −X ′)Is −E′

)− j E′ s ωs (6.3.14)

where

Tr =Lr

Rr

X = ωs Ls = Xs + Xm

It is worth noticing that stator voltages and currents in (6.3.14) are com-plex quantities defined or expressed according to (6.1.8) and (6.3.12).

6.4 P and Q in the third order model 87

Adopting a synchronously rotating reference frame and assuming a bal-anced voltage system, voltages Us and currents Is will be the phasors cor-responding to the voltage and current at phase a. It is worth noticing thatthis voltage phasor cannot be considered a static phase reference. In fact, avariation in the stator voltage phase angle θ is expected due to firing anglevariations.

6.4 P and Q in the third order model

An alternative expression for (6.3.14) is

d Us

d t− d Is

d tZ′ = −j ωs (Us − IsZ′)− 1

Tr(Us − Is Z) (6.4.1)

where

Z = Rs + jX (6.4.2)

Once this simplification is made, if the conjugate of (6.4.1) is multiplied byU, it yields

Usd U∗

s

d t− dI∗s

dtUs Z′∗ = j ωs (U2

s − S ·Z′∗)− 1Tr

(U2s − S ·Z∗) (6.4.3)

where S is the single-phase complex power. Solving this equation for S,gives

S1fase 'Us

dU∗s

dt− dI∗s

dtUZ′∗ + U2

s ωs

(Rr

Xr + Xm− j s

)

ωs

(Rr

Xr + XmZ∗ − j s Z′∗

) (6.4.4)

Assuming the complex voltage and current in the form U = U ej θ andI = I ej θ+ϕ the first two addends in the numerator are

UsdU∗

s

dt= Us

(ej θ

) dUs e−j θ

dt= Us

dUs

dt− j U2

s

dθ

dt(6.4.5)

UsdI∗sdt

= Us

(ej θ

) dIs e−j (θ+ϕ)

dt= Us

dIs

dte−j ϕ − j I · U

(dθ

dt+

dϕ

dt

)e−j ϕ


and hence complex power S, expressed in p.u. yield

p + j · q 'us

dus

dt+ u2

sωs

(rr

xr + xm− j s− j

dθ

dt

)

ωs

(rr

xr + xmz∗ − j s z′∗

) +

+

(us

disdt − j is us

(dθ

dt+

dϕ

dt

))z′∗e−jϕ

ωs

(rr


) (6.4.6)

where phase voltage and one third of the generator rate capacity have beentaken as base magnitudes.

Ub =UL√

3typically 398 V

Sb =MV Aturbine

3

Zb =U2

b

Sb

Ib =Sb

Ub.

Since

p + j · q = u · i · e−jφ, (6.4.7)

then (6.4.6) can also be expressed as

p+ j ·q 'us

dus

dt+ u2

sωs

(rr

xr + xm− j s− j

dθ

dt

)+ us

disdt

z′∗e−jϕ

ωs

(rr


)+ j is us

(dθ

dt+

dϕ

dt

)z′∗

(6.4.8)

For large induction machines as used to be installed in wind turbines,the value for Z′ is small and current is indirectly controlled such that itsevolution will not be too fast. Specifically, for the tested induction machinewhose parameters are indicated in Table 6.1, Z′ = 0.0059 + j 0.1475 Ω.

6.4 P and Q in the third order model 89

Figure 6.4: Real and Reactive Power. Comparison of steady state, third and fifthorder models.

Therefore, the derivative of the current term in (6.4.6) can be neglectedwithout a significant error, giving

p + j · q 'us

dus

dt+ u2

sωs

(rr

xr + xm− j s− j

dθ

dt

)

ωs

(rr


) . (6.4.9)

Fig. 6.4 visualizes the close agreement between the fifth and third ordermodels and the validity of disregarding the derivative of currents. Unac-ceptable values are obtained from the steady state model, whose evolutionis far from the fifth and third order models. The power values calculated byPSCAD/EMTDC using a complete model appear as Pgen and Qgen. Theother two curves correspond to the reduced order model, either including ordisregarding the derivative of currents.

Chapter 7

Sliding-mode control to limitvoltage dropout

Voltage dropout at a given node in a power system depends on the real andreactive power flowing from the network towards that node.

In order to keep the voltage within the regulated limit, the proposed soft-starter controller must be able to estimate these power components andimpose a suitable action. Controllers based on the variable structuresystem theory have received much attention in recent years to design robuststate feedback systems, mainly for controlling dc and ac servo drives [101,102, 103].

A variable structure control system based on sliding-mode techniques canbe switched between two distinct control structures, constraining the systemstate trajectory to a region known as a switching surface or in general,switching hyperplane [101, 104].

In general, there are two basic steps in the design of the variable structurecontroller: the design of the switching phase and the design of the reachingor switching control.

With regard to the design of the sliding hyperplane (a line in a two-dimension case), it is solely defined by parameters that are independent of

92 Chap. 7: Sliding-mode control to limit voltage dropout

the plant model, at least in an explicit way. Therefore, once the controlledsystems states enter the sliding mode, the choice of sliding hyperplanes deter-mines the dynamics of the system which is provided insensitivity to boundedplant parameter changes, external disturbance rejection and fast dynamicresponse. In the present study the sliding line has been chosen in order toreduce the voltage dropout to a limited value.

In relation to the design of the law control, the parameters involved init have to be chosen in order to guarantee that the system must reach theswitching surface (hitting phase). When all the state variables of the con-trolled system are constrained to lie in a switching hyperplane, the closedloop dynamics are said to be in a sliding mode, or an sliding mode occurs(sliding phase).

The advantages of the sliding-mode control have been employed to controlthe position and speed of ac servo systems, where the main difficulty is toprecisely measure or accurately estimate, due to the noisy environment, thediscrete resolution of speed transducers or inaccurate system parameters.

With regard to the electrical magnitudes involved in the electrical connec-tion process of a wind turbine, for the definition of the variable structurecontroller, the following two issues must be taken into account:

• an expression for the voltage dropout will be determined starting fromthe complex power flowing from the wind turbine generator and

• the generator voltage and its derivative are the main magnitudes in-fluencing the complex power delivered by the induction generator, andin turn the complex power flowing from the wind turbine.

According to the first item, a variable structure control strategy will beused to control the relationship between real and reactive power in the highvoltage side of a wind turbine interconnection. Along the sliding-line, thesystem will describe a trajectory defined by a desired relationship betweenstate variables. Therefore, according to the second item, forcing the systemto follow a sliding trajectory given by a suitable relationship between gener-ator voltage and its derivative will, theoretically, produce the desired voltagedropout. In fact, in order to make the system asymptotically convergent tothe sliding trajectory, the voltage at the generator terminals and its deriva-tive will not be chosen as state variables, but some one to one function ofthem.

93

Once the system has reached the switching hyperplane (a line in a two-dimensional problem) the controller will constrain the system state trajec-tory to a band around it, thus limiting the voltage dropout around thedesired value. When the connection process is to be finally fulfilled, the sys-tem will naturally separate from the sliding trajectory, and the voltage atthe point common coupling begins to recover, thus completing the start-upprocess.

The reference value for the voltage dropout will be determined as a func-tion of the estimated rotor acceleration and must always be sufficiently in-ferior to the permitted voltage dropout set by local regulations.

Therefore, a sliding-mode based controller has been considered to be themore suitable controller for this task due to its robustness and because itscontrol action fits closely with the aim of taking the system to a state wherea determined variable (the voltage dropout in this case) is kept within anarrow interval.

In the first section of this chapter the expressions linking the voltagedropout at the interconnection and the real and reactive power flowing to-wards the induction machine are explained.

In section two the sliding or switching trajectory in order to keep thevoltage dropout close to the prefixed value is established.

Section three will present the theory of design of the proposed controller.

An analysis of a specific system will be presented in section four, andthe control law parameters to guarantee system stability will be derived.This means that the system will always be directed to the sliding trajectory,where theoretically the voltage dropout is close to the desired one.

Particular details of the implementation of the sliding-mode controllersare described in section five.

Start-up simulations when controlling the soft-starter by means of severalcontrollers and a comparison of the obtained results are presented in sectionssix and seven.

More simulation results will be shown in section eight, but focused onproviding some ideas about the influence of line impedance on the voltageevolution.


Figure 7.1: Single wind turbine feeding a consumer in a weak grid.

7.1 Voltage dropout in a weak grid

The voltage dropout controller has been designed and tested consideringan electrical system with a single wind turbine feeding a consumer that isconnected to a weak grid (Fig. 7.1).

The voltage modulus difference in per unit between Thevenin voltagesource and the point of common coupling (PCC) takes the form (Fig. 7.1)

Enw − UPCC ' PnwRlin + QnwXlin. (7.1.1)

It should be noticed that all magnitudes are real values, not complex ones(not in bold type).

