Multi-Physical Domain Modeling of a DFIG Wind … domain modeling of a DFIG wind turbine system...

Multi-Physical Domain Modeling of a DFIGWind Turbine System using PLECS®

Min LuoPlexim GmbH

Technoparkstrasse 18005 Zürich Switzerland

1 Introduction

A cost and energy efficient method of wind powergeneration is to connect the output of the turbineto a doubly-fed induction generator (DFIG), allow-ing operation at a range of variable speeds. Whilefor electrical engineers the electromagnetic compo-nents in such a system, like the electric machine,power electronic converter and magnetic filters areof most interest, a DFIG wind turbine is a com-plex design involving multiple physical domainsstrongly interacting with each other. The electricalsystem, for instance, is influenced by the converter’scooling system and mechanical components, includ-ing the rotor blades, shaft and gearbox. This meansthat during component selection and design of con-trol schemes, the influence of domains on one an-other must be considered in order to achieve an op-timized overall system performance such that thedesign is dynamic, efficient and cost-effective. Inaddition to creating an accurate model of the entiresystem, it is also important to model the real-worldoperating and fault conditions. For fast prototypingand performance prediction, computer-based sim-ulation has been widely adopted in the engineer-ing development process. Modeling such complexsystems while including switching power electronicconverters requires a powerful and robust simula-tion tool. Furthermore, a rapid solver is criticalto allow for developing multiple iterative enhance-ments based on insight gained through system sim-ulation studies.

PLECS is a simulation platform developed forpower electronic engineers that allows for very ef-ficient and robust modeling of such systems withmulti-physical domains and associated controls.This application note presents a DFIG wind tur-bine system that is designed in detail using PLECS,where components from its different physical do-main libraries, including electrical, magnetic, ther-mal and mechanical, as well as signal processingand control systems, are coupled together and the

effects of the multi-domain interactions are investi-gated.

2 System Overview

2.1 Power in the wind

Wind turbines are capable of converting only a por-tion of the available wind power into mechanicalpower due to mechanical design considerations ofthe system. This mechanical power is expressed as:

Pmech =1

2⇢AC

p

v3, (1)

where ⇢ is the air density, A is the area swept by theturbine blades, C

p

is the performance coefficient ofthe turbine, and v is the wind velocity. For steady-state calculations of the mechanical power, the typ-ical C

p

(l, b) curve can be used [1] , as shown in Fig.1.

Fig. 1: Typical performance coefficient vs. tip speed ratio curve.

In the curve, b represents the blade pitch angle andl is the tip speed ratio, given by:

l =WRv

, (2)

Application Example ver 02-14

Multi-physical domain modeling of a DFIG wind turbine system

where W is the mechanical rotational speed of theturbine and R is the turbine radius. It can be ob-served that a certain turbine rotational speed mustbe maintained in order to achieve the maximummechanical power input under a given wind speedand blades pitch angle. In normal operation thepitch angle remains constant, while in special casessuch as under strong winds, the pitch control is ac-tivated to shed the excess wind power and protectthe wind turbine from damage.

2.2 Electromagnetic system

The electrical part of the DFIG wind turbine con-sists of a wound-rotor type induction machine. Themachine’s stator terminals are directly connected tothe medium-voltage grid via a three-winding trans-former, while the rotor is excited by one end of thepower electronic converter, consisting of two AC-DCconverters in a back-to-back configuration with acommon DC-link bus. The grid-side of the converterfeeds the rotor power into the grid via the trans-former’s tertiary winding. The system overview isshown in Fig. 2.

Fig. 2: System overview of the wind turbine with DFIG.

Under a limited variable-speed range (e.g. ±30%)the converter only needs to handle a percentage(20 � 30%) of the total power [2], which in steady-state is given by:

Pr

=s

1−sPmech

, (3)

The power flow on the stator is given by:

Ps

=Pmech

1−s, (4)

In both of the above equations, s is the slip of themachine, and is defined by:

s =w1−ww1

, (5)

where w1 is the stator electrical rotational fre-quency, which is synchronous with the grid, and

w is the electrical rotational speed of the machine.The DFIG configuration is significantly more costeffective and less lossy as compared to a configura-tion using a permanent magnet generator (PMSM),which is the other common option and where theconverter uses the full power range.

