G m b H
Technical Documentation
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
DIgSILENT GmbH Heinrich-Hertz-Strasse 9 D-72810 Gomaringen Tel.: +49 7072 9168 – 0 Fax: +49 7072 9168- 88 http://www.digsilent.d e-mail:
[email protected]
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators Published by DIgSILENT GmbH, Germany Copyright 2003. All rights reserved. Unauthorised copying or publishing of this or any part of this document is prohibited. doc.TechRef, 14 August 2003
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
1
1 Introduction
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.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
2
2 The Doubly-Fed Induction Machine Concept
2 The Doubly-Fed Induction Machine Concept DFIG Prime Mover Grid Side Converter Rotor Side Converter
External Grid
Control
Control
Protection 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 gridside 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 protection philosophy. 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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
3
3 The DFIG Wind-Generator Model
3 The DFIG Wind-Generator Model
DIgSILENT
3.1 Overview DFIG: speed
Prime Mover pt beta
Pitch Control *
vw
Turbine *
Pwind
Shaft *
omega..
Pref
MPT ElmMpt*
Ifq_ref;Ifd_ref Pfq;Pfd
Pmq ; Pmd
DFIG ElmAsm*
Qref
PQ Control ElmGen*
Current Control *
Transformatio.. *
bypass
Protection ElmPro*
u
(From Protection System)
Ifq;I..
cosph..
Power Measurement StaPqmea
P;Q
psis_.. V meas. StaVmea*
Current Measurement *
iq;id
Irot
(To Protection System)
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)
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
4
3 The DFIG Wind-Generator Model
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:
Ek =
m 2 ⋅ vw 2
(1)
The power associated to this moving air mass is the derivative of the kinetic energy with respect to time.
P0 =
∂E k 1 ∂m 1 2 2 = ⋅ ⋅ vw = ⋅ q ⋅ vw ∂t 2 ∂t 2
(2)
where q represents the mass flow given by the expression:
q = ρ ⋅ vw ⋅ A
(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:
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
5
3 The DFIG Wind-Generator Model
Figure 3: Typical Cp(β, λ) Characteristic
Cp =
PWind P0
(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:
λ=
ωTUR ⋅ R
(5)
vw
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 twodimensional, 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:
Pmech =
ρ 2
⋅ π ⋅ R 2 ⋅ Cp (λ , β ) ⋅ vw
3
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
(6)
6
3 The DFIG Wind-Generator Model
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.
beta
vw
Wind-Turbine
Pwind
omega_tur
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)
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
7
3 The DFIG Wind-Generator Model
DIgSILENT
3.2.2 Blade Angle Control Blade Angle Control:
BLADE ANGLE CONTROLLER
SERVO
ref
rate_op
Vrmax
speed
-
Ymax
beta_ref PI controller Ka,Tr,Ta
beta
-
Time Const T
Vrmin
Limiter
rate_cl
{1/s}
Ymin
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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
8
3 The DFIG Wind-Generator Model
Blade Angle Controller
speed
beta
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.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
9
3 The DFIG Wind-Generator Model
3.2.3 Shaft Jg
ωg
Dtg Jt
ωt
Ktg
ω’g
Dg
Dt
DIgSILENT
Figure 7: Spring-Mass Model of Second Order
Shaft Model:
0
0
Pwind
Twind
0
Torque
-
tdif
Tmec
omega_tur Mass_1Torque D_turb,J
0
Spring K,D_shaft
1
0
RatePt Pbase
1
pt
1
1
1
speed_gen
Gear Box RPMnom
omega_gen
Figure 8: Block Diagram of Shaft
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
10
3 The DFIG Wind-Generator Model
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 stiffness 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.
Pwind
omega_tur
Shaft speed_gen
pt
Figure 9: Input/Output Definition of Shaft
Table 7: Input Definition of Shaft Input
Description
Unit
Pwind
Turbine Power
MW
speed_gen
Generator Speed
p.u.