Before the connection process the real and reactive power componentstransferred from the network to the PCC are the only power componentsdetermining the voltage dropout at the local load node

Pwt = Qwt = 0 ⇒ Pcons = Pnw, Qcons = Qnw ⇒Enw − U0

PCC ' PconsRlin + QconsXlin (7.1.2)

but once the wind turbine begins its electrical connection

Pwt, Qwt 6= 0 ⇒ Enw − UPCC ' PnwRlin + QnwXlin =(Pcons + Pwt) Rlin + (Qcons + Qwt) Xlin (7.1.3)

where Pwt and Qwt are the real and reactive power entering the wind tur-bine and hence are considered positive when flowing towards the generator

7.1 Voltage dropout in a weak grid 95

(motor convention). Neglecting real (power losses) and reactive power takenby the transformer and in the medium voltage line conductors linking thewind turbine to the PCC, Pwt and Qwt can be obtained from the powersconsumed/generated by the induction machine as

Pwt ' Pgen (7.1.4)

Qwt '√

U 2lv

U 2gen

Q 2gen + P 2

gen

(U 2

lv

U 2gen

− 1)

(7.1.5)

where Pgen and Qgen are the real and reactive power taken by the induc-tion machine and Ulv is the voltage at the low voltage side of the powertransformer.

Previous equations lead to

4U = U0PCC − UPCC ' PgenRlin + QwtXlin ⇒

4U ' PgenRlin + Xlin

√U 2

lv

U 2gen

Q 2gen + P 2

gen

(U 2

lv

U 2gen

− 1)

(7.1.6)

This means that there will be a voltage dropout with respect to voltageprevious to the connection process, that depends on the real and reactivepower as shown in (7.1.6). To observe regulations currently in force in manycountries, the voltage dropout must be below a certain limit of around 2-3%. Regarding the short term flicker value Pst, at low frequencies, up to 3%voltage variation is acceptable [26]. However, the conditions under whichthis dropout must be measured are not well defined.

Indeed, during the electrical connection of the wind generator to the net-work, there will be a first stage in which the turbine induction machine be-haves as a motor, extracting real power from the network the wind turbineis connected to. In Fig. 7.1 this network is represented as its single-phaseequivalent source and an impedance. With no interruption and slightly afterthe synchronous speed is reached, the induction machine will behave as agenerator, transferring power to the consumer or to the network.

Therefore, it is expected that before initiating the wind generator connec-tion, the voltage at the consumer point U0

pcc will be greater than the voltageduring most of the connection process but lower than the voltage when theconnection is completely accomplished, Uf

pcc (Fig. 7.2). Papers dealing with


Figure 7.2: Voltage in the PCC during the connection process.

the switching operation impact calculate or estimate the voltage changestarting the inrush current. Therefore, they implicitly equate the voltagechange with the voltage dropout. However the maximum voltage changeduring the electrical connection should be considered [29, Standard CEI61400-21], which may involve the final voltage once the electrical connectionhas been accomplished.

According to Fig. 7.2 the voltage dropout strictly speaking was definedin section 3.4.3 as the maximum drop in the rms value of the voltage at thepoint of common coupling with respect to the voltage prior to the connection.Voltage change was denoted as the maximum difference in voltage duringthe connection transient.

Since the final value of the voltage cannot be determined during the start-up, in order to have a reference to adjust and compare different controllers,the voltage dropout instead of voltage change will be the magnitude to beoptimized. In any case, since the final value is independent of the start-upprocess, minimizing voltage dropout means optimizing voltage change.

Thus, with the objective of decreasing the voltage dropout, a variablestructure control scheme will be designed starting from (7.1.6).

7.2 Definition of the sliding trajectory 97

7.2 Definition of the sliding trajectory

Neglecting the derivatives of current, the complex power (in a phase or inper unit) takes the form:

Sgen 'Ugen

dU∗gen

dt+ U2

gen ωs

(Rr

Xr + Xm− j s

)

ωs

(Rr

Xr + XmZ∗ − j sZ ′∗

) (7.2.1)

where

Z = Rs + j(Xs + Xm

)

Z ′ = Rs + j(Xs +

Xr Xm

Xr + Xm

)(7.2.2)

Real and reactive powers are considered positive when they are flowing to-wards the generator. A moving frame in which the stator voltage angle θis always zero can be considered. However, its derivative cannot be disre-garded.

Ugen

dU∗gen

dt= Ugen ej θ d

dt

(Ugen e−j θ

)= Ugen

dUgen

dt− jU2

gen ej θ dθ

dt

=12

dU2gen

dt− jU2

gen

dθ

dt(7.2.3)

and considering that Xm À Xr, Rr and s ' 0, which implies

ωs

(Rr

Xr + XmZ∗ − j sZ ′∗

)' −jωs Rr (7.2.4)

then approximated values for the real and reactive power can be derived

Pgen ' U 2gen

s

Rr+ U 2

gen

1Rr ωs

dθ

dt= U 2

gen αP (s) + U 2gen βP (θ) (7.2.5)

Qgen ' UgendUgen

dt

1ωs Rr

+ U 2gen

1Xr + Xm

= UgendUgen

dtαQ + U 2

genβQ (7.2.6)


where, logically

αP (s) =s

Rr

βP (θ) =1

Rr ωs

dθ

dt

αQ =1

ωs Rr

βQ =1

Xr + Xm(7.2.7)

Equations (7.2.5) and (7.2.6) provide approximative expressions for realand reactive power as functions of the generator voltage and its derivative.Equation (7.1.6) links both components of complex power in a expressionfor the voltage dropout. Thus, a sliding trajectory can be defined in whichthe voltage dropout equals its limit value 4UL

1

σ = 0 ⇔4U = 4UL ⇒ σ = Q 2wt −

(4UL − Pgen Rlin)2

X 2lin

. (7.2.8)

Pgen and Qnw are functions of Ugen and its derivative but instead of them,it is more convenient using

x =(

x1

x2

)=

Ulv − Ugen

−dUgen

dt

'

Ulv − Ugen

ddt

(Ulv − Ugen)

(7.2.9)

as the components of the phase plane where the sliding mode will be defined.

For actual connection transients, real power will present a close-to-zeropositive value (motor) or negative values (generator). Therefore, positivevalues of σ means that the voltage dropout is higher than 4UL and thus,the system should be steered towards the sliding trajectory, to decrease thisvoltage dropout. Negative values mean that the system is not surpassing thepermitted limit, but if the value is too low or is kept low enough for a rel-atively long time, the transient would delay too much over the synchronousspeed and the shaft torque would reach an excessive value.

1henceforth, electrical magnitudes will be expressed in p.u., although uppercase letterswill be maintained for sake of clarity


Figure 7.3: Sliding trajectories for different αP + βP .

Thus, from (7.1.5),(7.2.5), (7.2.6) and (7.2.8)

σ = −(4UL)2

X 2lin

− U 4gen (αP + βP )2

R 2lin

X 2lin

+ 2 U2gen

Rlin

X2lin

4UL

(αP + βP

)+

+x 22 U 2

lvα2Q + U 2

gen U 2lvβ

2Q − 2x2 Ugen αQ βQ U 2

lv +

+U 2gen U 2

lv

(αP + βP

)2 − U 4gen

(αP + βP

)2 (7.2.10)

For the sake of clarity, Ulv − x1 has not been substituted for Ugen.

Besides being a function of x1 and x2, σ also depends on the slip s and thederivative of stator voltage angle θ. In the phase plane, there is a family ofcurves σ = 0 as long as the connection progresses (see Fig.7.3).

If the following generalized Lyapunov function is introduced

V (x1, x2) =14

σ2(x1, x2) (7.2.11)

and if αP , βP , αQ and βQ could be considered as constants or slow variables,a sliding mode will be present if

dV (x1, x2)dt

< 0 ⇔ 12

σ (∇σ · x) < 0 (7.2.12)

This condition can be geometrically understood taking into account that asliding mode is guaranteed if vector (x1, x2) points toward the sliding lineat every instant in the connection transient. Fig. 7.4 shows a curve σ = 0


0 0.2 0.4 0.6 0.8 1−7

−6

−5

−4

−3

−2

−1

0

x1(p.u.) = Ulv − Ugen

x2(p

.u./s

) =

− d

Uge

n/dt

σ = 0

σ < 0

σ > 0

Sliding trajectory and its gradient

(x1,x2)· ·

(will cross)

(x1,x2)· ·

(will not cross)

∇ σ

Figure 7.4: σ and ∇σ in the phase plane.

0 0.2 0.4 0.6 0.8 1−7

−6

−5

−4

−3

−2

−1

0

1

x1(p.u.) = Ulv − Ugen

x2(p

.u./s

) =

−dU

gen/

dt

σ = 0 (αΡ + βΡ = 0.5)

σ = 0 (αΡ + βΡ = −0.5)

might not cross sliding trajectory

x ∇ σ .