2.3 Cooling system

Power is dissipated during the wind turbine’s op-eration, in part due to the conduction and switch-ing losses of the semiconductor devices (IGBTs anddiodes) in the converter. The power losses not onlyreduce the available electrical power that can be fedinto the grid but also lead to high junction temper-atures, which may destroy the semiconductor de-vices. Therefore, a proper cooling system should beused with the converter system such that as muchheat-conduction will be transferred away from thesemiconductors as is possible.

2.4 Mechanical system

The rotational components of the wind turbine cou-ple the mechanical and electrical systems. Thethree blades transfer the wind torque to the hubshaft, which is connected to a gearbox. Using aspecific gear ratio the gearbox boosts the rotationalspeed of the hub shaft onto the shaft of the induc-tion machine’s rotor. The coupling between the com-ponents shows elastic and damping effects due tothe material characteristics, and friction occurs onthe bearings, which also leads to power losses.

Fig. 3: Mechanical system of a wind turbine.

Application Example 2


Fig. 4: Schematic of the DFIG wind turbine model in PLECS.

3 Modeling in PLECS

A 2 MW DFIG wind turbine model has been de-signed in PLECS and a top-level diagram is shownin Fig. 4. The components of the system are fromthe libraries for the different physical domains, in-cluding electrical, magnetic, mechanical, as well assignal processing and control systems.

3.1 Electrical domain

The wound-rotor induction machine, power elec-tronic converter and LCL filter, as well as the longdistance transmission line and medium-voltage(MV) grid are all modeled in the electrical domain:

• Induction machine: The wound-rotor induc-tion machine model (the “Induction Machine(Slip Ring)” library component) is based on astationary reference frame (Clarke transforma-tion). A proper implementation of the Clarketransformation facilitates the connection of ex-ternal inductances in series with the statorwindings, which in this case are the leakage in-ductances of the transformer. External induc-tors cannot be connected to the rotor windingsthough, due to the fact that the electrical inter-faces there are modeled as controlled currentsources.

Fig. 5: The PLECS induction machine component.

• Power converter: The back-to-back convertertopology is selected for control of the rotor

power, where two three-leg, two-level IGBTbridges are connected together via a DC-linkcapacitor. For protection reasons a chopperIGBT and break resistor is connected onto theDC-link to clamp the capacitor voltage to asafe level. The switch will be turned on todischarge the DC-link in the case of overvolt-age conditions, and turned off when the voltagefalls back to the nominal value. The rotor-sideinverter is directly connected to the inductionmachine’s rotor, while the grid-side inverter isconnected through an LCL filter to the tertiarywinding of the transformer. The IGBTs of theinverters are modeled as ideal switches to guar-antee a fast simulation at system level.

Fig. 6: Back-to-back converter model.

• Filter: The LCL-type filter is used to smooththe current ripple caused by the PWM modula-tion of the grid-side inverter. According to theelectric grid code for renewable energy genera-tion, a certain THD standard needs to be ful-filled when selecting the inductance and capac-itance values. In comparison to the inductor-only filter, the LCL filter is able to suppress theharmonics with much smaller inductance val-ues, and the reduced weight and volume there-fore leads to a higher power density. Two res-onant frequencies are introduced into the sys-tem due to the capacitor, however, which maygive rise to stability issues [3].

Fig. 7: LCL filter model.



• Transmission line: The wind capacity isstrongly influenced by an area’s geography.Wind turbines are often placed far from thehigh voltage-to-medium voltage (HV/MV) sub-station, so the transmission line (normally anunderground cable in Europe) that transfersthe wind power to the upper-level grid canbe tens of kilometers in length. To modela cable of such a long distance, one can ei-ther connect multiple PI-sections (capacitor-inductor-capacitor) together in series, or im-itate the traveling-wave behavior of the cur-rent and voltage. Both options are providedin the transmission line model found in PLECSand can be selected based on different require-ments. The PI-section implementation is intu-itive to the user, however, implementing an ac-curate cable model with it requires many sec-tions. This create a large number of state vari-ables and may slow down the simulation dras-tically. The distributed parameter line imple-mentation based on the analytical solution of atraveling wave calculates the delay time of thecurrent or voltage waveform as it propagatesfrom one end of the cable to the other [4], andthus avoids the simulation speed issue relatedto an increase in state variables. But unlikethe PI-section implementation, it models thepower losses as lumped resistances, and onlythe case of symmetrical parameters (e.g. induc-tance) among the three phases can be modeled.

