Dynamic Modelling of Doubly-Fed Induction Machine Wind Generators

8/9/2019 Dynamic Modelling of Doubly-Fed Induction Machine Wind Generators

1/39

Technical Documentat ion

Dynamic Modelling of Doubly-Fed

Induction Machine Wind-Generators

G m b H


2/39

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


3/39

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 scenarios

are foreseen in other parts of the world. This aspect, together with the significant size of new wind farm projects, requires

realistic modelling capabilities of wind generators for proper assessment of power system planning and impact analysis of future

wind generation.

As a result of research and consulting activities of DIgSILENT, generic dynamic models of different types of wind power

generation 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 same

time, 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 to

network faults was in the centre of interest, but the models can also be used for simulating the impact of wind fluctuations to

power systems.

There is no wind model included in this description. However, any type of stochastic or deterministic wind model, or measured

wind 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 also

possible 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.


4/39

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 Doubly-Fed Induction Machine Concept

DFIG

External Grid

Prime

Mover

Grid Side

Converter

Rotor Side

Converter

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 induction

generator. The stator of the DFIG is directly connected to the grid, the slip-rings of the rotor are fed by self-commutated

converters. These converters allow controlling the rotor voltage in magnitude and phase angle and can therefore be used for

active- 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 control

loops 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-side

converter against over-currents, it is usual practice to bypass the rotor-side converter during system faults. Whether the DFIG is

totally 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 voltage

stability of large farms during faults in the transmission- or distribution network. For this reason, it is necessary to model even

the fast current controls of the rotor side converter to effectively determine the operation of the crow bar. Other protection

functions also found in DFIG such as over/under-speed and over/under-voltage are considered in the proposed model as wel


5/39

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

Pwind

beta

u

bypass

P;Q

c o s p h . .

Ifq_ref;Ifd_ref

Pref

iq;id

Pfq;Pfd

psis_..

speed

Pmq ; Pmd

Irot

I f q ; I . .

Shaft*

Pitch Control*

Transformatio..*

Current Measurement*

V meas.StaVmea*

ProtectionElmPro*

Turbine*

vw

MPTElmMpt*

PQ ControlElmGen*

Qref

Current Control*

DFIGElmAsm*

Power MeasurementStaPqmea

DFIG: D I g S I L E N T

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 a

maximum power tracking strategy (MPT, Power Measurement, PQ Control, Current Control, Current Measurement)

• Protection-system (V meas., Protection)


6/39



The models of all major components are described in the following sections. It is important to point out that these models can

be used in combinations that differ from Figure 2, e.g. realizing power-dependent speed control instead of the speed-dependent

power control.

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

frequency 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 the

blades 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 relevance

for the stability model are explained.

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

2

2 wk v

m E ⋅= (1)

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

22

02

1

2

1ww

k vqvt

m

t

E 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 control

turbines) and on the turbine design. It is usually denominated aerodynamic efficiency Cp :


7/39



Figure 3: Typical Cp(β , λ) Characteristic

0 P P Cp 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

v

R⋅= 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 accuracy

of 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 usually

available 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 vCp R P ⋅⋅⋅⋅= β λ π ρ

(6)


8/39



The Cp -characteristic can be calculated using special software for aerodynamic designs that is usually based on blade-iteration

techniques 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 stall

dynamics.

The input/output diagram of the turbine model is depicted in Figure 4 and the input-, output- and parameter definitions are

presented in Table 1 to

Table 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-Turbine

vw

omega_tur

Pwind


9/39



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: D I g S I L E N T

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 turned

into 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 and

hence reducing the generated power.

The model presented here is generic and captures the main characteristics of pitch angle controls of existing wind generation

technologies. 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 the

controller 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


10/39



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


11/39


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

TmecTwind

tdif omega_tur -

Gear BoxRPMnom

RatePtPbase

0

1

SpringK,D_shaft

0

1

Mass_1TorqueD_turb,J

Torque

0

1

Shaft Model:

0

1

0

1

D I g S I L E N T

Figure 8: Block Diagram of Shaft

DgDt

ωgJg

Jtωt

K tg

Dtg

ω’ g


12/39



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 with

sufficient 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 st iffness of

the 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 Figure

7). The model according to Figure 7 and Figure 8 represents the turbine inertia and the coupling between turbine- and

generator. The generator inertia however, is modelled inside the built-in induction machine model. The generator inertia is

specified in the form of an acceleration time constant in the induction generator type. The inertia of the gear-box is not

modelled 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, a

second 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


13/39



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. In

this 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 and

control structures.