Figure 7.5: Example of ~x = (x1, x2) that might not reach σ = 0.


for given values of αP and βP , and the arrows show the direction of−→∇σ

pointing to increasing values of σ. For positive values of σ, the system willbe directed to the sliding trajectory if vector

−→x = (x1, x2) has the opposite

direction to−→∇σ , that is

−→∇σ · −→x < 0. For negative values of σ, the vector−→x = (x1, x2) and

−→∇σ should have the same direction (−→∇σ · −→x > 0). This

means that, in order to reach the voltage dropout and not exceed it, then

ifσ > 0 → and−→∇σ · −→x < 0

ifσ < 0 → and−→∇σ · −→x > 0

⇔ σ

−→∇σ · −→x < 0 (7.2.13)

If αP , βP , αQ and βQ cannot be considered constants or slow variables, thecondition in (7.2.12) would not be a sufficient one to assure that the systemhead for the sliding trajectory. Fig. (7.5) visualizes this situation.

In the represented example, a vector ~x = (x1, x2) that satisfies σ ~∇σ · ~x < 0might not cross the sliding trajectory if αP + βP moves too fast.

To be precise, previous conditions 7.2.12 or 7.2.13 turn into

12

σ

(−→∇σ · −→x +dσ

dαP

dαP

dt+

dσ

dβP

dβP

dt

)< 0 (7.2.14)

From 7.2.10 and 7.2.14

12

σdσ

dt= 2σU 3

gen x2 (αP + βP )2R 2

lin

X 2lin

− 2σ Ugen x2Rlin

X2lin

4UL

(αP + βP

)+

+ σx2 x2 U 2lvα

2Q − σUgen x2 U 2

lvβ2Q + σ

(x2

2 − Ugen x2

)αQ βQ U 2

lv +

− σUgen x2 U 2lv

(αP + βP

)2 + 2 σU 3gen x2

(αP + βP

)2 +

+ σ

(U 2

gen U 2lv − U 4

gen

(1 +

R 2lin

X 2lin

))(αP + βP )

(αP + βP

)

+ σU2gen

Rlin

X2lin

4UL

(αP + βP

)< 0 (7.2.15)


Grouping, it yields

σUgen x2

[2U 2

gen (αP + βP )2R 2

lin

X 2lin

− 2Rlin

X2lin

4UL

(αP + βP

)+

− U 2lvβ

2Q − U 2

lv

(αP + βP

)2 + 2 U 2gen

(αP + βP

)2]

+

+ σx22 αQ βQ U 2

lv +

+ σx2 x2 U 2lvα

2Q +

− σUgenx2 αQ βQ U 2lv +

+ σ U 2gen

(αP + βP

)[U 2

lv − U 2gen

(1 +

R 2lin

X 2lin

)](αP + βP ) +

Rlin

X2lin

4UL

< 0 (7.2.16)

7.3 Sliding mode controller with integral compen-sation

In this section and in the following, the gains involved in the variable struc-ture of the controllers will be chosen in order to assure the stability of thesystem, referred to as the ability of keeping the voltage dropout within acertain value 4UL.

A sliding mode controller with integral compensation [105, 106] will beused in which the control law usl is integrated to give place to the controlsignal α. The firing angle α is the angle, starting from the ascending zero-crossing of the phase voltage (see figure 7.6), that controls the rms value ofthe voltage applied to the induction machine. Firing angle is scaled so asα = 1 corresponds to half a period.

α(t) =∫ t

0usl dτ (7.3.1)

A desirable control law usl will take the form

usl(x1, x2, σ) = Ψ1(σ, x1) · x1 + Ψ2(σ, x2) · x2 (7.3.2)

and will be limited in the firing angle variation rate

−ulimsl < usl < ulim

sl (7.3.3)

7.3 Sliding mode controller with integral compensation 103

Figure 7.6: Simplified performance of the soft-starter.

Finally, to bring the analysis to a close, it is necessary to find the sys-tem response to the control signal α. It has been finally observed that arelationship of the type

x2 = kss(x1, s) · usl + k0ss(x1, s)

kss(x1, s), k0ss(x1, s) > 0 (7.3.4)

can be found between the second derivative of the generator voltage andthe derivative of the firing angle.


Thus, (7.2.16) can be rewritten as

σUgen x2

2U 2

gen (αP + βP )2[

R 2lin

X 2lin

+ 1]− 2

Rlin

X2lin

4UL

(αP + βP

)+

− U 2lvβ

2Q − U 2

lv

(αP + βP

)2

+

+σ x22 αQ βQ U 2

lv +

+σ[k0

ss + kss (Ψ1(s) · x1 + Ψ2(s) · x2)] (

x2 U 2lvα

2Q − Ugen U 2

lv αQ βQ

)+

+σ U 2gen

(αP + βP

)[U 2

lv − U 2gen

(1 +

R 2lin

X 2lin

)](αP + βP ) +

Rlin

X2lin

4UL

< 0 (7.3.5)

which is composed of several addends. A sufficient condition for the inequal-ity (7.3.5) to be true is that all these addends are negative.

σU2gen

(αP + βP

)[(U 2

lv − U 2gen

(1 +

R 2lin

X 2lin

))(αP + βP ) +

Rlin

X2lin

4UL

]+

− αQβQU 2lv

Ugen

(kss Ψ1 x1 + k0

ss

)< 0 (7.3.6)

σ x2

Ugen

[(αP + βP )2

(2U 2

gen

(R 2

lin

X 2lin

+ 1)− U 2

lv

)− 2

Rlin

X2lin

4UL

(αP + βP

)+

− U 2lvβ

2Q − kss Ψ2 U 2

lvαQ βQ

]+ U 2

lv α 2Qk0

ss

+ σ kssΨ1 x1 x2 U 2

lvα2Q < 0 (7.3.7)

σx22

(αQ βQ U 2

lv + kss Ψ2 U 2lv α2

Q

)< 0 (7.3.8)

In order to make these inequalities true, a switching in the values of thecontrol law parameters can be forced if:

• the sign of σ changes and/or

• the sign of x2 changes

7.3 Sliding mode controller with integral compensation 105

The first state variable x1 = Ulv − Ugen will always be positive.

Previous equations can be developed, but prior to that, it is worth noticingthat αQ, βQ and kss > 0.

From (7.3.6) the following inequalities must be satisfied

σΨ1x1 >

σUgen

(αP + βP

)[U 2

lv − U2gen

(1 +

R 2lin

X 2lin

)](αP + βP ) +

Rlin

X 2lin

4UL

kss αQβQU 2lv

− σk0

ss

kss

if σ > 0 ⇒

Ψ+1 > (7.3.9)

(αP + βP

)Ugen

[U 2

lv − U2gen

(1 +

R 2lin

X 2lin

)](αP + βP ) +

Rlin

X 2lin

4UL

x1 kss αQβQU 2lv

− k0ss

kssx1

if σ < 0 ⇒

Ψ−1 < (7.3.10)

(αP + βP

)Ugen

[U 2

lv − U2gen

(1 +

R 2lin

X 2lin

)](αP + βP ) +

Rlin

X 2lin

4UL

x1 kss αQβQU 2lv

− k0ss

kssx1

at each moment of the connection process.

Figures 7.3 and 7.4 show that, for actual (αp + βp) values, then

σ > 0 ⇒ x2 < 0. (7.3.11)

Therefore the combination σ > 0, x2 > 0 is not feasible. On the otherhand, the combination σ < 0, x2 > 0 is feasible, but a logical connectiontransient implies that generator voltage increases continuously until the endof the process, which means x2 = −dUgen/d t < 0. In fact, in the casewhere x2 is close to zero values during the connection transient, the slidingcontroller will perform a correcting control that will tend to steer the systemtowards the sliding trajectory. When considering positive values of x2 more


variants are introduced that complicate the analysis. Instead of that, thecase where x2 is positive, will be treated separately. Under those conditions,sgn(σ) = −sgn(σx2)

From (7.3.8)

i f σ > 0 ⇒ kss Ψ−2 < −βQ

αQ=

−ωs Rr

Xr + Xm⇒ Ψ−

2 < − ωs Rr

Xr + Xm

1k min

ss

i f σ < 0 ⇒ kss Ψ+2 > −βQ

αQ=

−ωs Rr

Xr + Xm⇒ Ψ+

2 > − ωs Rr

Xr + Xm

1k max

ss

(7.3.12)

In a similar way, from (7.3.7)

if σ x2 > 0 ⇒

Ψ+2 > Ψ1

αQ x1

βQ Ugen+

k0ss

kss Ugen

αQ

βQ+ (7.3.13)

−(αP + βP )2

(−2U 2

gen

(R 2

lin

X 2lin

+ 1)