Fig. 8: The PLECS transmission line component.

• MV grid: The medium-voltage grid is simpli-fied as a three-phase voltage source with a line-to-line voltage of 10 kVrms.

Fig. 9: Medium-voltage grid model.

3.2 Magnetic domain

The three-phase, three-winding transformer inter-faces the 10 kV medium-voltage grid and the low-voltage terminals of the DFIG. A voltage of 690 V

Fig. 10: Transformer model in the PLECS magnetic domain.

(line-to-line rms) is chosen for the stator-side of theDFIG, while 400V is used for the rotor-side. In orderto eliminate the influence of the zero-sequence com-ponent, the windings have a �-connection at the10 kV side and a midpoint grounded Y-connectionat the low-voltage side. The transformer is mod-eled using components from the PLECS magneticlibrary. Magnetic modeling in PLECS offers apowerful method for modeling such components bydirectly capturing a magnetic circuit using wind-ings and lumped core parts with user-specified ge-ometries. These core parts are represented aslumped permeances and connected with each otherin PLECS to create a magnetic circuit [5]. Com-pared to a co-simulation with a finite element anal-ysis (FEA) tool, where magnetic field analysis isused in the modeling of a magnetic structure, thislumped magnetic circuit method is able to inte-grate magnetic component models into a systemlevel simulation without causing any substantialincrease in simulation time. It also provides moredetails than modeling a magnetic structure as apurely electrical equivalent circuit, such as non-linearities caused by saturation and hysteresis [6].In addition, the separation of electrical and mag-netic domains provides the user a clearer overviewwhen approaching the actual hardware construc-tion. In this model, the YY� connected three-legiron core transformer with laminated material isdesigned and each leg is modeled as a magnetic



permeance. Eddy current power losses are repre-sented by magnetic resistance components, whichare series-connected to the permeances. The wind-ing components serve as the interface between theelectrical and magnetic domains, and leakage fieldsare modeled with leakage permeances, which areconnected in parallel to the windings in the mag-netic domain. The complete model is shown in Fig.10, where the linear permeance core componentscan be replaced by permeances with saturation orpermeances with hysteresis to simulate nonlineareffects.

3.3 Thermal domain

The semiconductor power losses of the voltagesource inverters play an important role in the con-verter design and can be investigated using PLECS’thermal domain. The PLECS ideal switch approachyields fast and robust simulations. Accurate con-duction and switching loss calculations of the IGBT(and diodes) are achieved via look-up tables that areeasily populated with values from data sheets.

Fig. 11: The PLECS thermal look-up table interface. This shows the turn-on

loss table for an IGBT.

Fig. 11 demonstrates the two dimensional look-up table for turn-on losses in PLECS, with valuesobtained from a data sheet [ABB’s IGBT module5SNA1600N170100]. The data sheet provides thecurve of the loss energy vs. conducting current,however, for only one blocking voltage condition

(1500 V). The loss values for other blocking volt-ages are linearly extrapolated from 0 V, which hasbeen verified as a acceptable approximation in prac-tice. The dependence of temperature in determin-ing power losses can be established, and the ther-mal energy transfer characteristics from the junc-tion to the case can be specified.

The PLECS heat sink component absorbs the powerlosses produced by the components that it contains.It feeds these losses to the cooling system, which issimply modeled in this case as a thermal resistance.The ambient temperature is modeled as a constanttemperature sink. During the simulation, the junc-tion temperature of the IGBTs can be monitored toensure the cooling system is properly sized. Majorand minor temperature cycles of the semiconductordies can be used for life and reliability analyses.

Fig. 12: Cooling system modeled in the thermal domain.

3.4 Mechanical domain

The variations of the aerodynamic torque on theblades and, consequently, electrical torque on theinduction machine’s rotor are propagated to thedrivetrain of the wind turbine. The resulting fluc-tuations of the rotational speeds can lead to dis-turbances in the electrical domain, which dependsubstantially on the torsional characteristics of thedrivetrain to dampen out the oscillations. Thismodel uses a wind source to perturb the mechani-cal system in order to investigate the effects of suchsystem resonances. The three blades transfer thewind torque to the hub shaft, which is connected toa gearbox. Using a specific gear ratio, the gearboxincreases the rotational speed of the hub shaft ontothe induction machine’s rotor shaft. Friction occurson the bearings, leading to additional power losses.The mechanical portion of this model consists of anumber of lumped inertias [7], which are elasticallycoupled with each other, as shown in Fig. 13 andFig. 14.