This section starts with a description of the DFIG including the rotor-side converter. The grid-side converter with controls is

described 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 rotor

impedance as shown in Figure 10. In this figure, Rs and Xs are the resistance and leakage reactance of the stator winding; Xm

is the magnetizing reactance and Zrot is the rotor impedance.

Rs Xs

Xm

Zrot

U Ur t j r e

ω −Ur Ur'= 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 and

phase angle of the rotor voltage.

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

is applied.

In contrast to the normal induction machine model, in which the rotor is short-circuited, the winding ratio between rotor and

stator is important for calculating actual DC voltages. The nominal rotor voltage that can be measured at the slip rings under

open rotor conditions defines this winding ratio.


14/39



For load flow calculations and transients initialization, only active power (AC-side), reactive power and the slip have to be

specified. Internally, the corresponding modulation factors of the converter (Pmd, Pmq) are calculated and together with the

power 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 which

define the ratio between DC voltage and the AC-voltage at the slip rings. The modulation indices Pmd and Pmq are defined in a

rotor-oriented reference frame.

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

Manual .

3.3.2 Rotor-Side Converter Controller

(To Protection System)

(From Protection System)

Irot

bypass

P;Q

phim

Ifq_ref;Ifd_ref

Pref

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 controllers

regulating 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 be

transformed into a stator-flux oriented reference frame (psis_r, psis_i, see Figure 11).


15/39



3.3.2.1

Rotor-Current Controller

The block Current Measurement transforms rotor currents from the original, rotor-oriented reference frame to stator-flux

orientation. 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 a

component 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 can

be used for reactive power- or voltage control.

x3

Rotor-Side Converter

Current Control

x4

Pmd

Pmq

u d

u q

yi1

yi

bypass

o 1 6

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

MaxPmd

0

1

Current Control:

2

1

3

4

0

0

1

D I g S I L E N T

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 independent

proportional-integral-(P-I-) controllers, one for the d-axis component, one for the q-axis component. The output of the current

controller 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-controllers

are equipped with non-windup limiters.

By activating the additional input signal bypass, the pulse-width modulation indices are immediately set equal to zero, which is

equivalent 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, the

outputs of the rotor-current controller have to be transformed back from stator-flux-orientation to rotor-orientation. This

transformation is realized by the block Transformation .


16/39



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


17/39



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


18/39



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


19/39



3.3.2.2

Power-Controller

xQ

x2

xP

Reactive Power Control

Active Power Control

Active and Reactive Power Control

Rotor Side Converter

x1

Ifd_ref

Ifq_ref

bypas..

Q

Qref

P

Pref

module limiter

Max

0

1

0

1

non-windup PIKp,Tp

MinIfq

MaxIfq

0

1

(1/(1+sT)Ttr

-

-

non-windup PIKq,Tq

MinIfd

MaxIfd

0

1

(1/(1+sT)Ttr

PQ Control:

1

2

3

4

0

1

0

D I g S I L E N T

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 power

controllers according to Figure 16. Similar to the rotor-current controller, the power controller regulates active- and reactive

power by independent P-I-controllers. The P-I-controllers are equipped with non-windup limiters. The output limits the

magnitude of the rotor-current reference. In contrast to the output-limiter in Figure 12, the q-axis-component (active current

component) is prioritized.