+ U 2lv

)+ 2Rlin

X2lin4UL (αP + βP ) + U 2

lvβ2Q

kssU 2lvαQβQ

if σ x2 < 0 ⇒

Ψ−2 < Ψ1

αQ x1

βQ Ugen+

k0ss

kss Ugen

αQ

βQ+ (7.3.14)

−(αP + βP )2

(−2U 2

gen

(R 2

lin

X 2lin

+ 1)

+ U 2lv

)+ 2Rlin


lvβ2Q

kssU 2lvαQβQ

Eqs. (7.3.10) and (7.3.11) evidence that Ψ+1 > Ψ−

1 . If finally they arechosen such that Ψ+

1 > 0 > Ψ−1 , which implies σΨ1 > 0, and assuming

x2 < 0 which in turn implies σ x2 > 0 ⇔ σ < 0, then (7.3.13) and (7.3.14)must be rewritten as

Ψ+2 >

k0ss

kss Ugen

αQ

βQ+ (7.3.15)

−(αP + βP )2

(−2U 2

gen

(R 2

lin

X 2lin

+ 1)

+ U 2lv

)+ 2Rlin


lvβ2Q

kssU 2lvαQβQ

7.4 Control law parameters 107

Ψ−2 <

k0ss

kss Ugen

αQ

βQ+ (7.3.16)

−(αP + βP )2

(−2U 2

gen

(R 2

lin

X 2lin

+ 1)

+ U 2lv

)+ 2Rlin


lvβ2Q

kssU 2lvαQβQ

7.4 Control law parameters

At this point, few more analytical manipulations

At this point, some more analysis regarding the boundary control lawparameters Ψ+

1 , Ψ−1 , Ψ+

2 and Ψ−2 will be presented. The actual induction

generator constants and performance must be introduced in order to boundthese parameters.

With respect to electrical induction machine constants, Table 7.4 summa-rizes the steady state electrical constants for the analyzed wind generator.

Table 7.1: Electrical constants for stability study I.

Induction machine steady state constants

Rs Stator Resistance 0.0059 p.u.Rr Rotor Resistance 0.010 p.u.Xs Stator Reactance 0.0087 p.u.Xr Rotor Reactance 0.143 p.u.Xm Magnetizing Reactance 4.76 p.u.

Table 7.4 other independent values which are also needed for the boundaryof law control parameters.

The values of αQ and βQ appearing in previous inequalities are derivedfrom (7.2.7)

αQ =1

ωs Rr= 0.2122s/rad

βQ =1

Xr + Xm= 0.2094. (7.4.1)


Table 7.2: Electrical constants for stability study II.

Additional independent constants

ωs Electrical angular speed 314.1592 rad/sRlin Line Resistance 0.02441 p.u.Xlin Line Reactance 0.0176 p.u.4U0 Maximum voltage dropout 0.015 p.u.

Unfortunately, there are many other terms in previous inequalities thatare not constants. Furthermore, some of them are poorly modeled, as βP ,which makes it difficult for Ψ1 (and consequently Ψ2) to be bounded. Thus,an analysis has to be made of every term of (7.3.10) or (7.3.11) in order tobound the range of possible values for these expressions. In that sense somesensitivity tests have been performed in order to demonstrate that βP doesnot have a significant influence on the expressions.

Two issues must be pointed out before bounding Ψ1:

• as seen in Fig. 7.7 the boundary is not valid in the area in which kss = 0(in the referenced figure, this is the lower right area); fortunately thisis the last stage of the connection process and the generator voltagesmoothly develops to its uncontrolled final value and the real poweris high enough to compensate the effect of the reactive power in thevoltage dropout (see (7.1.1))

• the analysis has been made avoiding dependences on the type of con-trol; only the range for βP (and subsequently βP + αP ) has been ob-tained from analyzing several kinds of control in different conditionsand extracting the extreme values.

In this regard, the series of performed simulations yield the following rangefor βP

7.4 Control law parameters 109

0.2 0.4 0.6 0.8

−0.01

−0.005

0

0.005

0.01

0.015

0.02Relationship 1/(d2U/dt − d alpha/dt)

Generator voltage (p.u.)

slip

(p.

u.)

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Motor

Generator

Figure 7.7:1

kssat different generator voltages and slips.

− 32p.u.

s2<

d2θ

dt2< 50

p.u.

s2⇒

−10.611s

<dβP

dt=

1Rrωs

d2θ

dt2< 6.79

p.u.

s. (7.4.2)

With regard to αP = s/Rr, this value can be derived from the applied torqueTw, the inner electromechanical torque Tmi and the frictional term

−2Hds

dt= Twind − Tmi −Bωr < Twind 5 1 in p.u. (7.4.3)

which leads to

0 = αP =ds

dt

1Rr

= − 12HRr

= −12.65p.u.

s(7.4.4)

Therefore

−23.26p.u.

s< αP + βP < 5.86

p.u.

s(7.4.5)


This will lead to excessively high gains for the law control which is not desir-able. Instead of these values, (7.2.5) can be used to give place to a narrowerrange for αP + βP . Thus, a series of simulations in different conditions andwith different kinds of controls show that

−9p.u.

s<

ddt

Pgen

U2gen

' αP + βP < 4.6p.u.

s(7.4.6)

Within the valid region of Fig. 7.7, and making a sweep for αP + βP in therange of [−9, 4.6], it is obtained that the expression

(αP + βP

)Ugen

[U 2

lv − U2gen

(1 +

R 2lin

X 2lin

)](αP + βP ) +

Rlin

X 2lin

4UL

x1 kss αQβQU 2lv

− k0ss

kssx1

(7.4.7)

is delimited by -4 and 20. As referred in (7.3.10) and (7.3.11) these valueswill be assigned to Ψ+

1 and Ψ−1 of the control law

Ψ+1 = 4

1s

Ψ−1 = −20

1s. (7.4.8)

With regard to Ψ2, expressions (7.3.15) and (7.3.16) must be taken intoaccount. All the terms in these expressions, except βp, are constants orvalues related to the generator voltage x1 and/or the slip s. From a seriesof simulations in different conditions and controllers,

−0.52 < βp =θ

Rr ωs< 0.7 (7.4.9)

Within the valid region of Fig. 7.7, and making a sweep for βP in the rangeof [−0.52, 0.7], the following delimitation can be obtained.

− 6 < −(αP + βP )2

(−2U 2

gen

(R 2

lin

X 2lin

+ 1)

+ U 2lv

)

kssU 2lvαQβQ

+ (7.4.10)

−2Rlin


lvβ2Q

kssU 2lvαQβQ

+k0

ss αQ

kss x1 βQ< 5.5

7.5 Implementation of the proposed controller 111

In order to minimize the control effort, the control law parameters regardingto Ψ2 results in

Ψ+2 = 5.5 (7.4.11)

Ψ−2 = −6.0.

It does satisfy (7.3.12) since

− 9.2 = Ψ−2 < − ωs Rr

Xr + Xm

1k min

ss

= −314.1592 · 0.014.9 · 10

= −0.021 (7.4.12)

8.1 = Ψ+2 > − ωs Rr

Xr + Xm

1k max

ss

= −314.1592 · 0.014.9 · 37

= −0.026

The case where x2 > 0 means that the generator voltage is decreasing. Thesliding trajectory varies as long as αP + βP varies, but it is always found tobe below abscises axis (x2 = 0). Therefore, a suitable control action for thecase where x2 > 0 is to decrease the firing angle which will eventually makeUgen increase, thus approaching the vector state to the sliding line.

if x2 > 0 ⇒ usl =12

ulimsl (7.4.13)

7.5 Implementation of the proposed controller

A sliding-mode controller has been calculated starting from the characteris-tics extracted from the induction generator connected through a soft-starter.

The proposed sliding-mode controller presents an integral compensation(SLMCIC) as seen in Fig. 7.8, which gives place to a more continuousperformance of the system since the SLMCIC acquires a PI characteristic.

Apart from the generator voltage and its derivative, there are some otherinputs to the sliding-mode controller module:

Ulv Voltage at the network side of the soft-starter, although a not signifi-cant error is made if Ulv = 1 p.u. is considered.

slip The difference in per unit between the synchronous speed and the rotorspeed. This is required for the calculation of σ.


Figure 7.8: Sliding-mode controller with integral compensation.

dThU Derivative of the voltage generator angle. At each moment, the anglecan be considered equal to zero, but not its derivative. Neglecting itwould give place to unacceptable errors in the calculation of σ, thatwill deteriorate the controller performance. MATLAB Toolbox forSystem Identification has been used to estimate this from Ugen, theslip, and their derivatives.

The value for σ, whose sign dictates the shift in the control law parameters,is obtained from the following expressions previously presented.

