Aero Gener Adores

Technical Documentat ion

Dynamic Modelling of Doubly-Fed

Induction Machine Wind-Generators

G m b H

D y n a m i c M o d e l l i n g o f D o u b l y - F e d I n d u c t i o n M a c h i n e W i n d - G e n e r a t o r s 1

DIgSILENT GmbHHeinrich-Hertz-Strasse 9D-72810 GomaringenTel.: +49 7072 9168 – 0Fax: +49 7072 9168- 88http://www.digsilent.de-mail: [email protected]

Dynamic Modelling ofDoubly-Fed InductionMachine Wind-Generators

Published byDIgSILENT GmbH, Germany

Copyright 2003. All rightsreserved. Unauthorised copyingor publishing of this or any partof this document is prohibited.

doc.TechRef, 14 August 2003

1 I n t r o d u c t i o n


1 Introduction

The electrical systems of several European countries contain large amounts of embedded wind generation and similar scenariosare foreseen in other parts of the world. This aspect, together with the significant size of new wind farm projects, requiresrealistic modelling capabilities of wind generators for proper assessment of power system planning and impact analysis of futurewind generation.

As a result of research and consulting activities of DIgSILENT, generic dynamic models of different types of wind powergeneration were developed. These models are now available in the standard Wind-Power library of PowerFactory.

This document describes a doubly-fed induction generator wind turbine model including all relevant components. At the sametime, this document is a reference to all DFIG-related models of the Wind-Power library.

The presented models are mainly intended for stability analysis of large power systems. The proper response of the models tonetwork faults was in the centre of interest, but the models can also be used for simulating the impact of wind fluctuations topower systems.

There is no wind model included in this description. However, any type of stochastic or deterministic wind model, or measuredwind speeds can be connected to the wind speed input of the presented model.

The models are intended for balanced and unbalanced RMS calculations typically applied in stability studies. However, it is alsopossible to perform electromagnetic transient simulations with these models.

The basic structure of the model is briefly described in this section and more thoroughly analyzed in the following sections.

2 T h e D o u b l y - F e d I n d u c t i o n M a c h i n e C o n c e p t


2 The Doub ly-Fed Induction Machine Concept

DFIG

External Grid

PrimeMover

Grid SideConverter

Rotor SideConverter

Protection

Control Control

Figure 1: Doubly-Fed Induction Generator Concept

The general concept of a Doubly-Fed Induction Generator (DFIG) is shown in Figure 1.

The prime mover, consisting of a pitch-angle controlled wind turbine, the shaft and the gear-box drives a slip-ring inductiongenerator. The stator of the DFIG is directly connected to the grid, the slip-rings of the rotor are fed by self-commutatedconverters. These converters allow controlling the rotor voltage in magnitude and phase angle and can therefore be used foractive- and reactive power control.

In the presented model, the converters and controllers are represented to the necessary extent. Both the rotor- and the grid-side controllers are modelled in full detail, including fast current control loops. However, for many applications the fast controlloops of the grid side converter can be approximated by steady state models.

With the rotor side converter, the situation is different due to protective practices in DFIG. For protecting the rotor-sideconverter against over-currents, it is usual practice to bypass the rotor-side converter during system faults. Whether the DFIG istotally disconnected from the system or not, depends on the actual deepness of the voltage sag and on the applied protectionphilosophy. The correct modelling of the rotor bypass, usually called “crow bar protection”, is essential to assess voltagestability of large farms during faults in the transmission- or distribution network. For this reason, it is necessary to model eventhe fast current controls of the rotor side converter to effectively determine the operation of the crow bar. Other protectionfunctions also found in DFIG such as over/under-speed and over/under-voltage are considered in the proposed model as wel

3 T h e D F I G W i n d - G e n e r a t o r M o d e l


3 The DFIG Wind-Generator Model

3.1 Overview

Prime Mover

(To Protection System)

(From Protection System)

omega..

pt

Pwindbeta

u

bypass

P;Q

cosp

h..

Ifq_ref;Ifd_refPref

iq;id

Pfq;Pfd

psis_..

speed

Pmq ; Pmd

Irot

Ifq;I.

.

Shaft*

Pitch Control*

Transformatio..*

Current Measurement*

V meas.StaVmea*

ProtectionElmPro*

Turbine*

vw

MPTElmMpt*

PQ ControlElmGen*

Qref

Current Control*

DFIGElmAsm*

Power MeasurementStaPqmea

DFIG:

DIg

SILE

NT

Figure 2: Complete Scheme of the Doubly-Fed Induction Machine Wind Generator

The complete scheme of a doubly-fed induction machine wind generator is shown in Figure 2. The main components are:

• The prime mover consisting of the pitch angle controller, the wind turbine and the shaft (Pitch-Control, Turbine,Shaft)

• Doubly-Fed induction generator (DFIG)

• The control-system regulating active and reactive power of the DFIG through the rotor-side converter applying amaximum power tracking strategy (MPT, Power Measurement, PQ Control, Current Control, Current Measurement)

• Protection-system (V meas., Protection)



The models of all major components are described in the following sections. It is important to point out that these models canbe used in combinations that differ from Figure 2, e.g. realizing power-dependent speed control instead of the speed-dependentpower control.

Additionally, the model can be extended by stochastic or deterministic wind-speed models, more sophisticated voltage andfrequency control.

3.2 Prime Mover and Controller

The prime mover of a wind generator model represents the conversion of kinetic energy stored in the air flowing through theblades into rotational energy at the generator shaft.

The prime-mover model is subdivided into three sub-models, which are

• The turbine that transforms the wind energy into rotational energy at the turbine shaft.

• Blade angle controller.