The inertias of the three blades are shown as



Fig. 13: Complete drivetrain modeled in the PLECS mechanical domain.

Fig. 14: Propeller drivetrain model.

J_blade1, J_blade2, and J_blade3, J_hub is thehub inertia, J_Gearbox is the gearbox inertia, andthe inertia of the induction machine’s rotor is in-cluded under the machine component mask. Thespring constants k_hb1, k_hb2, k_hb3, k_hgb, andk_gbg model the elasticity between adjacent massesand d_hb1, d_hb2, d_hb3, d_hgb, and d_gbg repre-sent the mutual damping. J_blade1, J_blade2, andJ_blade3, J_hub, and J_Gearbox model the frictionin the system, which produces torque losses on in-dividual masses.

A wind torque input depending on wind speed andpropeller rotational speed is provided. As men-tioned previously the typical C

p

(l, b) curve can beadopted for modeling this, and can be transformedto a surface of wind torque vs. wind speed and tur-bine rotational speed as shown in Fig. 15.

3.5 Control design

A proportional-integral (PI) controller with activedamping and anti-windup is utilized for the controlof the machine-side and grid-side inverters, as de-scribed in [2]. The main task of the machine-sideinverter is to regulate the DFIG torque and thus therotational speed of the rotor, as well as the DFIG re-active power that is injected into the grid via the in-duction machine’s stator windings. The speed con-trol scheme comprises an inner fast current loop

Fig. 15: Wind torque vs. wind speed and turbine rotational speed surface.

that regulates the rotor current and an outer slowspeed loop, which provides the reference signal forq-axis current control. A similar structure is uti-lized for reactive power control.

The current control is implemented in a flux-oriented manner, where the rotor current is decom-posed into the d- and q-axis in the rotational frame,which are DC values during steady state. For pa-rameter selection the state-space model of the in-duction machine is derived in a form of complex vec-tors, where the physical variables have been trans-formed to the stator-side using the turns ratio:

vs

= Rs

is

+dY

s

dt+ jw1Ys

(6)

vR

= RR

iR

+dY

R

dt+ jw2YR

, (7)

where

Ys

= LM

(is

+ iR

) (8)

YR

= (LM

+ L�

)iR

+ LM

is

(9)

w2 = w1−w (10)

Note that the stator leakage inductance has beeneliminated in the equations above, due to the factthat the stator flux is selected as the reference vec-tor. Graphically the state-space model can be ex-pressed as a circuit schematic for the d- and q-axis,respectively, as shown in Fig. 16.

By substituting the equations for the stator voltageand flux linkage into the one for the rotor voltage,we find that:



Fig. 16: State-space model of the induction machine in the rotational frame.

vR

= (RR

+Rs

+ j!2L�

)iR

+ L�

diR

dt+ E, (11)

where the back EMF, E, is equal to:

E = vs

−(R

s

LM

+ jwYs

) (12)

Rewriting the equations in the d-q axes separatelyyields:

vRd

= (RR

+Rs

)iRd

−w2L�

iRq

+L�

diRd

dt+v

sd

� Rs

LM

s

(13)

vRq

= (RR

+Rs

)iRq

+w2L�

iRd

+ L�

diRq

dt+ v

sq

� ! s

(14)

The two equations above express the state-spacemodel of the rotor current i

R

with the rotor volt-age v

R

as the input variable. Variation of the backEMF may lead to tracking error, and like the crosscoupling term from the other orthogonal axis, canbe regarded as a disturbance. Such disturbancescan be suppressed effectively via feedforward con-trol. The resulting structure of the current con-troller is shown in Fig. 17 and Fig. 18. The outputof the current controller will be given to the spacevector pulse-width modulator (SVPWM) to generatethe PWM signals for the three-phase terminal of theIGBT bridge.

Fig. 17: D-axis current controller of the machine-side inverter.

Fig. 18: Q-axis current controller of the machine-side inverter.