Pgen ' U 2gen

s

Rr+ U 2

gen

1Rr ωs

dθ

dt

Qgen ' UgendUgen

dt

1ωs Rr

+ U 2gen

1Xr + Xm

Pwt ' Pgen

Qwt '√

U 2lv

U 2gen

Q 2gen + P 2

gen

(U 2

lv

U 2gen

− 1)

(7.5.1)

and

σ = Q 2wt −

(4UL − Pwt Rlin)2

X 2lin

(7.5.2)

As seen in Fig. 7.9 and eq. (7.5.2) the permitted voltage dropout appearsin the calculation of σ, and the expected derivative of voltage, in turn,

7.5 Implementation of the proposed controller 113

Figure 7.9: Calculation of σ.

determines the permitted voltage dropout. This is due to the fact that whenthe connection transient is fast, then keeping a low value for the voltagedropout will make the turbine overpass its final speed, and so will do theshaft torque. This is a consequence of the mechanical system equation

Twind = Jω + Bω +Pgen

ω. (7.5.3)

Disregarding the sign of Twind and Pgen, it can be found that a high windtorque must be compensated with a high inner mechanical torque from thegenerator in order to avoid an excessive speed increase. And for the realpower to be significant it is necessary that the generator voltage reachesa high value. For a high wind torque, these circumstances appear a shorttime after the connection process begins, which means that the voltage mustreach a high value in a short time, giving place to a high derivative, whichin turn produces a high reactive power and voltage dropout.

For low inertia values, low rotor resistance or high wind torque, there is atrade-off between a low dropout and a low speed overshot. Therefore, it isconvenient to relax the voltage dropout limit the controller should maintain,and allow a higher value in order to decrease the speed overshot. This isaccomplished by a component which estimates an optimum voltage dropoutfrom the rotor resistance and the initial derivative of slip, which is relatedto the wind turbine inertia and the wind torque.

This is another feature of the sliding-mode controller: the capability ofaccomplishing an optimized dropout performance, an optimized overshot


Figure 7.10: Sliding-mode controller simplified control law.

one or a trade-off performance, depending respectively on whether a lowdropout value is chosen in the calculation of σ, a high one, or a variable oneaccording to the connection transient speed.

Once σ is obtained, the control law output is derived from x1 = Ulv−Ugen

and x2 = x1. Integration of this output will give place to the firing anglevalue α being introduced in the soft-starter module. The control law ispresented in a simplified way in Fig. 7.10.

7.6 Simulation using the proposed controller

An overall scheme of the wind turbine connected to a weak grid is depictedin Fig. 7.11. A weak grid system is the best test bench to check the firingangle controller validity and to compare it to other kinds of controllers.

According to IEC 61400-21, switching operations have to be measuredduring the cut-in of a wind turbine and for switching operations betweengenerators, that are only relevant for wind turbines with more than onegenerator or a generator with two windings. However, simulations will onlybe plotted for the main generator since its connection gives places to a moreserious transient. There are several factors to consider:

7.6 Simulation using the proposed controller 115

Figure 7.11: Overall scheme of the wind turbine feeding a local load.

• From (4.1.33) it is clear that the inertia time constant H is lower for themain generator, even being faster, as the rated power is significantlyhigher

• Since the power flow is higher for the main winding, voltage dropoutis also more marked

• Rotor resistance is usually higher for the secondary winding.

Taking into account the values for the main winding of the inductionmachine and the values for the Thevenin impedance at the point of commoncoupling (at the consumer), the control law parameters have been calculatedin order to comply with the stability restraints and tuned to achieve to anoptimum performance.

The initial rotor speed at which the connection process should be initiatedhas been selected as 0.98 p.u. For the sliding-mode controller, as well as forthe rest of the controllers, the connection starts at a rotor speed that hasbeen chosen after a sweep within the range [0.96 - 0.99]. It has been checkedthat for low initial rotor speeds (high slips), the closed-loop controller muststop the generator voltage until the rotor speed approaches the synchronousone. The resulting performance is more unpredictable and generally worse.For open-loop controllers the result is definitely worse for initial rotor speedslower than 0.98.

It has also been checked that for low wind torque, a higher initial rotorspeed (0.99) gives place to a better performance of the system. However thisfeature has not been included because starting so close to the synchronous


speed will make the system behavior too sensitive to inaccurate rotor speedmeasurements and to changes in wind torque.

The result of the connection transient for Twind = −0.5 p.u. is depicted in7.12. It can be seen that:

Figure 7.12: Performance of the system connected through a soft-starter fired inaccordance with a sliding-mode controller action: voltage in p.u. seen by the con-sumer (upper left), induction generator slip in % (upper right), voltage generatorin p.u. (lower left) and σ (lower right).

• The load voltage seen by the consumer is well over 0.97 p.u. takinginto account that the initial and final values, which are independentof the connection transient, are 0.983 p.u. and 0.989 p.u. respectively.

• In a first stage, the rotor slip decrease is almost linear, due to thefact that the real power is low in relation to the wind torque. In a

7.7 Comparison to other control schemes 117

second stage, the generator voltage is high enough, which gives placesto a higher reactive power, but by contrast the real power turns out topresent such a value as to brake the turbine rotor and to counterbal-ance the reactive power effect over the voltage dropout. However, forlow inertia, low rotor resistance or high wind torque situations, the realpower will not be high enough until the last instants of the connectiontransient, and consequently it is expected that a speed overshot willoccur. The torque will also experience an overshot.

• The sliding-mode philosophy imposes that the system must be di-rected towards the sliding trajectory, and once the system has reachedit, it should follow this trajectory and be led to an equilibrium situ-ation. Since there are some delays and dead zones in the soft-starterelectronics, a chattering - small fluctuations around the sliding tra-jectory - is inevitable, as shown in the lower left hand plot. Finally,when the connection is accomplished, the real power largely surpassesthe reactive power and the dropout is rather negative in relation tothe initial voltage at the PCC. This is the equilibrium state, whenx1 = Ulv − Ugen = 0 and x2 = x1 = 0, and marks the end of theconnection process.

7.7 Comparison to other control schemes

In order to test the quality and robustness of the proposed sliding-modebased controller, an open-loop linear controller and a PI-controller2 havealso been simulated, and the results compared. Both of them have beentuned for the following case: H = 3.9 s, Rr = 0.015 p.u. and Tw = −0.5 p.u.

Fig. 7.13 shows the voltage at the PCC and slip results for the consideredwind turbine for the three time-firing angle strategies previously mentioned.

All of them show a good performance since the voltage dropout is wellbelow 1.5% referred to the voltage before the connection process. The speedovershot is not significant in either case.

As can be seen, the proposed sliding-mode controller is displayed to giveplace to a lower dropout than the PI controller which in turn is slightlybetter than the open-loop linear evolution scheme.

2Although there is no feedback from the voltage error, and hence it is not a PI controllerstrictly speaking, for sake of clarity this denomination will be kept


0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.97

0.975

0.98

0.985

0.99Linear evolution (·), PI controller (x), SLMC (o)

Vol

tage

at P

cc (

p.u.

)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−1

−0.5

0

0.5

1

1.5

2

Slip

(%

)

time (s)

Figure 7.13: Three firing angle control techniques: linear (blue and dot), PI (redand x-mark) and sliding-mode controller (black and circle).

Fig. 7.14 depicts the block diagram used for the latter controllers. Thelast component is an integrator which presents a lower limit for the firingangle in α = 0.2 p.u. and starts from α0 = 0.63 p.u. This initial value for αcorresponds to an angle equal to 113.4o, and in order to improve the per-formance of these controllers, it has been chosen instead of 150o

180o = 0.83 p.u.,that is the decreasing zero cross point for voltage Uab. A similar value canalso be found in [89] and in some manufacturers’ catalogues. For the sliding-mode controller, a initial value of α0 = 0.75 p.u. has been established fromsimulation results.

However, the robustness is the main feature of this controller, as havebeen fully tested in three broad scenarios:

Different conditions. The controller is adaptable to different conditionssuch as variable or different wind torques.


Figure 7.14: Firing angle controllers used as references.

Parameter sensitivity. The controller shows a good performance for awide range of variable parameters. For example, the rotor resistancevalue is one the parameters that more strongly determines the induc-tion machine response. The rotor resistance value (and other param-eters) cannot only vary from a wind turbine to other, but it is alwaysknown with a high degree of uncertainty related to:

• The standard tests to identify the induction machine parameters(no-load and locked-rotor) are performed with voltages, currentsor speed values far away from those related to full load

• Changes in rotor temperature related to variable load or ambienttemperature

• Changes in the load which are translated to changes in the slip,rotor frequency, currents or rotor current density

Wind turbine inertia. The value of the inertia time constant probably isthe parameter that more strongly influences the whole wind turbinedynamics, but this information is usually difficult to known (usually,manufactures do not provided this data), so an estimated value mustbe considered. If the actual value of the inertia time constant is dif-ferent from the considered value, the controller is able to adjust thevoltage dropout reference in order to avoid excessive speed overshot,or to keep the voltage dropout restraint, at the expense of a higherspeed overshot.