• Shaft coupling turbine and generator including the gear-box.

3.2.1 Wind Turbine

In this section all aspects related to the power conversion from kinetic wind energy to rotational energy that are of relevancefor the stability model are explained.

The kinetic energy of a mass of air m having the speed vw is given by:

2

2 wk vmE ⋅= (1)

The power associated to this moving air mass is the derivative of the kinetic energy with respect to time.

220 2

121

wwk vqv

tm

tE

P ⋅⋅=⋅∂∂⋅=

∂∂

= (2)

where q represents the mass flow given by the expression:

Avq w ⋅⋅= ρ (3)

ρ is the air density and A the cross section of the air mass flow.

Only a fraction of the total kinetic power can be extracted by a wind turbine and converted into rotational power at the shaft.This fraction of power (PWIND) depends on the wind speed, rotor speed and blade position (for pitch and active stall controlturbines) and on the turbine design. It is usually denominated aerodynamic efficiency Cp:



Figure 3: Typical Cp(β, λ) Characteristic

0P

PCp Wind= (4)

For a specific turbine design, the values of Cp are usually presented as a function of the pitch angle (β) and the tip speed ratio(λ). The tip speed ratio is given by:

w

TUR

vR⋅

=ω

λ (5)

R is the radius of the turbine blades and ωTUR is the turbine speed.

PowerFactory allows the input of a two-dimensional lookup characteristic (for different values of β and λ) to define Cp. A two-dimensional, cubic spline-interpolation method is used for calculating points between actually entered values. The high accuracyof the interpolation method avoids the need of entering a large number of points (see also Figure 3).

Alternatively, analytical approaches for approximating the Cp-characteristic could be used but since these data are usuallyavailable in tabular formats, no such model was included into the PowerFactory standard Wind-Power-Library.

Finally, the mechanical power extracted from the wind is calculated using:

( ) 32 ,2 wmech vCpRP ⋅⋅⋅⋅= βλπρ

(6)



The Cp-characteristic can be calculated using special software for aerodynamic designs that is usually based on blade-iterationtechniques or it can be obtained from actual measurements.

It has to be pointed out that the presented turbine model is based on a steady state approach and is not able to represent stalldynamics.

The input/output diagram of the turbine model is depicted in Figure 4 and the input-, output- and parameter definitions arepresented in Table 1 toTable 3.

Figure 4: Input/Output Definition of Wind-Turbine

Table 1:Input Definition of Wind-Turbine

Input Symbol Description Unit

beta β (6) Blade pitch angle degrees

vw vw (5,6) Wind Speed m/sec

omega_tur ωTUR (5) Turbine Angular Velocity rad/sec

Table 2: Output Definition of Wind-Turbine

Output Symbol Description Unit

Pwind Pmech (6) Generated, Mechanical Power MW

Table 3: Parameter-Definition of Wind-Turbine

Output Symbol Description Unit

R R (5,6) Rotor Blade Radius m

rho ρ (6) Air Densitiy kg/m3

Cp Cp(β,λ) (6) Cp-Characteristic (2-dim. Lookup-table)

beta

Wind-Turbinevw

omega_tur

Pwind



3.2.2 Blade Angle Control

SERVOBLADE ANGLE CONTROLLER

speedbeta_ref beta

ref

Time ConstT-

-PI controller

Ka,Tr,Ta

Vrmin

Vrmax

{1/s}

Ymin

Ymax

Limiter

rate_cl

rate_op

Blade Angle Control:

DIg

SILE

NT

Figure 5: Block Diagram of Blade Angle Controller

Adjusting the blade angle allows varying the power coefficient Cp, and hence controlling the power generated by a wind turbine(see also Figure 3).

The two common concepts are pitch-control and active-stall control. In a pitch-controlled wind turbine, the blades are turnedinto the wind for reducing the lift forces at the blades which lowers the power coefficient.

Active-stall controlled wind turbines turn the blades out of the wind flow for disturbing the laminar air flow at the blades andhence reducing the generated power.

The model presented here is generic and captures the main characteristics of pitch angle controls of existing wind generationtechnologies. Controller and servomechanism are depicted in Figure 5. The controller has a feedback of the generator speed.Its speed-reference is set to the maximum speed (usually above 20% nominal). The blade angle is at the minimum limit of thecontroller for all operating conditions below rated rotor speed. This minimum limit corresponds to the optimum blade angle1.The servomechanism model accounts for the associated time constant, rate-of-change limits and blade angle limitations.

1 Blade-Angle optimization can be realized using a variable minimum blade angle limit



Figure 6: Input/Output Definition of Blade Angle Controller

Table 4: Input Definition of Blade Angle Controller

Input Description Unit

speed Speed Input (from Generator) p.u.

Table 5: Output Definition of Blade Angle Controller

Output Description Unit

beta Blade Angle (Pitch-Angle) deg

Table 6: Parameter Definition of Blade Angle Controller

Parameter Description Unit

Ka Blade Angle Controller Gain deg/p.u.

Ta Blade Angle Controller Time Constant s

Tr Lead Time Constant s

T Servo Time Constant s

rate_op Opening Rate of Change Limit deg/s

rate_cl Closing Rate of Change Limit deg/s

beta_max Max. Blade Angle deg

beta_min Min. Blade Angle deg

ref_speed Speed Reference p.u.