Table 8: Output Definition of Shaft Output
Description
Unit
omega_tur
Turbine Speed (Angular Velocity)
rad/s
pt
Mechanical Power at Generator Inertia
p.u.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
11
3 The DFIG Wind-Generator Model
Table 9: Parameter Definition of Shaft Parameter
Description
Unit
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
U
Zrot
Xs
Xm
Ur
Ur'= e
− jω r t
Ur
UAC
UDC
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.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
12
3 The DFIG Wind-Generator Model
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
Pref Ifq_ref;Ifd_ref Pfq;Pfd
Pmq ; Pmd
Qref
P;Q
PQ Control ElmGen*
Current Control *
Transformatio.. *
bypass
(From Protection System)
Ifq;Ifd psis_r;psis_i Current Measurement *
Irot
iq;id
phim
(To Protection System)
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).
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
13
3 The DFIG Wind-Generator Model
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 protection model. 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
DIgSILENT
be used for reactive power- or voltage control.
Current Control:
Rotor-Side Converter Current Control
bypass
0
MaxPmq 0
yi
non-windup PI Kq,Tq 1
-
MinPmq
uq
Irq_ref
1
Max
x3 Irq
0
module limiter
(1/(1+sT)) Tr
1
1
Pmq Pmd
0
1
ud
2
0
MaxPmd 0
Ird_ref
3
yi1
non-windup PI Kd,Td 1
o16
-
4
MinPmd
x4
Ird (1/(1+sT)) Tr
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.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
14
3 The DFIG Wind-Generator Model
cosphim
ifd
sinphim
Rotor-Current Measurement
id iq psis_r
ifq
Irot
psis_i
Figure 13: Input/Output Definition of Rotor-Current Measurement
Table 10: Input Definition of Rotor-Current Measurement Input
Description
cosphim
Cosine of rotor angle
Unit
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 Output
Description
Unit
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 Parameter
Description
Unit
Tm
Measurement Delay Time
s
Urrated
Rated Rotor Voltage
kV
Srated
Rated Power of DFIG
MVA
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
15
3 The DFIG Wind-Generator Model
bypass Ifq_ref Ifq
Pmq
Rotor-Current Controller
Ifd_ref
Pmd
Ifd
Figure 14: Input/Output Definition of Rotor- Current Controller
Table 13: Input-Definition of Rotor- Current Controller Input
Description
bypass
Bypass-Signal
Iq_ref
q-Axis Current Reference
Unit
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 Output
Description
Pmq
q-Axis Pulse Width Modulation Index
Pmd
d-Axis Pulse Width Modulation Index
Unit
Table 15: Parameter-Definition of Rotor- Current Controller Parameter
Description
Unit
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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
16
3 The DFIG Wind-Generator Model
cosphim sinphim Pfd Pfq
Rotor-dqTransformation
psis_r
Pmdd
Pmq
psis_i
Figure 15: Input/Output Definition of Rotor-dq-Transformation
Table 16: Input Definition of Rotor-dq-Transformation Input
Description
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)
Unit
psis_r
Stator-Flux, Real Part
p.u.
psis_i
Stator-Flux, Imaginary Part
p.u.
Table 17: Output Definition of Rotor-dq-Transformation Output
Description
Pmd
d-Axis Modulation Index (Rotor-Orientation)
Pmq
q-Axis Modulation Index (Rotor-Orientation)
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
Unit
17
3 The DFIG Wind-Generator Model
DIgSILENT
3.3.2.2 Power-Controller PQ Control:
Active and Reactive Power Control Rotor Side Converter
bypas..
0
MaxIfq 0
Pref 1
1
xP
2
P
-
non-windup PI Kp,Tp MinIfq
x1
(1/(1+sT) Ttr
Max
Active Power Control 0
0
module limiter 1
1
Ifq_ref Ifd_ref
0
1
MaxIfd 0
3
Qref
1
-
non-windup PI Kq,Tq MinIfd
xQ x2 4
Q
Reactive Power Control
(1/(1+sT) Ttr
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.
bypass Pref
Ifd_ref
PQ-Controller
P Qref
Ifq_ref
Q
Figure 17: Input/Output Definition of PQ-Controller
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
18
3 The DFIG Wind-Generator Model
Table 18: Input Definition of PQ-Controller Input
Description
Unit
bypass
Bypass-Signal
Pref
Active Power Reference
P
q-Axis Current
p.u.
Qref
d-Axis Current Reference
p.u.
Q
d-Axis Current
p.u.
p.u.