The stator flux linkage Ys

is present in the feed-forward term of the back EMF, however this is noteasily measured in the hardware implementation.Therefore an estimation approach using the statorcurrent and voltage as input variables has beenadopted instead [8]. Based on the implementedstate-space model, the proportional and integralgains of the PI controller are selected as:

Kp = ↵c

L�

(15)

Ki

= ac

(RR

+Rs

+Ra

), (16)

where ac

is the desired bandwidth of the closed-loopsystem. It can be related to the rise time of a stepresponse as:

↵c

=ln(9)

trise

(17)

Also, a virtual resistance Ra

has been introduced tomake sure that the disturbance (e.g. the estimationerror of the back EMF) will be dampened with the



same time constant as the forward control scheme,which is also known as “active damping”. R

a

is de-fined as:

Ra

= ac

L�

−RR

−Rs

(18)

The reference signal for the q-axis current is pro-vided by the speed controller, whose design is basedon the simplified mechanical model of the wind tur-bine:

Jtotal

np

dwdt

= Te

−Twind

, (19)

where Jtotal

is the total sum of the inertia of allthe masses transformed to the high-speed side ofthe gearbox, n

p

is the number of pole pairs, Te

isthe electrical torque applied on the induction ma-chine’s rotor, and T

wind

is the wind torque trans-formed to the high-speed side of the gearbox. An“active damping” term is also introduced here to im-prove the damping of the disturbances. To avoidovershoot problems due to the clamping of the reg-ulator outputs, an anti-windup method is used.

Fig. 19: Speed controller of the machine-side inverter.

At the output of the speed controller, the referencetorque is converted to a current signal using:

i⇤Rq

=2T

e

3np

Ys

(20)

In a real wind turbine system, the turbine powercontroller often uses a maximum power point track-ing (MPPT) scheme to provide the reference signalfor the speed controller. In this case however, anMPPT scheme is not modeled considering the rela-tively short time range of the simulation and a con-stant value is instead given as the speed reference.

The reference signal of the d-axis current controlleris given by the reactive power controller. Accordingto the regulations of German transmission systemoperators [9], the wind generator should be able toprovide voltage support in terms of inductive or ca-pacitive reactive power injection during fault condi-tions. The instantaneous apparent power which isabsorbed by the induction machine’s stator termi-nals can be expressed in form of a complex vector:

Ss

= 3vs

i⇤s

= 3(Rs

is

+dY

s

dt+ jw1)i⇤

s

(21)

Under the assumption that the stator flux linkageschange only slightly, the reactive power can be ex-pressed in the d-q frame with the derivative termneglected:

Qs

= 3!1( sd

isd

+ sq

isq

) (22)

In a stator flux oriented system the q-axis compo-nent of the stator flux is zero, so the equation abovebecomes:

Qs

= 3!1 s

isd

= 3!1(Y

s

LM

� iRd

) (23)

This is rewritten as:

i⇤Rd

=Y

s

LM

� Qs

!1(24)

In this way a static algebraic relationship is estab-lished between the reactive power and d-axis rotorcurrent, and an integral controller (I controller) isapplied, as shown in Fig. 20. The integral factor ofthe I controller is given as:

KiQ

= � ↵Q

3!1 s

, (25)

Fig. 20: Reactive power controller of the machine-side inverter.

where aQ

is the desired bandwidth. Considering thefact that the stator resistance is usually small, thestator flux Y

s

in the equation above can be replacedby w1Vg,nom

, where Vg,nom

is the nominal grid peakvoltage on the stator-side of the induction machine.

The grid-side inverter maintains the DC-link volt-age at a constant level. Similar to the machine-sideinverter, a two-loop configuration is set up for thegrid-side inverter with an outer loop for voltage con-trol and an inner loop for current control. The cur-rent control loop is implemented in the d-q frameand is synchronized with the grid voltage, wherethe orientation reference is provided by a phase-locked loop (PLL).

An LCL filter is selected for the AC output terminal.Currently, this type is considered to be an attractive



solution to attenuate the switching frequency cur-rent ripple compared to the pure inductance filterdue to the lower size of the magnetic components.Given the maximum ripple current I

hfpp

(peak-to-peak) on the inverter output terminal, the induc-tances L

f1a, Lf1b, and L

f1c in Fig. 7 can be deter-mined by:

Lf1 = cos(

p6)2/3V

dc

−Vg3

Ihfpp

fsw

p3V

g3

Vdc

, (26)

where Vg3 is the nominal voltage (peak value) on

the tertiary winding of the transformer. The ratiobetween the inductance values L

f1 and Lf2 can be

treated as an operational variable for optimizationof overall size and cost. In this model it is assumedthat a value of L

f2 = 0.15Lf1 has been chosen as

a result of the optimization. According to the THDrequirement for the grid operator, which is the ratiobetween the peak-to-peak value of the nominal gridcurrent I

gpp

and ripple Ihfpp

, the capacitance valuecan be calculated as:

Cf

= 11

Lf2(2pfsw10

kA40dB )2

, (27)

where the attenuation kA

is given as:

kA

= 20log10(THDIgpp

Ihfpp

) (28)

4 Model Parameters and Simulation Scheme

The electrical parameters of the doubly-fed induc-tion machine according to [10] are listed below inTable 1, where the rotor parameters have been con-verted to the stator-side using the turns ratio.

Table 1: Electrical parameters of the induction machine.

Pole pairs np

2

Turns ratio ns

/nr

1/2.6

Stator leakage Ls�

0.12 mH

Rotor leakage L0

r�

0.05 mH

Main inductance Lm

2.9 mH

Stator resistance Rs

0.022 ⌦Rotor resistance R

0r

0.0018 ⌦

The transformation from the physical parametersin Table 1 above to the ones of the equivalent circuitin Fig. 16 is achieved via the following equations:

LM

= gLm

(29)

Lsigma

= gLs�

+ �2L0

r�

(30)

RR

= g2Rr

, (31)

where

� = (Ls�

+ Lm

)/Lm

(32)

As a result of the aforementioned design processfor the LCL filter, the inductance value of theconverter-side as well as grid-side inductors are cal-culated as 0.48mH and 0.044mH, respectively, whilethe capacitance value is 57 mF. For connectionfrom the turbine transformer to the 10 kV stiff grid,the model of a 10 kV medium-voltage cable (typeN2XSF2Y [10]) is established using the distributedparameter line component. The resistance, self-inductance and neutral capacitance per unit lengthare 0.206 W/km, 0.363 mH/km and 0.25 mF/km, re-spectively. The mutual inductance and coupling ca-pacitance are assumed to be one third of the self-and neutral values. The mechanical parameters ofan example 2MW wind turbine are provided by [10]and [7] in per unit values, and the transformationfrom per unit to real values has been described in[11].

Table 2: Mechanical parameters of the wind turbine.

Rotor inertia Jg

75 kgm2

Gearbox inertia Jgb

4.26⇥ 105 kgm2

Hub inertia Jh

6.03⇥ 104 kgm2

Blade inertia Jb

1.13⇥ 106 kgm2

Rotor friction Dg

0.81 Nms/rad

Gearbox friction Dgb

1.78⇥ 104 Nms/rad

Hub friction Dh

8.11⇥ 103 Nms/rad

Blade friction Db

1.08⇥ 103 Nms/rad

Gearbox to rotor stiffness kgbg

4.67⇥ 107 Nms/rad

Hub to gearbox stiffness khgb

1.39⇥ 101 Nms/rad

Blade to hub rotor stiffness kbh

1.07⇥ 101 Nms/rad

Gearbox to rotor damping dgbg

0.81⇥ 103 Nms/rad

Hub to gearbox damping dhgb

2.84⇥ 106 Nms/rad

Blade to hub rotor damping dbh

3.24⇥ 106 Nms/rad

During the simulation the following example sce-narios are executed successively:

• Initial state: At the simulation start the gen-erator operates at 157 rad/s, which is syn-chronous to the grid frequency. Most of the gen-erated active power is injected into the grid via



the stator winding of the induction machine,while due to the zero slip condition, virtuallyno power flows through the rotor except for theresistive losses. The reactive power generationis not activated yet at this stage.

• Acceleration: At 3 s the rotation speed ofthe turbine is accelerated to 175 rad/s via astep jump on the reference input of the speedcontroller, to achieve maximum power gener-ation under the given wind speed of 12 m/s.As mentioned previously, the external MPPTloop utilized in a practical implementation isnot present in this model. The step change ofthe speed reference is just a fictional one whichsets up the machine for an extreme test case toprove the system’s stability.