Blade Angle Controllerspeed beta


D y n a m i c M o d e l l i n g o f D o u b l y - F e d I n d u c t i o n M a c h i n e W i n d - G e n e r a t o r s 1 0

3.2.3 Shaft

Figure 7: Spring-Mass Model of Second Order

pt

Pwind

speed_gen omega_gen

TmecTwindtdif

omega_tur-

Gear BoxRPMnom

RatePtPbase

0

1

SpringK,D_shaft

0

1

Mass_1TorqueD_turb,J

Torque0

1

Shaft Model:

0

1

0

1

DIgS

ILEN

T

Figure 8: Block Diagram of Shaft

DgDt

ωgJg

Jtωt

Ktg

Dtg

ω’g



Under normal operating conditions, variable speed generators are “decoupled” from the grid; that is, with appropriate controls,torsional shaft oscillations are filtered by the converters and almost not noticeable as harmonics of the generated power.

However, during heavy faults, e.g. short circuits in the network, generator and turbine acceleration can only be simulated withsufficient accuracy if shaft oscillations are included in the model.

Shaft characteristics of wind generators are quite different from other types of generation due to the relatively low stiffness ofthe turbine shaft. This results in torsional resonance frequencies in a range of about 0.5 to 2 Hz.

The proposed model approximates the shaft by a two-mass model, represented by turbine- and generator inertia (see Figure7). The model according to Figure 7 and Figure 8 represents the turbine inertia and the coupling between turbine- andgenerator. The generator inertia however, is modelled inside the built-in induction machine model. The generator inertia isspecified in the form of an acceleration time constant in the induction generator type. The inertia of the gear-box is notmodelled separately but shall be included in the generator inertia.

The spring-constant K and the corresponding damping coefficient D are related to the turbine-side.

Shaft-models of higher order can easily be implemented by expanding the second order model. For stability analysis however, asecond order model provides sufficient accuracy.

Figure 9: Input/Output Definition of Shaft

Table 7: Input Definition of Shaft


Pwind Turbine Power MW

speed_gen Generator Speed p.u.

Table 8: Output Definition of Shaft


omega_tur Turbine Speed (Angular Velocity) rad/s

pt Mechanical Power at Generator Inertia p.u.

Shaft

Pwind

speed_gen

omega_tur

pt



Table 9: Parameter Definition of Shaft


Pbase Rated Power of Generator MW.

D_turb Turbine Damping Nms/rad

J_shaft Turbine Inertia kgm2

K_shaft Shaft-Stiffness Nm/rad

D_shaft Torsional Damping Nms/rad

RPMnom Nominal Rotor Speed rpm

3.3 Generator, Rotor-Side Converter and Controls

The electrical characteristics and hence the modelling requirements vary considerably with the different types of generators. Inthis section the available models for doubly-fed induction machines are presented.

Obviously, the equipment characteristics depend on the manufacturer. The models presented here reflect typical equipment andcontrol structures.

This section starts with a description of the DFIG including the rotor-side converter. The grid-side converter with controls isdescribed in section 0, followed by a presentation of DFIG protections.

3.3.1 Asynchronous machine and Rotor Side Converter

The doubly-fed induction machine model extends the usual induction machine by a PWM converter in series to the rotorimpedance as shown in Figure 10. In this figure, Rs and Xs are the resistance and leakage reactance of the stator winding; Xmis the magnetizing reactance and Zrot is the rotor impedance.

Rs Xs

Xm

Zrot

U Ur tj re ω− UrUr'= UDCUAC

Figure 10: Equivalent Circuit of the Doubly-Fed Induction Machine with Rotor-Side Converter

The PWM converter inserted in the rotor circuit allows for a flexible and fast control of the machine by modifying magnitude andphase angle of the rotor voltage.

It is assumed that a standard bridge consisting of six transistors builds the converter and that sinusoidal pulse width modulationis applied.

In contrast to the normal induction machine model, in which the rotor is short-circuited, the winding ratio between rotor andstator is important for calculating actual DC voltages. The nominal rotor voltage that can be measured at the slip rings underopen rotor conditions defines this winding ratio.



For load flow calculations and transients initialization, only active power (AC-side), reactive power and the slip have to bespecified. Internally, the corresponding modulation factors of the converter (Pmd, Pmq) are calculated and together with thepower balance between the AC and DC side of the converter, DC voltage and DC current are obtained.

During time domain simulations the converter is controlled through the pulse width modulation indices Pmd and Pmq whichdefine the ratio between DC voltage and the AC-voltage at the slip rings. The modulation indices Pmd and Pmq are defined in arotor-oriented reference frame.

For more details about the built-in DFIG model, please refer to the corresponding Model Description of the Technical ReferenceManual.

3.3.2 Rotor-Side Converter Controller

(To Protection System)

(From Protection System)

Irot

bypass

P;Q

phim

Ifq_ref;Ifd_refPref

Ifq;Ifd

Pfq;Pfd

psis_r;psis_i

iq;id

Pmq ; Pmd

Transformatio..*

Current Measurement*

PQ ControlElmGen*

Qref

Current Control*

Figure 11: Main Components of the Rotor-Side Converter Controller (Composite Model Frame)

The basic diagram (Frame) of the rotor-side converter controllers is shown in Figure 11.

The rotor-side converter is controlled by a two stage controller. The first stage consists of very fast current controllersregulating the machine’s rotor currents to reference values that are specified by a slower power-controller (second stage).

The rotor-side current-controller operates in a stator-flux oriented reference frame. Hence, rotor currents must first betransformed into a stator-flux oriented reference frame (psis_r, psis_i, see Figure 11).



3.3.2.1 Rotor-Current ControllerThe block Current Measurement transforms rotor currents from the original, rotor-oriented reference frame to stator-fluxorientation. Additionally, the magnitude (in kA) of the rotor-current phasor is calculated and sent to the rotor current protectionmodel. For considering flux-measurement delays (or flux-observer delays), a delay time constant can be entered.