Voltage control can either be realized by connecting a voltage controller behind the reactive power reference or by replacing the

reactive 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


20/39



Table 18: Input Definition of PQ-Controller

Input Description Unitbypass 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 wind

turbine 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 wind

turbine always operates at this optimum point, the actual wind speed and hence the maximum possible active power can be

calculated 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 to

the 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 power

is measured and mechanical speed is calculated by the inverse MPT-characteristic. In this case, the calculated speed is sent as


21/39



speed-reference to a speed-controller. Replacing the active power controller according to Figure 16 by a speed-controller and

connecting 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


22/39



3.4 Grid-Side-Converter with Controls

L 1

C 1

PWM U1

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 input

variables 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 of

the reference machine) in case of an RMS simulation. However, the reference frame has no influence to the system’s

performance, 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 corresponding

Model 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. The

PLL-output is used for transforming the current measurement into the voltage-oriented reference frame (dq- transf) and for

transforming the controller outputs (pulse-width modulation indices) back to the global reference frame ( ph-transf ).


23/39


24/39



The grid-side controller (Figure 21) is very similar to the rotor-side current controller (Figure 12). However, since it operates in

a voltage-oriented reference frame and not in a flux-oriented reference frame the role of d- and q-axis is inverted: the d-axis

component 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


25/39



Fmeas

cosphi

sinphi

y i

om

o m_

n o m

dom

K p p h i

K i p h i

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

D I g S I L E N T

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 model

that refers directly to a bus-bar or terminal. The block-diagram is shown in Figure 23, however, the input voltage is not defined

by a composite model but directly by a node-reference in the input-dialogue box of the PLL, as shown in Figure 24.


26/39



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 the

AC-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


27/39



Table 29: Input Definition of Grid-dq-Transformation

Input Description Unitir 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


28/39



3.4.1.2

DC-Voltage Controller

xidref

id_ref udc

udc_ref

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

Min_idref

Max_idref

-

DC Voltage Control:

0

1

D I g S I L E N T

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 of the 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


29/39



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


30/39



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

D I g S I L E N T

Figure 30: Block Diagram of DFIG-Protection

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

1. Under-/Over-Voltage

2. Under-/Over-Speed

3. 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 for

under-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 t j r e

ω −Ur Ur'=

AdditionalImpedance

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


31/39



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 additional

impedance (see Figure 31). This additional impedance reduces the amount of reactive power absorbed by the machine and

improves the torque characteristic during voltage sags. While the Crow-Bar is inserted, the integral actions of the rotor-side

controllers are set to zero (see Figure 12 and Figure 16) for minimizing discontinuities in the rotor current when the Crow-Bar is

removed. Those discontinuities would eventually lead to subsequent operations of the Crow-Bar protection. When the Crow-Bar

is released, the rotor side converter is unblocked. For simulating cases, in which doubly-fed induction generators remain in the

system during faults, as recommended by the latest E.ON. guidelines, the operation of the Crow-Bar protection does not open

the machine breaker. For simulating synchronous operation of Crow-Bar protection and machine breaker, the model can easily

be 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


32/39



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


33/39

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 are

presented in Figure 33 to Figure 35.

4.0003.0002.0001.0000.00 ..

1.200

0.80

0.40

0.00

-0.400

-0.800

PQ Control: Total Active Power (P)

4.0003.0002.0001.0000.00 ..

1.000

0.00

-1.000

-2.000

-3.000

PQ Control: Total Reactive Power (Q)

4.0003.0002.0001.0000.00 ..

1.200

1.00

0.80

0.60

0.40

0.20

0.00

T3WT1: AC Voltage at HV side (u)

DIgSILENTDoubly-fed Induction Generator - Example Plot-1

Date: 5/26/2003

Annex: /1

D I g S I L E N T

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


34/39



4.0003.0002.0001.0000.00 ..

7.500

5.000

2.500

0.00

-2.500

-5.000

-7.500

G1d: Stator Reactive Power

4.0003.0002.0001.0000.00 ..

5.500

5.000

4.500

4.000

3.500

3.000

G1d: Stator Active Power

4.0003.0002.0001.0000.00 ..

0.50

0.25

0.00

-0.250

-0.500

-0.750

PWM U1: Grid Side Converter Active Power

4.0003.0002.0001.0000.00 ..