Fig. 7.15 depicts the voltage dropout at the consumer side over thirty sixsituations.

The voltage dropout is calculated as the maximum difference between thevoltage before the connection process and the voltage during the transient atthe consumer side. The thirty six situations have been obtained by varyingthe turbine inertia time constant H, the rotor resistance Rr and the windtorque within the following values:

H = 3.0 s, 3.5 s, 4.0 sRr = 0.007 p.u., 0.010 p.u., 0.015 p.u.

Twind = −0.25 p.u., −0.5 p.u., −0.75 p.u., −1 p.u.

It is worth noticing that, for PSCAD/EMTDC a torque in p.u. equal to−0.9 p.u. is approximately equivalent to the rated torque TN , as they arerelated through the expression

TPSCADp.u. =

cosϕN

ηmec (1− sN )T

TN' 0.9

T

TN(7.7.1)

where ηmec is the mechanical efficiency after extracting all mechanical losses(aerodynamical drag, ventilation, friction...), sN is the rated slip (sN < 0for a generator), and cosϕN is the rated power factor.

It can be seen how the linearly ascending firing angle scheme gives placeto a good performance for a reduced number of situations. They correspondto the values of the parameters similar to the used to tune the controller.That is Rr = 0.015 and Twind = −0.3 p.u.,−0.5 p.u.

Taking the open-loop linear scheme as a reference, a PI-controller improvesthe soft-starter performance, as the voltage dropout is lower.

The best performance however corresponds to the proposed sliding-modecontroller, which is shown controlling two different soft-starters. The first isa symmetrical soft-starter identical in hardware to that tested for the open-loop and PI controllers. In the second case, an asymmetrical soft-starterhas been used in order to decrease the rms value of the voltage generatedby means of the soft-starter. Its pulse train sequence and a representationof the phase current waveforms was previously presented in Chapter 5.

As to the voltage dropout refers, both sliding-mode based controllers aredefinitely better than the other controllers. And in turn, for the same fir-ing angle control an asymmetrical soft-starter is slightly better than the


10 20 300

0.5

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# Situation(Rr,H,Twind)

Vol

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(%

)Unsorted

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º PI

·SLMC sm

◊ SLMC as

10 20 300

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1

1.5

2

2.5

Vol

tage

dro

pout

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)

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∗ Linear

º PI

·SLMC sm

◊ SLMC as

Figure 7.15: Voltage dropout for different control schemes: linear (black and as-terisk), PI (magenta and circle), sliding-mode controller (red and dot) and sliding-mode controller with asymmetrical soft-starter (blue and diamond).

symmetrical one, although it presents a higher shaft torque due to a higherovershot in the slip. This is a repetitive issue in the performance of sev-eral firing angle controllers based in sliding-mode techniques. The morerestrained voltage dropout, the higher the overshot and the higher the shafttorque, mainly for low inertia, low rotor resistance or high wind torque sit-uations. The presented controllers are the product of a trade-off between alower dropout and an acceptable shaft torque.

The left hand graph of Fig. 7.16 shows a comparison of the voltage changethat different controllers produce, taken as a reference in this case to the finalvoltage at the consumer side. Once the connection process is accomplished,a negative (generated) real power will raise the voltage at the network con-nection point, and this is the voltage taken into account in the voltage


10 20 300

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·SLMC sm◊ SLMC as

10 20 30−150

−100

−50

0

Sha

ft T

orqu

e (%

)

Sorted

∗ Linear

º PI·SLMC sm◊ SLMC as

Figure 7.16: Voltage change and shaft torque for different control schemes: linear(black and asterisk), PI (magenta and circle), sliding-mode controller (red and dot)and sliding-mode controller with asymmetrical soft-starter (blue and diamond).

dropout calculation3. The graph at the right side shows the maximum shafttorque during the start-up process. A difference with respect to PI andlinear controllers can be observed for both sliding-mode based controllers.However, for higher wind torques giving place to higher final shaft torques,the behavior of the symmetrical sliding-mode controller agrees closely withthe linear and PI-controller. The torque with the asymmetrical controller is7% higher. For lower wind torques, a torque lower than the rated value isexerted on the shaft, and hence a slight torque overshot is not a concern.

Fig. 7.17 shows a comparison of the performance of the same controllersfor a generator having different electrical parameters (Rs = 0.01p.u. Xs =0.1p.u. Rr = 0.01p.u. Xs = 0.1p.u. Xm = 3.7p.u.). As can be seen, bothsliding-mode based controllers give place to lower voltage dropouts.

7.8 Sensitivity to speed and voltage measurements 123

0.4 0.6 0.80.8

1

1.2

1.4

1.6

1.8

Torque (p.u)

Vol

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0.4 0.6 0.8−120

−100

−80

−60

−40

−20

Torque (p.u.)

Sha

ft T

orqu

e (%

)

Figure 7.17: Performance of tested control schemes for another generator: linear(black and asterisk), PI (magenta and circle), sliding-mode controller (red and dot)and sliding-mode controller with asymmetrical soft-starter (blue and diamond).

7.8 Sensitivity to speed and voltage measurements

The input values for the sliding-mode based controller are the inductiongenerator voltage and the slip. The derivatives of these magnitudes are alsoneeded in the σ calculation and in the control law.

For a real system acquiring the generator voltage and the induction ma-chine slip, it is expected that a noise in the measurements and a discretiza-tion in the analog to digital conversion will be introduced in the input val-ues. The discretization can also be understood as a non-zero resolution ofthe measuring device. In order to take into account these practical effects,a new PSCAD component has been designed (Fig. 7.18) that adds a zero-mean random noise to the voltage or the speed and simulates a discretizationprocess in the distorted signal.

For the induction machine speed, random values in the range of±0.005 p.u.are added to the pure value, which means ±7.5 rpm for a four pole inductionmachine (50 Hz). A small variation in the speed will give place to a highvariation in the slip within the connection/operation range as can be seenin Fig. 7.19. After noise addition, a resolution of 1 rpm is supposed for thespeed measuring device.

3Final voltage is even higher after the capacitor bank connection


Figure 7.18: New PSCAD component designed to simulate the presence of noise inthe speed and voltage measurements and the discretization process.

With regard to the generator voltage, a random noise of the same±0.005 p.u.value is considered, which yields ±3.5V for a 690 V induction generatorrated voltage. Regarding to the discretization process, the voltmeter reso-lution has been fixed to 0.69 V.

The same simulations as in the non-distorted situations have been per-formed considering noise in the generator voltage and speed signals. In thecase of the open-loop linear controller it makes no sense performing newsimulations as there are no inputs for the controller. In the case of the PIcontroller, noise in the generator voltage signal has been considered. In thecase of the proposed sliding mode controller, noisy voltage signal as well asspeed noisy signal situations have been tested.

Fig. 7.20 shows the voltage dropout and shaft torque for the tested con-trollers.

The original PI controller performance is represented by the black dottedline. The black dots correspond to the same controller where the voltageis affected by a random noise. As can be seen, for the PI controller, in thetested range there is no performance degradation when noise and discretiza-tion are considered in voltage signals.

The SLMC performance is depicted with a solid red line. Plus (+) markscorrespond to simulations where the noise and discretization in the genera-tor voltage signal are considered. It can be seen how the proposed controller

7.8 Sensitivity to speed and voltage measurements 125

Figure 7.19: Performance of the sliding-mode controller when noise and discretiza-tion are added to the speed signal.

is more sensitive to voltage noise. However, the performance of the slidingmode based controller is better than the performance of the linear and PIcontrollers in any situation. Different simulations have shown that the con-trollers are hardly sensitive to the tested discretization when it is appliedwithout noise. With regard to simulations considering noise in the speedsignals, diamond (♦) marks represent these situations showing a satisfac-tory insensitivity to random variations around the actual value in the orderof ±7.5 rpm.

To sum up, a closed-loop in the firing angle control of the trains of pulsesexciting the thyristors gates will reduce the impact of the electrical connec-tion of the wind turbine to the network since the voltage dropout decreases.This can be achieved with a PI-controller, integrating a control law outputthat involves the generator voltage and its derivative. The improvementachieved is higher for the more problematic conditions (high wind torque,low rotor inertia and low rotor resistance), when the voltage dropout can


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−SLMC

+SLMC U noise◊ SLMC s noise

10 20 30−150

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orqu

e (%

)

Sorted

−−PI

·PI U noise

−SLMC

+SLMC U noise◊ SLMC s noise

Figure 7.20: Controllers’ performance when a random noise in voltage and speedsignals are considered.

be expected to be higher. If the slip measurement is included in the con-trol unit, a sliding-mode based controller can replace the PI controller tocalculate the firing angle at each moment. This gives places to the best per-formance since an eventual consumer in the network connection point willsuffer lower voltage dropouts at its terminals. Voltage change, as defined insection 3.4.3 is improved in a parallel way.