This transformation decomposes the rotor currents into a component that is in-phase with stator flux (d-component) and acomponent that is orthogonal to stator flux (q-component). The q-component of the rotor current directly influences the torque,why the q-axis can be used for torque- or active power control. The d-axis component is a reactive current component and canbe used for reactive power- or voltage control.

x3

Rotor-Side ConverterCurrent Control

x4

Pmd

Pmq

uduq

yi1

yi

bypass

o16

Ird

Ird_ref

Irq_ref

Irqmodule limiter

Max

0

1

0

1

non-windup PIKq,Tq

MinPmq

MaxPmq

0

1

(1/(1+sT))Tr

(1/(1+sT))Tr

-

-

non-windup PIKd,Td

MinPmd

MaxPmd0

1

Current Control:

2

1

3

4

0

0

1

DIg

SILE

NT

Figure 12: Block Diagram of Rotor-Current Controller

The block-diagram depicted in Figure 12 is the implementation of the rotor-current controller. There are two independentproportional-integral-(P-I-) controllers, one for the d-axis component, one for the q-axis component. The output of the currentcontroller defines the pulse-width modulation indices in stator-flux orientation.

For limiting harmonics, the magnitude of the pulse-width modulation index is limited to the parameter Max. Both P-I-controllersare equipped with non-windup limiters.

By activating the additional input signal bypass, the pulse-width modulation indices are immediately set equal to zero, which isequivalent to blocking and bypassing the rotor-side converter (“Crow-Bar protection”, see section 3.5).

Because the modulation index of the doubly-fed induction machine must be defined in a rotor-oriented reference frame, theoutputs of the rotor-current controller have to be transformed back from stator-flux-orientation to rotor-orientation. Thistransformation is realized by the block Transformation.



Figure 13: Input/Output Definition of Rotor-Current Measurement

Table 10: Input Definition of Rotor-Current Measurement


cosphim Cosine of rotor angle

sinphim Sine of rotor angle

id Rotor-Current (d-axis, in rotor-oriented reference frame) p.u.

iq Rotor-Current (q-axis, in rotor-oriented reference frame) p.u.

psis_r Stator Flux, real part p.u.

psis_i Stator Flux, imaginary part p.u.

Table 11: Output Definition of Rotor-Current Measurement


ifd Rotor-Current (d-axis, Stator-Flux Orientation) p.u.

ifq Rotor-Current (q-axis, Stator-Flux Orientation)

Irot Rotor-Current (Magnitude of current-phasor) kA

Table 12: Parameters of Rotor-Current Measurement


Tm Measurement Delay Time s

Urrated Rated Rotor Voltage kV

Srated Rated Power of DFIG MVA

Rotor-CurrentMeasurement

cosphim

sinphim

id

iq

psis_r

psis_i

ifd

ifq

Irot



Figure 14: Input/Output Definition of Rotor- Current Controller

Table 13: Input-Definition of Rotor- Current Controller


bypass Bypass-Signal

Iq_ref q-Axis Current Reference p.u.

Ifq q-Axis Current p.u.

Id_ref d-Axis Current Reference p.u.

Id d-Axis Current p.u.

Table 14: Output-Definition of Rotor-Current Controller


Pmq q-Axis Pulse Width Modulation Index

Pmd d-Axis Pulse Width Modulation Index

Table 15: Parameter-Definition of Rotor- Current Controller


Tr Current Measurement Time Constant sec

Kq q-Axis Gain p.u

Tq q-Axis Time Constant sec

Kd d-Axis Gain p.u

Td d-Axis Time Constant sec

MinPmq Min. q-Axis Pulse-Width Modulation Index p.u

MinPmd Min. d-Axis Pulse-Width Modulation Index p.u

MaxPmq Max. q-Axis Pulse-Width Modulation Index p.u

MaxPmd Max. d-Axis Pulse-Width Modulation Index t p.u

Max Max. Magnitude of Pulse-Width Modulation Index p.u

Rotor-CurrentController

bypass

Ifq_ref

Ifq

Ifd_ref

Ifd

Pmq

Pmd



Figure 15: Input/Output Definition of Rotor-dq-Transformation

Table 16: Input Definition of Rotor-dq-Transformation


cosphim Cosine of Rotor-Angle

sinphim Sine of Rotor-Angle

Pfd d-Axis Modulation Index (Stator-Flux Orienation)

Pfq q-Axis Modulation Index (Stator-Flux Orientatin)

psis_r Stator-Flux, Real Part p.u.

psis_i Stator-Flux, Imaginary Part p.u.

Table 17: Output Definition of Rotor-dq-Transformation


Pmd d-Axis Modulation Index (Rotor-Orientation)

Pmq q-Axis Modulation Index (Rotor-Orientation)

Rotor-dq-Transformation

cosphim

sinphim

Pfd

Pfq

psis_r

psis_i

Pmdd

Pmq



3.3.2.2 Power-Controller

xQx2

xP

Reactive Power Control

Active Power Control

Active and Reactive Power ControlRotor Side Converter

x1

Ifd_ref

Ifq_ref

bypas..

Q

Qref

P

Pref

module limiter

Max

0

1

0

1

non-windup PIKp,Tp

MinIfq

MaxIfq0

1

(1/(1+sT)Ttr

-

-

non-windup PIKq,Tq

MinIfd

MaxIfd0

1

(1/(1+sT)Ttr

PQ Control:

1

2

3

4

0

1

0

DIg

SILE

NT

Figure 16: Block-Diagram of PQ-Controller

D-axis and q-axis component of the rotor current are controlled to reference values specified by active- and reactive powercontrollers according to Figure 16. Similar to the rotor-current controller, the power controller regulates active- and reactivepower by independent P-I-controllers. The P-I-controllers are equipped with non-windup limiters. The output limits themagnitude of the rotor-current reference. In contrast to the output-limiter in Figure 12, the q-axis-component (active currentcomponent) is prioritized.