• Grid fault: At 12 s a three-phase short circuitfault occurs on the 10 kV medium-voltage grid,which is modeled using a controllable voltagesource. Three fault options regarding the resid-ual voltage’s profile can be chosen. The first op-tion is a 0.2 s zero voltage sag, while the othertwo options are described in the 2007 GermanTransmission Code Standards [9], as Fig. 21shows.The duration of the simulation has been setto 25 s, which should be sufficient to inves-tigate the reaction from the overall systemstandpoint, especially considering the mechan-ical part. This timeframe is however, relativelylong compared to the switching frequency ofthe back-to-back converter (5 kHz). If the cur-rent ripple due to the switching frequency andpower losses of the semiconductors are not ofinterest for certain applications, an averagedconverter model can be used to speed up thesimulation. The averaged model is establishedvia controlled voltage and current sources, asshown in Fig. 22, and can be optionally selectedfrom the mask.

Fig. 21: Voltage profiles during the event of a grid fault.

Fig. 22: Averaged model of the three-phase inverter.

5 Results and Discussion

By simulating the scenarios described above, therobustness of the design is observed and improve-ments can be made, namely with the control tech-niques. The various parameters in the system arechosen to provide desirable results during the en-tire operating range of the turbine. At the startof the simulation, a damped oscillation can be ob-served due to the elastic and lossy coupling betweenthe mechanical parts, as shown in Fig. 23.

Fig. 23: Mechanical oscillation at startup of the wind turbine.

As the step change for the speed reference isapplied, the speed controller generates a torquereference for the q-axis current controller of themachine-side inverter which is higher than thewind torque applied on the blades, thus the turbineaccelerates. The behavior of rotational speed andtorque is illustrated in Fig. 24, where the speedvalues of the hub and blades have been convertedto the high-speed side of the gearbox (the inductionmachine shaft side). After approximately 7 s, theelectrical torque of the induction machine and thewind torque enter a balanced state and the rota-



tional speed remains 175 rad/s. As a result of the�11% slip rate, about 10% of the real power will nowbe transmitted out of the rotor winding, as shown inFig. 25.

Fig. 24: Mechanical reaction during acceleration.

Fig. 25: Active and reactive power flow out of the stator and rotor during

acceleration.

If the averaged model is chosen for the simulation,the electrical torque waveform will be ripple-freeand match the mean value of the torque waveformfor the model with ideal switches, as seen in Fig. 26.

Fig. 26: Electrical torque of the induction machine in the averaged model.

To evaluate the performance of the wind turbine

during a worst case grid-side fault condition, knownas “low voltage ride through” (LVRT) behavior, andthe borderline 2 scenario from Fig. 21, is set upfor the voltage profile during the grid short circuit.As the grid voltage falls to zero at 14 s, the statorflux deceases to an extremely small value, wherethe induction machine is no longer able to gener-ate electrical torque. When this happens, the powerabsorbed by the blades from the wind will be com-pletely stored in the rotating mechanical compo-nents in the form of kinetic energy, and the tur-bine will accelerate. After the voltage starts to re-cover due to the clearing of the fault after 0.15 s, thestator flux recovers gradually such that electricaltorque can be produced again to counteract the driv-ing torque from the wind. As a result the speed willbe restored back to the reference value 175 rad/s, asshown in Fig. 27.

Fig. 27: Mechanical transient during the grid fault.

The electrical transient of voltage and current onthe primary winding (10 kV side) of the transformer,as well as the DC-link voltage of the back-to-backconverter, is displayed in Fig. 28. The AC volt-age on the transformer terminal does not fall tozero as the grid is stiff due to the inductance of thetransmission line in between. The AC current ex-hibits a large peak immediately after the fault oc-curs, and then is maintained below a certain rangebecause of the saturated input of the current con-troller. Due to the voltage drop at the transformer’stertiary winding, the grid-side inverter is also nolonger able to transfer power, so the DC-link voltageis nearly uncontrolled in the first seconds after thefault. The DC-link capacitor is then charged or dis-charged purely by the machine-side inverter. Thetransient of the active power from the machine-sideinverter can be analyzed using the q-axis equiva-lent circuit in Fig. 16.Immediately after the fault occurs, the q-axis volt-age v

Rq

and current iRq

of the rotor still remainas the same values seen during normal operation.



Fig. 28: Electrical transient during the grid fault.

Therefore, nearly the identical amount of activepower as before the fault charges the capacitor, suchthat the voltage rises quickly. The voltage will notexceed 108% of the nominal voltage (950V), however,and is clamped to a safe level due to the activation ofthe chopper circuit. The speed controller will thendeliver a higher reference value for the q-axis cur-rent to the current controller to pull the rotationalspeed back to 175 rad/s, although it is unsuccessful.