7.9 Influence of the line impedance

Fig. 7.21 shows a comparison among the three tested structures for differ-ent line impedance ratios and different short-circuit ratios, defined as the

7.9 Influence of the line impedance 127

quotient between the short-circuit power and the wind turbine capacity. Ascan be seen the sliding-mode based controller shows the best result4.

Figure 7.21: Comparison of tested controllers for different line impedances.

Fig. 7.22 is similar, but only the results of the sliding-based controllerwith the line resistance and reactance characteristic of the weak grid areconsidered. This figure plots the voltage dropout and the [maximum] voltagechange, such as defined in section 7.1, against the line impedance. The lineresistance does not influence the voltage dropout too much, and thus, as longas the line reactance remains constant, a higher capacity of the evacuationline will not decrease this value. However, if the start-up impact is referredto the maximum voltage change, the right hand plot indicates that lowerline resistances, corresponding to higher capacity lines, give place to lowervoltage changes. This is due to the fact that a higher resistance will increasethe voltage at the end of the connection transient, since it is mainly relatedto the real power delivered by the induction generator of the wind turbineaccording to

4UPCC = Pgen Rlin + Qgen Xlin (7.9.1)

4The component that calculates the permitted voltage dropout (Fig. 7.9) has beenadded the line resistance and reactance as new inputs


5 10 15 20 250

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Rlin (Ohm)

Xlin = 5

Xlin = 10

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Xlin = 20

Xlin = 25

5 10 15 20 250

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10

Vol

tage

cha

nge

(%)

Rlin (Ohm)

Xlin = 5

Xlin = 10

Xlin = 15

Xlin = 20

Xlin = 25

Figure 7.22: Voltage dropout and voltage change vs. line impedance.

where4UPCC is the difference between the voltage before and after the soft-starter operation and Pgen and Qgen are the real and reactive power deliveredby the wind turbine induction generator once the electrical connection isaccomplished (Pgen is negative and Qgen is positive).

Chapter 8

Conclusions

This final chapter is integrated by to sections: Conclusions and Future work.The first section compiles the more relevant features of the proposed con-troller and some ideas derived from the analysis of the mechanical and elec-trical components of a wind turbine. The main contributions of this workand the conclusions derived from the theoretical analysis and the simula-tion results are also listed in this section. The second section offers someguides and suggestions for future research work that may continue the issuestackled in this thesis.

8.1 Conclusions

The concern about the negative impact of wind turbines on the power qualitythat utilities are responsible to supply is one of the limiting factors takeninto account when selecting a wind turbine model to be placed at a specificsite. The impact can be quantified and measured by means of the voltagechange at the point of common coupling. Wind turbine switching operations,mainly the start-up, is one of the causes of this power quality decline.

Voltage changes due to the starting transient are higher for stall-controlledwind turbines, since the accelerating wind torque is not controlled and the

130 Chap. 8: Conclusions

connection transients give place to higher reactive power demand and hencehigher voltage dropouts. The voltage change generated by switching opera-tions is even higher for isolated wind turbines or small wind farms placed faraway from the electrical distribution network. This electrical configuration,where a local load or a small power station is connected to the distributionnetwork through a rather long line or a high short-circuit impedance valueis usually referred to as a weak grid. This is a very demanding situationsince real power fluctuations or reactive power demand is translated intoamplified voltage fluctuations at the interconnection node.

The main components of a weak grid have been analyzed and parameter-ized in order to design a scenario where a wind turbine start-up transientcould be analyzed in a realistic way.

The impact of stall-controlled wind turbines starting transient on thepower quality at the point of common coupling has been analyzed, simu-lating the designed weak grid in different conditions.

A simplified structural analysis of a wind turbine blade has beenperformed. The analysis was mainly focused on the relationship betweenthe inertia time constant of a wind turbine rotor and the blade length andweight. As a result, an approximate expression relating the inertia timeconstant and the wind turbine rated capacity has been derived. A similartrend expression for the self damping has also been presented. In orderto estimate this statistical expressions, different MS Excel sheets with awide number of wind turbine records have been developed, which are freelyavailable at the author´s research page.

Dispersed information about soft-starters has been gathered and clas-sified, putting special emphasis on the triggering of the thyristors. Mostof the technical literature about soft-starters deals with induction motorperformance, where the main objective is to reduce the inrush current fol-lowing the motor start-up process in order to fulfil technical and normativeregulations. However, conditions and regulations regarding to induction gen-erators are quite different. While induction motors starts from standstill,induction generators are connected to distribution network when the rotorspeed is close to the synchronous value. While induction motor regulationslimit the inrush current during the start-up process, induction generatorregulations limit the voltage variations at the point of common coupling tothe distribution network1.

1The inrush current must also be limited but this is a less restricted condition

8.1 Conclusions 131

In this thesis, the performance of soft-starting devices with wind turbineinduction generators has been addressed in order to cover the lack of work inthis area. Differences between the regulations and the performance of soft-starters working with motors and generators have been thoroughly analyzed.As a result, a new approach to the design of the soft-starter controller hasbeen proposed, focused on the voltage at the point of common couplingrather than in the inrush current. To reach this goal the controller limitsthe reactive power flow and compensates, as far as possible, the associatedvoltage dropout with the real power injection.

Apart from the design of a new control strategy to regulate the firingangles in order to maintain the voltage dropout, modifications to the logiccontrol of the triggering of the thyristor gates have also been presented. Oneof the modifications means an asymmetry in the currents flowing through thesoft-starter that provides an improved control of the rms voltage suppliedto the induction generator of the wind turbine.

The main goal of the present work has been to proof that the third ordermodel of the induction machine is the most suitable model to understandthe start-up transients. A small signal linear model of the induction gen-erator and a comparison based on the root loci techniques have been usedto test and proof the feasibility of this reduced induction generator model.Simplified, but accurate enough, analytical expressions for real and reactivepower components during the connection transients have been derived fromthe third order model, showing the influence of the derivative of the voltageon these magnitudes.

A soft-starter connected to a specific generator has been simulated bymeans of the Electromagnetic Transient Simulator (EMTDC), whose graph-ical user interface is called PSCAD. Same simulations have also been per-formed with the MATLAB power system toolbox, but it has been rejecteddue to the fact that simulations are carried out in a significant higher time.

Thus, PSCAD/EMTDC package has been chosen to simulate a weakgrid whose component has been parameterized. In order to include thepower electronic circuit, the logic control circuit for the thyristor triggeringand the tested controllers, some PSCAD/EMTDC simulation componentshave been customized and more than fifty new specific modules have beendesigned, tested, tuned and, finally, integrated into the simulation cases.

Starting from the performance of the soft-starter derived from these sim-ulations, a firing angle controller has been designed based on sliding-mode


techniques. The gains involved in the variable structure of the controllershave been chosen in order to assure the stability of the system, referred toas the ability to maintain the voltage dropout within a certain value.

The performance of the new closed-loop control strategy has been thor-oughly tested in a broad variety of simulation scenarios. As a result, theimprovement of the induction generator soft starting has been fully demon-strated. The new soft-starter controller performance has been superior andfavorable compared with the classical open-loop controller.

For a comparison purpose, a PI-controller based on the integration of asignal function of the generator voltage and its derivative has also beendesigned, tuned and simulated, resulting in an intermediate performancebetween the open-loop controller and the proposed sliding-mode based con-troller.

Real practical effects distorting the signals, such as the presence of noisein the speed and voltage signals or errors associated to the discretizationprocess performed by analog-to-digital converters have also been taken intoaccount. The performance of both closed-loop controllers, PI and sliding-mode based controllers, has no significant variation when introducing thesesimulated distortions in the measurements.

Robustness is the main feature of the new proposed sliding-mode con-troller, as have been fully tested, especially in three main areas: adaptabilityto different conditions (such as variable or different wind torques), param-eter sensitivity (as in the case of the rotor resistance), and capability tomanage estimated values of wind turbine inertia time constant (a piece ofinformation that is not usually provided by manufactures).

The proposed soft-starting controller needs no more hardware, since volt-age, current or speed transducers already installed in wind turbines couldbe used. Therefore the changes to implement the new approach are limitedto the software control (fast and cheap), even for previously installed windturbines.

8.2 Future research

A sliding-mode based controller has been designed and tested for a singlewind turbine in a weak grid. This configuration is a good test bench to

8.2 Future research 133

check the validity of the controller. However this is not an usual situation incountries like Spain. One aspect of this work to be given further considera-tion is the simulation of a wind turbine start-up being part of a wind farmwhere the higher-capacity overhead line will make the grid stronger and theinterconnection stiffer.