Voltage control can either be realized by connecting a voltage controller behind the reactive power reference or by replacing thereactive power controller by a voltage controller defining the d-axis current reference.

Figure 17: Input/Output Definition of PQ-Controller

PQ-Controller

bypass

Pref

P

Qref

Q

Ifd_ref

Ifq_ref



Table 18: Input Definition of PQ-Controller


bypass Bypass-Signal

Pref Active Power Reference p.u.

P q-Axis Current p.u.

Qref d-Axis Current Reference p.u.

Q d-Axis Current p.u.

Table 19: Output-Definition of PQ-Controller


Ifq_ref q-Axis Current Reference p.u.

Ifd_ref d-Axis Current Reference p.u.

Table 20: Parameter Definition of PQ-Controller

Parameter Description Units

Ttr Measuring time constant sec

Kp Active Power Control Gain p.u

Tp Active Power Control Time Constant sec

Kq Reactive Power Control Gain p.u

Tq Reactive Power Control Time Constant sec

MinIfq Min. q-axis current reference p.u

MinIfd Min. d-axis current reference p.u

MaxIfq Max. q-axis current reference p.u

MaxIfd Max. d-axis current reference p.u

Max Max. current magnitude reference p.u

3.3.3 Maximum Power Tracking

According to the classical control strategy the active power dispatch of wind-turbines is permanently optimized. Hence, the windturbine operates with maximum possible active power output, depending on actual wind speed.

As shown in Figure 3 there is, for every wind speed, an optimum mechanical speed (optimum λ). Assuming that the windturbine always operates at this optimum point, the actual wind speed and hence the maximum possible active power can becalculated from the mechanical speed, without the necessity of wind-speed measurements.

Calculating the table of max. power versus mechanical speed and applying the maximum power as active power reference tothe PQ-controller drives the wind turbine into the optimum point. In the PowerFactory model, the power vs. speed characteristic(or MPT-characteristic) is defined using a linearly interpolated table.

Alternatively, many doubly-fed induction machines are operated using a slightly different control-scheme, in which active poweris measured and mechanical speed is calculated by the inverse MPT-characteristic. In this case, the calculated speed is sent as



speed-reference to a speed-controller. Replacing the active power controller according to Figure 16 by a speed-controller andconnecting an inverse MPT table to the speed-reference point realizes this alternative control scheme.

Figure 18; Input/Output Definition of MPT-Characteristic

Table 21: Input Definition of MPT-Characteristic


speed Mechanical Speed p.u.

Table 22: Output Definition of MPT-Characteristic


Pref Active Power Reference p.u.

Table 23: Parameter Definition of MPT-Characteristic


array_MPT Array of Power Reference Points p.u.

speed MPT-Characteristic Pref



3.4 Grid-Side-Converter with ControlsL1

C1

PWM U1

U11

Figure 19: Grid-Side Converter

The grid-side converter consists of a 6-pulse bridge (PWM U1 in Figure 19), the AC-inductance (L1) and the DC-capacitance(C1).

Like the rotor-side converter, the grid-side PWM converter is modelled using a fundamental frequency approach. The inputvariables Pmr and Pmi, together with the DC-voltage, define magnitude and phase angle of the AC-voltage at the PWM-converter’s AC-terminal. The pulse-width modulation indices Pmr and Pmi are referred to the so-called global reference frame,which is in EMT-simulations a steady state reference frame and which rotates with reference frequency (mechanical speed ofthe reference machine) in case of an RMS simulation. However, the reference frame has no influence to the system’sperformance, as long as all quantities are given in the correct reference frames.

More information about the PWM-controller, the AC-inductance and the DC-capacitance can be found in the correspondingModel Descriptions.

The basic diagram of the grid-side controller is shown in Figure 20.

The modulation indices of the Converter are imposed from a Current Control through a reference frame transformation (ph-transf). The Current Control operates in an AC-voltage oriented reference frame. It contains two current control loops: direct(active-) and quadrature (reactive-) axis current components (id and iq). The reference of the direct axis current component(id_ref) is set by DC voltage control. The reference of the quadrature axis current component (id_ref ) is, kept constant (const.reactive power) in this case.

For defining the AC-voltage oriented reference frame, a PLL (phase-locked-loop) is required measuring the voltage angle. ThePLL-output is used for transforming the current measurement into the voltage-oriented reference frame (dq-transf) and fortransforming the controller outputs (pulse-width modulation indices) back to the global reference frame (ph-transf).



Pmi

PmrPmd

Pmq

id

iq

sinph..

cosph..

ii

ir

id_refudc

ConverterElmVsc*

Current ControlElmCur*

iq_ref

DC Voltage ControlElmDc *

udc_ref

DC Voltage measurementStaVmea*

ph-transfElmDq-*

Current MeasurementStaImea*

dq transfElmDq-*

PLLElmPll*,ElmPhi*

Grid Side Converter: DIg

SILE

NT

Figure 20: Grid-Side Converter- Frame

3.4.1.1 Grid-Side Current Controller

x3

Grid-Side ConverterCurrent Control

x4

Pmq

Pmd

iq

iq_ref

id_ref

id

module limiter

Max

0

1

0

1

{K (1+1/sT)}Kd,Td

Min_Pmd

Max_Pmd

(1/(1+sT))Tr

(1/(1+sT))Tr

-

-

{K (1+1/sT)}Kq,Tq

Min_Pmq

Max_Pmq

Current Control:

1

0

2

3

0

1

DIg

SILE

NT

Figure 21: Block Diagram of Grid-Side Current Controller



The grid-side controller (Figure 21) is very similar to the rotor-side current controller (Figure 12). However, since it operates ina voltage-oriented reference frame and not in a flux-oriented reference frame the role of d- and q-axis is inverted: the d-axiscomponent defines active-current and the q-axis component defines reactive current.