0.00

-0.100

-0.200

-0.300

-0.400

PWM U1: Grid Side Converter Reactive Power


Date: 5/26/2003

Annex: /2

D I g S I L E N T

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

4.0003.0002.0001.0000.00 ..

4.500

4.400

4.300

4.200

4.100

4.000

Prime Mover: Wind Power

4.0003.0002.0001.0000.00 ..

3.000

2.000

1.000

0.00

-1.000

Prime Mover: Blade pitch Angle

4.0003.0002.0001.0000.00 ..

1.000

0.99

0.98

0.97

0.96

0.95

0.94

G1d: Generator Speed


Date: 5/26/2003

Annex: /3

D I g S I L E N T

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


35/39



Figure 33 shows that the total active and reactive power at the connection point is quickly restored. The active power of the

stator has an oscillatory component due to torsional oscillations that is almost perfectly damped by the active power controller

of the grid-side converter (Figure 34). The speed deviations are not large enough to cause a variation of the blade angles the

pitch 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 the

under-voltage protection is set to avoid the disconnection from the grid under these circumstances. The results are presented

in 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 the

crow bar (Figure 36). The total reactive power is almost zero during the fault and is negative during the time between clearing

the fault and removing the crow bar protection at t=0.5s. In this case, the speed deviation is larger than in the previous case

and 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 the

voltage stability of the system when a significant number of units are connected. The modelling of the operation of this

protective function should be particularly considered in the design of transmission systems connecting large wind farms to utility

grids.

4.0003.0002.0001.0000.00 ..

1.200

0.80

0.40

0.00

-0.400

-0.800


4.0003.0002.0001.0000.00 ..

1.000

0.00

-1.000

-2.000

-3.000


4.0003.0002.0001.0000.00 ..

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

Annex: /1

D I g S I L E N T

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


36/39



4.0003.0002.0001.0000.00 ..

8.000

4.000

0.00

-4.000

-8.000

-12.00


4.0003.0002.0001.0000.00 ..

6.000

4.000

2.000

0.00

-2.000

-4.000


4.0003.0002.0001.0000.00 ..

1.200

0.80

0.40

0.00

-0.400

-0.800

-1.200


4.0003.0002.0001.0000.00 ..

4.000

3.000

2.000

1.000

0.00

-1.000



Date: 5/26/2003

Annex: /2

D I g S I L E N T

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

4.0003.0002.0001.0000.00 ..

4.400

4.300

4.200

4.100

4.000

3.900

Prime Mover: Wind Power

4.0003.0002.0001.0000.00 ..

0.30

0.20

0.10

0.00

-0.100

Prime Mover: Blade pitch Angle

4.0003.0002.0001.0000.00 ..

1.140

1.100

1.060

1.020

0.98

0.94



Date: 5/26/2003

Annex: /3

D

I g S I L E N T

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


37/39



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 the

machine transformer is simulated assuming that the under-voltage protection is set to avoid the disconnection from the grid

under 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 absorption

significantly increases until the crow bar protection is removed at t=0.5s. The speed deviation is less than in the previous case

and 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 equations

for 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.

DIgSILENTDoubly-fed Induction Generator - Example Results at Connection Point

Date: 8/11/2003

Annex: 1 /1

D I g S I L E N T

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


38/39



1.000.750.500.25-0.00 [s]

9.00

6.00

3.00

0.00

-3.00

-6.00


1.000.750.500.25-0.00 [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


1.000.750.500.25-0.00 [s]

3.00

2.00

1.00

0.00

-1.00


DIgSILENTDoubly-fed Induction Generator - Example Active/Reactive Power

Date: 8/11/2003

Annex: 1 /2

D I g S I L E N T

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


DIgSILENTDoubly-fed Induction Generator - Example Mechanical Results

Date: 8/11/2003

Annex: 1 /3

D I g S I L E N T

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


39/39

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 a

typical DFIG-example. The models include the conversion from wind- to mechanical energy, pitch control, maximum power

tracking 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 PowerFactory

standard library efficiently.

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

presented approach

Documents

Dynamic Modelling of Doubly-Fed Induction Machine Wind Generators