As a result, the current controller applies a q-axisvoltage v

Rq

of opposite polarity compared to beforethe fault, because of the nearly zero value of theback EMF wY

s

. Hence, the active power becomesnegative for a short time, and the capacitor is dis-charged and the voltage falls until approximately12.3 s. After that, as the grid voltage recovers, theback EMF wY

s

rises so vRq

changes its polarity backto what it was before the fault, and the active powerbecomes positive, effectively re-charging the capac-itor. At this moment the grid-side inverter is stillnot able to transfer a large amount of power, there-fore the net power flowing into the capacitor is stillin surplus and the voltage rises further. Because ofthe chopper circuit, the voltage oscillates betweenthe limitation and the nominal value in the follow-ing several seconds, until the grid voltage totallyrecovers and the grid-side inverter is again able totransfer enough power.

If this fault scenario is simulated with the averagedinverter model, the result shows slight differencesfrom that with the full switching model, because theswitching period is comparable to the transient dur-

ing the fault condition. This issue should be consid-ered if the averaged model is used to accelerate thesimulation speed. As shown in Fig. 29, the lighterred curve corresponds to the switched model.

The thermal information, including the junctiontemperature and losses for one IGBT over thecourse of the total simulation, is depicted in Fig. 30.Note that the switched inverter model must be en-abled in order to view these waveforms.

Fig. 29: Comparison of the DC-link voltage between the averaged and

switched inverter model.

Fig. 30: Junction temperature, conduction and switching losses of one IGBT.



6 Conclusion

The modeling and simulation of a complete DFIGwind turbine model has been presented in this re-port. With the help of PLECS, the transient effectsfrom multiple physical domains can be evaluatedin a single system model without requiring exces-sive simulation times, thereby providing an effec-tive and accurate means for investigating and ad-dressing issues related to inter-physical domain in-teractions. Such fully integrated models providepower electronic designers with more insight intothe system before hardware is built, leading to timeand cost savings.

References

[1] J. Schönberger, “Modeling a dfig wind turbinesystem using plecs,” in Application Note ofPlexim GmbH.

[2] A. Petersson, Analysis, Modeling and Controlof Doubly-Fed Induction Generators for WindTurbines. PhD thesis, Chalmes University ofTechnology, Göteborg, Sweden, 2005.

[3] R. Teodorescu, M. Liserre, and P. Rodriguez,Grid Converters for Photovoltaic and WindPower Systems. Aalborg: John Wiley & Sons,Ltd, 1. edition ed., 2011.

[4] H. Dommel, “Digital computer solution of elec-tromagnetic transients in single and multiplenetworks,” in IEEE Transactions on Power Ap-paratus and Systems, pp. Vol. PAS88, No. 4.

[5] J. van Vlerken and P. Blanken, “Lumped mod-eling of rotary transformers, heads and elec-tronics for helical-scan recording,” in Controland Modeling for Power Electronics (COM-PEL), IEEE 13th Workshop on, 2012.

[6] J. Allmeling, W. Hammer, and J. Schönberger,“Transient simulation of magnetic circuits us-ing the permeance-capacitance analogy,” inControl and Modeling for Power Electronics(COMPEL), IEEE 13th Workshop on, 2012.

[7] S. M. Muyeen, M. H. Ali, R. Takahashi, T. Mu-rata, J. Tamura, Y. Tomaki, A. Sakahara, andE. Sasano, “Blade-shaft torsional oscillationminimization of wind turbine generator sys-tem by using statcom/ess,” in Power Tech, 2007IEEE Lausanne, pp. 184–189.

[8] Analog Devices Inc, “Flux and speed estima-tion for induction machines,” in ApplicationNote AN331-29.

[9] Verband der Netzbetreiber VDN e.V. beimVDEW, “Network and system rules of the ger-man transmission system operators,” in Trans-mission Code, 2007.

[10] T. Thiringer, J. Paixao, and M. Bongiorno,“Monitoring of the ride-through ability of a2 mw wind turbine in tvaaker, halland,” inElforsk rapport 09:26.

[11] A. G. G. Rodriguez, A. G. Rodriguez, and M. B.Payan, “Estimating wind turbines mechanicalconstants,”


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