Figure 22: Input/Output Definition of Grid-Side Current Controller

Table 24: Input Definition of Grid-Side Current Controller


Id_ref d-Axis Current Reference p.u.

Id d-Axis Current p.u.

Iq_ref q-Axis Current Reference p.u.

Iq q-Axis Current p.u.

Table 25: Output Definition of Grid-Side Current Controller


Pmd d-Axis Pulse Width Modulation Index

Pmq q-Axis Pulse Width Modulation Index

Table 26: Parameter Definition of Grid-Side Current Controller


Kd d-axis proportional gain p.u.

Td d-axis integral time constant Sec

Kq q-axis proportional gain p.u

Tq q-axis integral time constant Sec

Tr Current measurement time constant Sec

Min_Pmd Min. d-axis modulation factor p.u.

Min_Pmq Min. q-axis modulation factor p.u.

Max_Pmd Max. d-axis modulation factor p.u.

Max_Pmq Max. q-axis modulation factor p.u.

Grid-Side CurrentController

Id_ref

Id

Iq_ref

Iq

Pmd

Pmq



Fmeas

cosphi

sinphi

yi

om

om_n

om

dom

Kpph

iKi

phi

dphi

ii

rr

vi

vr

1/(2pi)

cos(x)

sin(x)

1/s

K/s_limK

dommin

dommax

KKp

PLL:

0

1

0

1

2

DIg

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NT

Figure 23: Block-Diagram of PLL

Figure 24: Basic-Data-Page of PLL Showing Node-Reference

The reference angle of the current controller is provided by a PLL (phase locked loop). The PLL is a PowerFactory built-in modelthat refers directly to a bus-bar or terminal. The block-diagram is shown in Figure 23, however, the input voltage is not definedby a composite model but directly by a node-reference in the input-dialogue box of the PLL, as shown in Figure 24.



Figure 25: Input/Output Definition of PLL (Built-In Model)

Table 27: Output Definition of PLL


Fmeas Measured Frequency Hz

sinphi Sine of Voltage Angle

cosphi Cosine of Voltage Angle

Table 28: Parameter Definition of PLL


Kp Controller Gain

Ki Integration Gain 1/a

ommax Upper Frequency Limit p.u.

ommin Lower Frequency Limit p.u.

The input/output definition of the transformation blocks carrying out the transformation from the global reference system to theAC-voltage oriented reference system and back are shown in Figure 26.

Figure 26: Input/Output Definition of Grid-dq-Transformation

Grid-dq-Transformation

iq

idir

ii

sinphi

cosphi

PLL

cosphi

sinphi

Fmeas



Table 29: Input Definition of Grid-dq-Transformation


ir Real Part of Input Signal in Global Reference System p.u.

ii Im. Part of Input Signal in Global Reference System p.u.

sinphi Cosine of Reference Angle

cosphi Cosine of Reference Angle

Table 30: Output Definition of Grid-dq-Transformation


id d-Axis Current p.u.

iq q-Axis Current p.u.

Figure 27: Input/Output Definition of Phase-Transformation

Table 31: Input Definition of Phase-Transformation


id d-Axis Component of Input Signal p.u.

iq q-Axis Component of Input Signal p.u.

sinphi Cosine of Reference Angle

cosphi Cosine of Reference Angle

Table 32: Output Definition of Phase-Transformation


ir Real Part of Output Signal p.u.

ii Im. Part of Output Signal p.u.

Phase-Transformation

ii

irid

iq

sinphi

cosphi



3.4.1.2 DC-Voltage Controller

xidref

id_refudc

udc_ref

dudc{K (1+1/sT)}Kudc,Tudc

Min_idref

Max_idref

-

DC Voltage Control:

0

1

DIg

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Figure 28: DC-Voltage Controller

The P-I-controller shown in Figure 28 controls the DC-voltage and sets the d-axis current reference. Time constant and gain ofthe controller must be set in accordance with the DC-capacitance (see Figure 19).

Figure 29: Input/Output Definition of DC-Voltage Controller

Table 33: Input Definition of DC-Voltage Controller

Input Description Units

udc_ref DC-Voltage, Reference Value p.u.

udc DC-Voltage sec

DC-VoltageController

id_ref

udc_ref

udc



Table 34: Output Definition of DC-Voltage Controller

Ouput Description Units

id_ref d-Axis Current Reference p.u.

Table 35: Parameter Definition of DC-Voltage Controller


Kudc Proportional Gain p.u.

Tudc Integral Time Constant sec

Min_idref Min. d-axis current reference p.u.

Max_idref Max. d-axis current reference p.u



3.5 Protection

CrowBar

u

speed

Irot

bypass

TripVoltage

TripSpeed

Rotor BypassMaxIrotor, tbypass

Max

0

1

2

VoltageProtMaxVoltage1,ttripMaxV1, ..

SpeedProtMaxSpeed1,ttripMaxS1, Ma..

Protection:

0

1

2

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Figure 30: Block Diagram of DFIG-Protection

The following protective functions are implemented in the block diagram according to Figure 30:

1. Under-/Over-Voltage2. Under-/Over-Speed3. Rotor-Over-Current (“Crow-Bar Protection”)

The Under/Over-Voltage unit supervises the voltage at the HV side of the transformer and has four voltage levels, two forunder-voltage and two for over-voltage. If this protective unit triggers the machine breaker is opened.