Table 19: Output-Definition of PQ-Controller Output
Description
Unit
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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
19
3 The DFIG Wind-Generator Model
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.
speed
MPT-Characteristic
Pref
Figure 18; Input/Output Definition of MPT-Characteristic
Table 21: Input Definition of MPT-Characteristic Input
Description
Unit
speed
Mechanical Speed
p.u.
Table 22: Output Definition of MPT-Characteristic Output
Description
Unit
Pref
Active Power Reference
p.u.
Table 23: Parameter Definition of MPT-Characteristic Parameter
Description
Unit
array_MPT
Array of Power Reference Points
p.u.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
20
3 The DFIG Wind-Generator Model
3.4 Grid-Side-Converter with Controls
L1
U11
C1
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 PWMconverter’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).
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
21
DIgSILENT
3 The DFIG Wind-Generator Model
Grid Side Converter:
udc_ref
udc
DC Voltage measurement StaVmea*
iq_ref
id_ref
DC Voltage Control ElmDc *
ir Current Measurement StaImea*
Current Control ElmCur*
ii
iq
Pmq
id
Pmd
Pmr
cosph.. PLL ElmPll*,ElmPhi*
dq transf ElmDq-*
ph-transf ElmDq-*
Converter ElmVsc*
Pmi
sinph..
Figure 20: Grid-Side Converter- Frame
DIgSILENT
3.4.1.1 Grid-Side Current Controller Current Control:
Grid-Side Converter Current Control
Max_Pmd id_ref
0
{K (1+1/sT)} Kd,Td
-
Min_Pmd 1
id
Max
x3
(1/(1+sT)) Tr
0
0
module limiter 1
1
Pmd Pmq
0
1
Max_Pmq iq_ref
2
-
{K (1+1/sT)} Kq,Tq Min_Pmq
3
iq (1/(1+sT)) Tr
x4
Figure 21: Block Diagram of Grid-Side Current Controller
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
22
3 The DFIG Wind-Generator Model
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.
Id_ref Id Iq_ref
Grid-Side Current Controller
Iq
Pmd
Pmq
Figure 22: Input/Output Definition of Grid-Side Current Controller
Table 24: Input Definition of Grid-Side Current Controller Input
Description
Unit
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 Output
Description
Pmd
d-Axis Pulse Width Modulation Index
Pmq
q-Axis Pulse Width Modulation Index
Unit
Table 26: Parameter Definition of Grid-Side Current Controller Parameter
Description
Units
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.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
23
DIgSILENT
3 The DFIG Wind-Generator Model
PLL:
Kpphi
0
K Kp
rr
dphi
sinphi 0
om_nom
sin(x) vr
dom
om
1/s
vi
ii K/s_lim K
yi
1
Kiphi
dommax
cosphi cos(x)
1
dommin
1/(2pi)
Fmeas
2
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.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
24
3 The DFIG Wind-Generator Model
Fmeas
PLL
sinphi cosphi
Figure 25: Input/Output Definition of PLL (Built-In Model)
Table 27: Output Definition of PLL Output
Description
Unit
Fmeas
Measured Frequency
Hz
sinphi
Sine of Voltage Angle
cosphi
Cosine of Voltage Angle
Table 28: Parameter Definition of PLL Parameter
Description
Kp
Controller Gain
Unit
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.
ir ii sinphi
Grid-dqTransformation
id iq
cosphi
Figure 26: Input/Output Definition of Grid-dq-Transformation
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
25
3 The DFIG Wind-Generator Model
Table 29: Input Definition of Grid-dq-Transformation Input
Description
Unit
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 Output
Description
Unit
id
d-Axis Current
p.u.
iq
q-Axis Current
p.u.
id iq sinphi
PhaseTransformation
ir ii
cosphi
Figure 27: Input/Output Definition of Phase-Transformation
Table 31: Input Definition of Phase-Transformation Input
Description
Unit
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 Output
Description
Unit
ir
Real Part of Output Signal
p.u.
ii
Im. Part of Output Signal
p.u.
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
26
3 The DFIG Wind-Generator Model
DIgSILENT
3.4.1.2 DC-Voltage Controller DC Voltage Control:
0
udc_ref
Max_idref
1
udc
-
dudc
id_ref
{K (1+1/sT)} Kudc,Tudc Min_idref
xidref
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).
udc_ref
DC-Voltage Controller
udc
id_ref
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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
27
3 The DFIG Wind-Generator Model
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 Parameter
Description
Units
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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
28
3 The DFIG Wind-Generator Model
DIgSILENT
3.5 Protection Protection:
Irot
0
Rotor Bypass MaxIrotor, tbypass
CrowBar
0
TripSpeed
speed
1
SpeedProt MaxSpeed1,ttripMaxS1, Ma..