The inputs of the sliding-mode based controller are the voltage and itsderivative. Gains for the control law have been derived starting from thesimulation of the performance of the soft-starter under different conditions.The resulting gains are quite high, which makes it necessary to saturatethe output to be integrated. Including a suitable third input (αP + βP in(7.2.7)) might provide lower gains thus smoothing the performance of thesoft-starter.

Another issue that could be furthered is how to derive more genericallythe voltage dropout that the controller should try to maintain as a functionof the rotor acceleration, the rotor resistance and the line impedance. Fuzzylogic seems a good choice, although four inputs are too many for a fuzzy-logic controller, and thus one or two heuristic combinations of them shouldbe attempted in order to reduce this number.

A very simplified structural analysis has been made with the aim of en-couraging deeper studies by mechanical experts that could provide morerealistic estimations of the inertia time constants as a function of the bladecharacteristics.

Simulations performed for different values of the electrical parameters ofthe induction generator have shown that a better performance is obtainedby reducing the rotor reactance to a 60% of its actual value. It is worthinvestigating if this improvement is generalized for all squirrel cage inductiongenerators and if so, study its cause.

Exploitation of the soft-starter in continuous operation at low load hasbeen studied for typical Weibull distribution and power-wind speed charac-teristics. An increase in the efficiency up to 4% can be achieved by control-ling the voltage at the induction generator terminals, not only during thestart-up, but also in continuous operation at low wind speeds. Capacitorsbanks should then be provided with resonant filters to draw the harmonicscurrent, mainly for the fifth, seventh, eleventh and thirteenth harmonics.

And finally, although simulations have been done pursuing the closestagreement with real conditions, the controllers should be tested in a real


wind turbine or, if not available, connected to a large induction machinedriven by a dc machine with the possibility of controlling its armature cur-rent.

Appendix A

Weight and size for differentblades

Table A.1: Weight (kg), size (m) and corresponding power (kW) for several bladesI.

Blade type Length Weight Diameter Power

NOI 16.2 16,2 750 300NOI 16.5 16,5 800LM 17.2 17,15 1620 37.3Bazan Bonus 600 kW Mk IV 19 1800 44 600LM 19.1 19,04 1960 44Ecotecnia 600 19,1 2900 44 600NOI 19.3 19,3 1650 500

136 Chap. A: Weight and size for different blades

Table A.2: Weight (kg), size (m) and corresponding power (kW) for several bladesII.


NOI 20.0 20,8 1800LM 21.0 21 2200 47LM 21.5 21,5 2700 48NOI 21.8 21,9 1670 600NOI 22.1 22,15 1720Gamesa V47-660kW 23 1500 47 660Gamesa G47-660 Ingecon-W 23 1600 47 660LM 23.0 P 23 3000 48Dewind Iberica D48-600 kW 23,1 1800 48 600LM 23.2 23,2 2990 48,4LM 23.3 23,3 2990 50NOI 23.3 23,36 1970NOI 24.0 24,2 2200 750EU50.1250-3 24,3 1900 50 750EU50.1250-2 24,3 2100 50 750NOI 25.0 25 2400LM 25.1 P 25,1 3100 52EU53.1400-1 25,65 2800 53 850NOI 26.0 26 2600LM 26.1 P 26,04 4250 54LM 26.1 26,04 4350 54NOI 26.9 26,9 3050 1000NOI 27.1 27,1 3150EU56.1400-2 27,5 2850 56,8 850NOI 28.5 28,5 3250Nordex N62/1.3 MW 29 4300 62 1300LM 29.0 P 29 4550 62LM 29.0 29 4850 62EU60.1400-3 29,05 3200 60 1000NOI 29.1 29,1 3500

137

Table A.3: Weight (kg), size (m) and corresponding power (kW) for several bladesIII.


Dewind Iberica D62-1000 kW 29,1 4300 62 1000LM 29.1 P 29,15 4175 62,3LM 29.1 29,15 4900 62,3Dewind Iberica D64-1250 kW 31,1 4800 64 1250Neg Micon NM1500/64 31,2 6900 64 1500EU65.1600-3 31,7 3550 63 1200Vestas V66-1.65 32,15 3800 66 1650UM70 34 4550 70 1500SSP 34 34 4600 70 1500UM70-2 34 4650 70 2000Sudwind s70/1500 34 5200 70 1500NOI 34.0 34 5450 1500LM 34.0 P 34 5600 70,5EU70.1800-2 34,5 5100 70 1500LM 36.8 P 36,8 9125 76LM 37.3 P 37,25 6035 77EU77.1800-3 37,5 5500 77 1500NOI 37.5 37,5 5800UM77 37,5 6100 77 1500NOI 38,0 38 5400LM 38.8 P 38,8 8650 80EU80.1800-3 39 6000 80 1500EU80.2000-1 39 6600 80 2000NOI 39.0 39 7400 2500LM 43.8 P 43,8 10100 90EU90.2300-1 44 8900 90 3000NOI 44.0 44 9900 3000EU90.2300-2 44 10500 90 3000LM 44.8 P 44,8 9980 92NOI 46.0 46 11500NOI 48.0 48 12700EU100.2300-3 48,8 11500 100 3000EU100.2300-2 48,8 11900 100 3000LM 54.0 P 54 13500 110.8LM 61.5 P 61,5 17740 126.3

138 Chap. A: Weight and size for different blades

Appendix B

Extended power-diametertable

Table B.1: Diameter and power for several wind turbines I.

Blade type Diameter (m) Power (kW)

Enercon E33 33,4 330Suzlon 350 33,4 350WindWorld W37/550 37 550Gamesa G39 39 500Vestas V39 39 500Ecotecnia 40/500 40 500Enercon EN-40 40,3 500Gamesa G42 42 600

140 Chap. B: Extended power-diameter table

Table B.2: Diameter and power for several wind turbines II.


WindWorld W42/600 42 600Neg Micon 600/43 43 600Nordex N43/600 43 600Nordtank 43 600Bazan Bonus Mk IV 44 600Ecotecnia 600 44 600Gamesa G44 44 600Neg Micon 750/44 44 750DESA 45 650Genesis 600 45,9 600Dewind Iberica D46 46 600MADE AE 46/I 46 660Gamesa G47-660 47 660Gamesa V47-660kW 47 660Dewind Iberica D48 48 600Neg Micon 600 48 600Ecotecnia 750 48 750Jeumont 750 48 750Neg Micon 750/48 48 750WindWorld W48/750 48 750Enercon E48 48 800FuhrLander 48 800FuhrLander 50 600Nordex N 50 50 800WindWorld W52/750 52 750MADE AE 52 52 800Gamesa G52 850 52 850Vestas V52 850 52 850NEG Micon NM 900 52,2 900Fuhrlander FL 800 52,7 800FuhrLander FL 1000 54 1000Nordex N54 54 1000

141

Table B.3: Diameter and power for several wind turbines III.


Nordic 1000 54 1000Bonus 1MW 54,2 1000Enron Wind 900s 55 900MADE AE 56 56 800MWT 1000 56 1000Wind Wind 56 56 1000Frisia F 56/850 kW 56,3 850Gamesa G58 850 58 850Enercon E-58 58 1000FuhrLander 58 1000MADE AE 59 59 800Neg Micon 1000/60 60 1000Suzlon S60 1MW 60 1000Wind Wind 60 60 1000DeWind D60 60 1250Suzlon S60 1.25MW 60 1250Nordex N60 60 1300MADE AE 61 61 1320DeWind D62 62 1000Suzlon S62 1MW 62 1000DeWind D62 62 1250Bonus 1,3MW 62 1300Ecotecnia 62 1300 62 1300Nordex N62 62 1300Suzlon 950 64 950Suzlon S64 1MW 64 1000Dewind Iberica D64 64 1250Suzlon S64 1.25MW 64 1250Neg Micon NM1500 64 1500Suzlon S66 1.25MW 66 1250

142 Chap. B: Extended power-diameter table

Table B.4: Diameter and power for several wind turbines IV.


Enercon E-66/15,66 66 1500PWE 1566 66 1500Vestas V66-1.65 66 1650BWU/Jacobs MD 70 70 1500FuhrLander MD 70 70 1500Sudwind s70/1500 70 1500Nordex S70 70 1615Enercon E-66/18,70 70 1800Enron EW 1,5s 70,5 1500GE Wind Energy 1.5sl 70,5 1500Jacobs MD 70 70,5 1500Enercon E70 71 2000Mtorres 72 72 1500TWT 1750 72 1750NEG Micon NM 2000 72 2000Ecotecnia 74 1670 74 1670AN Bonus 2 MW/76 76 2000Bonus 2MW 76 2000BWU/Jacobs MD 77 77 1500Fuhrlander MD 77 77 1500Sudwind S-77 77 1500Nordex S77 77 1615Vestas V80/2,0 MW 80 2000Nordex N-80 80 2500

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