The Under/Over-speed protection unit supervises the generator speed and consists of four levels, two for under-speed and twofor over-speed. If this protective unit triggers the machine breaker is opened.

Rs Xs

Xm

Zrot

U Ur tj re ω− UrUr'= AdditionalImpedance

Figure 31: Equivalent Circuit Diagram of DFIG During Crow-Bar Protection



The Crow-Bar protection is specific to doubly-fed induction generators and protects the rotor-side converter against over-currents. When the rotor current exceeds a threshold value, the converter is blocked and bypassed through an additionalimpedance (see Figure 31). This additional impedance reduces the amount of reactive power absorbed by the machine andimproves the torque characteristic during voltage sags. While the Crow-Bar is inserted, the integral actions of the rotor-sidecontrollers are set to zero (see Figure 12 and Figure 16) for minimizing discontinuities in the rotor current when the Crow-Bar isremoved. Those discontinuities would eventually lead to subsequent operations of the Crow-Bar protection. When the Crow-Baris released, the rotor side converter is unblocked. For simulating cases, in which doubly-fed induction generators remain in thesystem during faults, as recommended by the latest E.ON. guidelines, the operation of the Crow-Bar protection does not openthe machine breaker. For simulating synchronous operation of Crow-Bar protection and machine breaker, the model can easilybe modified.

Figure 32: Input/Output Definition of DFIG-Protection

Table 36: Input Definition of DFIG-Protection

Input Description Units

Irot Rotor Current Magnitude kA

speed Generator Speed sec

u Bus-Bar Voltage p.u

Table 37: Output Definition of DFIG-Protection

Output Description Units

bypass Bypass-Signal (for Crow-Bar Insertion)

DFIG-Protectionbypass

Irot

speed

u



Table 38: Parameter Definition of DFIG-Protection


MaxIrotor Rotor Current for Crow Bar Insertion kA

tbypass Crow Bar Insertion Time sec

MaxSpeed1 Overspeed Setting step 1 p.u

ttripMaxS1 Overspeed Time Setting step 1 sec

MaxSpeed2 Overspeed Setting step 2 p.u

ttripMaxS2 Overspeed Time Setting step 2 sec

MinSpeed1 Underspeed Setting step 1 p.u

ttripMinS1 Underspeed Time Setting step 1 sec

MinSpeed2 Underspeed Setting step 2 p.u

ttripMinS2 Underspeed Time Setting step 2 sec

MaxVoltage1 Overvoltage Setting step 1 p.u

ttripMaxV1 Overvoltage Time Setting step 1 sec

MaxVoltage2 Overvoltage Setting step 2 p.u

ttripMaxV2 Overvoltage Time Setting step 2 sec

MinVoltage1 Undervoltage Setting step 1 p.u

ttripMinV1 Undervoltage Time Setting step 1 sec

MinVoltage2 Undervoltage Setting step 2 p.u

ttripMinV2 Undervoltage Time Setting step 2 sec

4 S i m u l a t i o n E x a m p l e s


4 Simulation Examples

In this section the behaviour of the proposed DFIG model under different types of system faults is presented.

4.1 Three-Phase Fault, Far from Wind Generation

In this case, a three phase fault cleared after 200 ms causing a voltage depression of about 25% is simulated. The results arepresented in Figure 33 to Figure 35.

4.0003.0002.0001.000 0.00 ..

1.200

0.80

0.40

0.00

-0.400

-0.800

PQ Control: Total Active Power (P)

4.0003.0002.0001.000 0.00 ..

1.000

0.00

-1.000

-2.000

-3.000

PQ Control: Total Reactive Power (Q)

4.0003.0002.0001.000 0.00 ..

1.200

1.00

0.80

0.60

0.40

0.20

0.00

T3WT1: AC Voltage at HV side (u)

DIgSILENT Doubly-fed Induction Generator - Example Plot-1

Date: 5/26/2003

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Figure 33: Three-Phase Fault Far from Wind Generation, Connection Point



4.0003.0002.0001.000 0.00 ..

7.500

5.000

2.500

0.00

-2.500

-5.000

-7.500

G1d: Stator Reactive Power4.0003.0002.0001.000 0.00 ..

5.500

5.000

4.500

4.000

3.500

3.000

G1d: Stator Active Power

4.0003.0002.0001.000 0.00 ..

0.50

0.25

0.00

-0.250

-0.500

-0.750

PWM U1: Grid Side Converter Active Power4.0003.0002.0001.000 0.00 ..

0.00

-0.100

-0.200

-0.300

-0.400

PWM U1: Grid Side Converter Reactive Power


Date: 5/26/2003

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Figure 34: Three-Phase Fault Far from Wind Generation, Stator- and Grid-Side Results

4.0003.0002.0001.000 0.00 ..

4.500

4.400

4.300

4.200

4.100

4.000

Prime Mover: Wind Power

4.0003.0002.0001.000 0.00 ..

3.000

2.000

1.000

0.00

-1.000

Prime Mover: Blade pitch Angle

4.0003.0002.0001.000 0.00 ..

1.000

0.99

0.98

0.97

0.96

0.95

0.94

G1d: Generator Speed


Date: 5/26/2003

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Figure 35: Three-Phase Fault Far from Wind Generation, Mechanical Variables



Figure 33 shows that the total active and reactive power at the connection point is quickly restored. The active power of thestator has an oscillatory component due to torsional oscillations that is almost perfectly damped by the active power controllerof the grid-side converter (Figure 34). The speed deviations are not large enough to cause a variation of the blade angles thepitch control.

4.2 Three Phase Fault Close to Wind Generation

In this case, a three phase fault cleared after 400 ms causing a voltage depression of about 85% is simulated assuming that theunder-voltage protection is set to avoid the disconnection from the grid under these circumstances. The results are presentedin Figure 36 to Figure 38.