1
bypass Max
2
u
2
TripVoltage VoltageProt MaxVoltage1,ttripMaxV1, ..
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 two for over-speed. If this protective unit triggers the machine breaker is opened. Rs
U
Zrot
Xs
Xm
Ur
Ur'= e
− jω r t
Ur
Additional Impedance
Figure 31: Equivalent Circuit Diagram of DFIG During Crow-Bar Protection
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
29
3 The DFIG Wind-Generator Model
The Crow-Bar protection is specific to doubly-fed induction generators and protects the rotor-side converter against overcurrents. 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.
Irot speed
DFIG-Protection bypass
u
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
bypass
Bypass-Signal (for Crow-Bar Insertion)
Units
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
30
3 The DFIG Wind-Generator Model
Table 38: Parameter Definition of DFIG-Protection Parameter
Description
Units
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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
31
4 Simulation Examples
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
DIgSILENT
presented in Figure 33 to Figure 35. 1.000 0.00 -1.000 -2.000 -3.000
0.00
1.000 PQ Control: Total Reactive Power (Q)
2.000
3.000
..
4.000
0.00
1.000 PQ Control: Total Active Power (P)
2.000
3.000
..
4.000
0.00
1.000 T3WT1: AC Voltage at HV side (u)
2.000
3.000
..
4.000
1.200 0.80 0.40 0.00 -0.400 -0.800
1.200 1.00 0.80 0.60 0.40 0.20 0.00
DIgSILENT
Doubly-fed Induction Generator - Example
Plot-1
Date: 5/26/2003 Annex: /1
Figure 33: Three-Phase Fault Far from Wind Generation, Connection Point
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
32
5.500
DIgSILENT
4 Simulation Examples
7.500 5.000
5.000
2.500 4.500 0.00 4.000 -2.500 3.500
3.000
-5.000
0.00
1.000 2.000 G1d: Stator Active Power
3.000
..
4.000
0.50
-7.500
0.00
1.000 2.000 G1d: Stator Reactive Power
3.000
..
4.000
0.00
1.000 2.000 3.000 PWM U1: Grid Side Converter Reactive Power
..
4.000
0.00
0.25
-0.100
0.00 -0.200 -0.250 -0.300
-0.500
-0.750
0.00
1.000 2.000 3.000 PWM U1: Grid Side Converter Active Power
..
4.000
-0.400
Doubly-fed Induction Generator - Example
DIgSILENT
Plot-2
Date: 5/26/2003 Annex: /2
DIgSILENT
Figure 34: Three-Phase Fault Far from Wind Generation, Stator- and Grid-Side Results
1.000 0.99 0.98 0.97 0.96 0.95 0.94
0.00
1.000
2.000
3.000
..
4.000
1.000 Prime Mover: Blade pitch Angle
2.000
3.000
..
4.000
1.000
2.000
3.000
..
4.000
G1d: Generator Speed 3.000 2.000 1.000 0.00 -1.000
0.00
4.500 4.400 4.300 4.200 4.100 4.000
0.00 Prime Mover: Wind Power
DIgSILENT
Doubly-fed Induction Generator - Example
Plot-3
Date: 5/26/2003 Annex: /3
Figure 35: Three-Phase Fault Far from Wind Generation, Mechanical Variables
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
33
4 Simulation Examples
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
DIgSILENT
grids. 1.000 0.00 -1.000 -2.000 -3.000
0.00
1.000 PQ Control: Total Reactive Power (Q)
2.000
3.000
..
4.000
0.00
1.000 PQ Control: Total Active Power (P)
2.000
3.000
..
4.000
0.00
1.000 T3WT1: AC Voltage at HV side (u)
2.000
3.000
..