In this case, it takes longer to restore total active and reactive power than in the previous case, due to the operation of thecrow bar (Figure 36). The total reactive power is almost zero during the fault and is negative during the time between clearingthe fault and removing the crow bar protection at t=0.5s. In this case, the speed deviation is larger than in the previous caseand the blade angle is increased to reduce the power extracted from the wind.

The reactive power absorbed by the generator during the time that the crow bar is inserted may have a negative impact on thevoltage stability of the system when a significant number of units are connected. The modelling of the operation of thisprotective function should be particularly considered in the design of transmission systems connecting large wind farms to utilitygrids.

4.0003.0002.0001.000 0.00 ..

1.200

0.80

0.40

0.00

-0.400

-0.800


4.0003.0002.0001.000 0.00 ..

1.000

0.00

-1.000

-2.000

-3.000


4.0003.0002.0001.000 0.00 ..

1.200

1.00

0.80

0.60

0.40

0.20

0.00

T3WT1: AC Voltage at HV side (u)


Date: 5/26/2003

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Figure 36: Three-Phase Fault Close to Wind Generation, Connection Point



4.0003.0002.0001.000 0.00 ..

8.000

4.000

0.00

-4.000

-8.000

-12.00

G1d: Stator Reactive Power4.0003.0002.0001.000 0.00 ..

6.000

4.000

2.000

0.00

-2.000

-4.000


4.0003.0002.0001.000 0.00 ..

1.200

0.80

0.40

0.00

-0.400

-0.800

-1.200

PWM U1: Grid Side Converter Active Power4.0003.0002.0001.000 0.00 ..

4.000

3.000

2.000

1.000

0.00

-1.000



Date: 5/26/2003

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Figure 37: Three-Phase Fault Close to Wind Generation, Stator- and Grid-Side Results

4.0003.0002.0001.000 0.00 ..

4.400

4.300

4.200

4.100

4.000

3.900

Prime Mover: Wind Power

4.0003.0002.0001.000 0.00 ..

0.30

0.20

0.10

0.00

-0.100

Prime Mover: Blade pitch Angle

4.0003.0002.0001.000 0.00 ..

1.140

1.100

1.060

1.020

0.98

0.94



Date: 5/26/2003

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Figure 38: Three-Phase Fault Close to Wind Generation, Mechanical Variables



4.3 Single Phase Fault Close to Wind Generation

In this case, a single phase fault cleared after 400 ms causing a total voltage depression in phase A at the HV side of themachine transformer is simulated assuming that the under-voltage protection is set to avoid the disconnection from the gridunder this circumstances. The results are presented in Figure 39 to Figure 41.

In this case, the total active power does not decrease during the fault as in the previous case due to the fault type. However,the increasing rotor current causes the Crow-Bar protection to trip. Consequently, the total reactive power absorptionsignificantly increases until the crow bar protection is removed at t=0.5s. The speed deviation is less than in the previous caseand the blade angle is kept constant.

In contrast to the previous cases, this case was simulated using an instantaneous-value representation of the AC-system (EMT-simulation). This more accurate model uses fifth-order generator models, including stator transients and differential equationsfor all network components.

1.000.750.500.25-0.00 [s]

2.00

1.00

-0.00

-1.00


1.000.750.500.25-0.00 [s]

2.00

1.00

-0.00

-1.00

-2.00


1.000.750.500.25-0.00 [s]

2.00

1.00

-0.00

-1.00

-2.00

T3WT1: Phasenspannung L1/OS-Seite in p.u.

DIgSILENT Doubly-fed Induction Generator - Example Results at Connection Point

Date: 8/11/2003

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Figure 39: Single-Phase Fault Close to Wind Generation, Connection Point



1.000.750.500.25-0.00 [s]

9.00

6.00

3.00

0.00

-3.00

-6.00

G1d: Stator Reactive Power1.000.750.500.25-0.00 [s]

7.50

5.00

2.50

0.00

-2.50

-5.00


1.000.750.500.25-0.00 [s]

3.00

2.00

1.00

0.00

-1.00

PWM U1: Grid Side Converter Active Power1.000.750.500.25-0.00 [s]

3.00

2.00

1.00

0.00

-1.00


DIgSILENT Doubly-fed Induction Generator - Example Active/Reactive Power

Date: 8/11/2003

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Figure 40: Single Phase Fault Close to Wind Generation, Stator- and Grid-Side Results

1.000.750.500.25-0.00 [s]

4.40

4.30

4.20

4.10

4.00

3.90

Turbine: Wind Power

1.000.750.500.25-0.00 [s]

0.15

0.10

0.05

0.00

-0.05

-0.10

-0.15

Pitch Control: Blade pitch Angle

1.000.750.500.25-0.00 [s]

1.14

1.10

1.06

1.02

0.98

0.94


DIgSILENT Doubly-fed Induction Generator - Example Mechanical Results

Date: 8/11/2003

Annex: 1 /3

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Figure 41: Single-Phase Fault Close to Wind Generation, Mechanical Variables

5 C o n c l u s i o n s


5 Conclusions

The PowerFactory standard library of generic models for simulating DFIG-based wind power plants was described using atypical DFIG-example. The models include the conversion from wind- to mechanical energy, pitch control, maximum powertracking and controllers for the rotor-side- and grid-side converters.

The described models can easily be extended for different reactive and active power control schemes.

All block diagrams, equations and input/output definitions were presented in this document allowing to use the PowerFactorystandard library efficiently.

Simulation examples showing the dynamic response of the described models illustrate the validity and accuracy of thepresented approach

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