4.000
1.200 0.80 0.40 0.00 -0.400 -0.800
1.200 1.00 0.80 0.60 0.40 0.20 0.00
DIgSILENT
Doubly-fed Induction Generator - Example
Plot-1
Date: 5/26/2003 Annex: /1
Figure 36: Three-Phase Fault Close to Wind Generation, Connection Point
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
34
6.000
8.000
4.000
4.000
2.000
0.00
0.00
-4.000
-2.000
-8.000
-4.000
0.00
1.000 2.000 G1d: Stator Active Power
3.000
..
4.000
1.200
-12.00
DIgSILENT
4 Simulation Examples
0.00
1.000 2.000 G1d: Stator Reactive Power
3.000
..
4.000
0.00
1.000 2.000 3.000 PWM U1: Grid Side Converter Reactive Power
..
4.000
4.000
0.80
3.000
0.40 2.000 0.00 1.000 -0.400 0.00
-0.800 -1.200
0.00
1.000 2.000 3.000 PWM U1: Grid Side Converter Active Power
..
4.000
-1.000
Doubly-fed Induction Generator - Example
DIgSILENT
Plot-2
Date: 5/26/2003 Annex: /2
DIgSILENT
Figure 37: Three-Phase Fault Close to Wind Generation, Stator- and Grid-Side Results
1.140 1.100 1.060 1.020 0.98 0.94
0.00
1.000
2.000
3.000
..
4.000
1.000 Prime Mover: Blade pitch Angle
2.000
3.000
..
4.000
1.000
2.000
3.000
..
4.000
G1d: Generator Speed 0.30 0.20 0.10 0.00 -0.100
0.00
4.400 4.300 4.200 4.100 4.000 3.900
0.00 Prime Mover: Wind Power
DIgSILENT
Doubly-fed Induction Generator - Example
Plot-3
Date: 5/26/2003 Annex: /3
Figure 38: Three-Phase Fault Close to Wind Generation, Mechanical Variables
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
35
4 Simulation Examples
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 (EMTsimulation). This more accurate model uses fifth-order generator models, including stator transients and differential equations
DIgSILENT
for all network components. 2.00 1.00 -0.00 -1.00 -2.00
-0.00 0.25 PQ Control: Total Reactive Power (Q)
0.50
0.75
[s]
1.00
-0.00 PQ Control: Total Active Power (P)
0.50
0.75
[s]
1.00
0.50
0.75
[s]
1.00
2.00
1.00
-0.00
-1.00
0.25
2.00 1.00 -0.00 -1.00 -2.00
DIgSILENT
-0.00 0.25 T3WT1: Phasenspannung L1/OS-Seite in p.u.
Doubly-fed Induction Generator - Example
Results at Connection Point Date: 8/11/2003 Annex: 1 /1
Figure 39: Single-Phase Fault Close to Wind Generation, Connection Point
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
36
7.50
9.00
5.00
6.00
2.50
3.00
0.00
0.00
-2.50
-3.00
-5.00
-0.00
0.25 G1d: Stator Active Power
0.50
0.75
[s]
1.00
-6.00
3.00
3.00
2.00
2.00
1.00
1.00
0.00
0.00
-1.00
-0.00
0.25 0.50 0.75 PWM U1: Grid Side Converter Active Power
[s]
1.00
-1.00
DIgSILENT
4 Simulation Examples
-0.00
0.25 0.50 G1d: Stator Reactive Power
0.75
[s]
1.00
-0.00
0.25 0.50 0.75 PWM U1: Grid Side Converter Reactive Power
[s]
1.00
Doubly-fed Induction Generator - Example
DIgSILENT
Active/Reactive Power
Date: 8/11/2003 Annex: 1 /2
DIgSILENT
Figure 40: Single Phase Fault Close to Wind Generation, Stator- and Grid-Side Results
1.14 1.10 1.06 1.02 0.98 0.94
-0.00 G1d: Generator Speed
0.25
0.50
0.75
[s]
1.00
-0.00 Pitch Control: Blade pitch Angle
0.25
0.50
0.75
[s]
1.00
-0.00 Turbine: Wind Power
0.25
0.50
0.75
[s]
1.00
0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15
4.40 4.30 4.20 4.10 4.00 3.90
DIgSILENT
Doubly-fed Induction Generator - Example
Mechanical Results Date: 8/11/2003 Annex: 1 /3
Figure 41: Single-Phase Fault Close to Wind Generation, Mechanical Variables
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
37
5 Conclusions
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
Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators
38
