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Transients in doubly-fed induction machines due to supplyvoltage sags

Y. Plotkin1

, C. Saniter1

, D. Schulz2

, R. Hanitsch1

1Institute of Energy and Automation Technology, Technical University of Berlin,

Einsteinufer 11, D-10587 Berlin, ,

2University of Applied Sciences Bremerhaven,

Research and Coordination Center Wind Energy,An der Karlstadt 8, D-27568 Bremerhafen

Abstract Transients in doubly-fed inductionmachines (DFIM) caused by supply voltage sags areinvestigated. They are explained in a comprehensibleway by decomposing the stator and rotor fields intostationary and rotating components. This method issimilar to the well known analysis for synchronousmachines.

I. Introduction

Increasing the share of electric power generatedby renewable energy sources is an importantpolitical goal in Europe and in many other

countries in the world. It reduces theenvironmental pollution caused by traditionalpower plants as well as the dependence on fossilfuels, which have limited reserves.

Electric energy, generated by wind power plantsis the fastest developing and most promisingrenewable energy source in Europe. Off-shorewind power plants provide higher yields becauseof better wind conditions. The power output of awind turbine is proportional to the cube of thewind speed (see Eq.1). Its theoretical limit is59.3% of the wind power input (Betz).

pcvAP =3

2

1 (1)

with

- air densityA rotor swept areav- wind velocitycp- power coefficient

The power coefficient depends on the pitch angleand the rotor speed to wind speed ratio (tip-speed ratio).

In Fig.1 the power output is plotted against therotors angular velocity at a constant pitch angle.Each curve represents a different wind speed.

Rotor

Power

VWind

Figure 1. Extracted wind power at a constant pitch angle.

It can be seen from the Fig.1, that the rotorspeed must be adapted if the wind speedchanges, in order to extract the maximum power.Thus, variable-speed and pitch-controlled windpower plants are dominating the marketnowadays. They are replacing the grid-connected induction generators which use thestall effect to limit their power output. Additionally, modern wind power plants allowpower factor control (normally cos=1), which isimpossible with uncontrolled turbines.


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grid side converter generator side converter

grid transformer

DFIMn1

n2

crow bar

a)

grid side converter

grid transformer

generator side converter

SMn1

n2

b)

Figure 2. Generator types in wind power plantsa) doubly-fed induction machineb) synchronous machine

II. Major Wind Power Plants Configurations

The two most common modern wind power plantconfigurations are:

a) Wind power plants with a synchronousgenerator and two full-sized converters or

b) doubly-fed induction generators with twoconverters in the rotor circuit.

Schematic representations are shown in Fig. 2.

In order to enable variable speed operationsynchronous generators are decoupled from thepower grid with its fixed frequency (50 or 60Hz)through two back-to-back frequency converters,which have a common dc-link. The maindisadvantage of this topology is that thefrequency converters are designed to handle thefull generator power output. This inevitablymeans higher costs.

Speed and power factor control for a doubly-fedinduction generator is achieved by controlling therotor currents [7]. The power delivered to, ortaken from, the rotor can be calculated usingEq.2.

sPPr = (2)

with

rP - rotor power

P - air gap power

s - slip

By limiting the speed range to +/- 30% ofsynchronous speed, the power rating of thefrequency converters is reduced advantageouslyto only 30% of the generators rated power. Thisresults in substantial cost savings.

III. Ride-through capability during voltage sags

Due to increasing contributions of wind farms tothe overall power generation, the necessity oftheir participation in grid stabilisation arises[1,2,4,6]. Especially under fault conditions theymust perform similarly to conventional powerplants. In recent years, grid codes have emergedin many countries, forcing wind farms to stayconnected and maintain operations for a certainperiod of time during voltage sags. The level ofthe voltage sags during which safe operation hasto be guaranteed differs greatly, e.g. down to

zero voltage in Australia or 15% in Germany.Such a voltage sag is not critical for wind powerplants using synchronous generators that areconnected to the grid through converters [5].The current into the grid is controlled by the gridside converter. In the case of a grid fault, theexcessive power produced by the generator iscontrolled through a chopper circuit, to keep thedc-link voltage constant. Thus, the operation of asynchronous generator during voltage sagsremains undisturbed.


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Such fault conditions are very demanding forwind energy converters using doubly-fedinduction generators (see Fig. 2a) [2,3]. Highvoltages are induced in the rotor winding duringvoltage sags. These voltages put the rotor sideconverter at risk. The rotor is short-circuited with

a so-called crow bar in order to protect theconverter. However, this may lead to a significantinitial torque, which may destroy the gear box.Additionally, undesired torque pulsations can beobserved.

IV. Transients of DFIM during voltage sags

Field components are analysed in order tounderstand the effects taking place in a doubly-fed induction machine during voltage sags. Thismethod is similar to the short circuit analysis forsynchronous machines. The time domainsimulation program Simplorer was used to

verify the theoretical predictions. Simplorerallows any power electronic circuit model to bebuilt up and include its respective control.Additionally, models for all major machine typesare provided.The simulations were carried out under thefollowing conditions:

The machine is operating at a sub-synchronous speed of 40Hz

The rotor terminals are short circuited atthe same moment as the voltage sagoccurs to simulate the crow baroperation.

Firstly, a voltage sag down to 0% (short circuit)was investigated.Sinusoidal currents flowing in the stator windingsform a spatially rotating field. After the shortcircuit has occurred on the stator terminals, thestator currents retain their phase angle and beginto decay. Thus, a spatially stationary field that isdecaying with time results. A similar process isobserved in the rotor, with one significantdifference: the decaying rotor currents form afield, which is stationary relative to the rotatingrotor. Thus, two superimposing field components

interact: the first one, stationary with respect tothe stator and the second one, stationary withrespect to the rotor rotating at some angularvelocity. These field components form a torquewhich is alternating with the angular frequency ofthe rotor (first torque component, shown below).The stationary stator field components inducevoltages and currents in the rotor windings,resulting in a non-pulsating torque that isopposing the rotation (second torque component,shown below). The torque is proportional to therotor angular velocity and to the amplitude of the

stationary stator field. This effect is similar to theone which takes place when deliberately brakingan induction motor using dc currents in the statorwinding.Parameters of a 1.5 MW wind plant generatorwere assigned to the DFIM model from the

Simplorer-library. These parameters were usedto simulate short circuiting of the stator - androtor terminals. Simulation results clearly showboth torque components described above (Fig.3a). One can recognise an alternatingcomponent (fist torque component) with adecaying offset (second torque component).Fourier-analysis over a short time span showsthat the frequency of the alternating componentis directly related to the rotor angular frequency(see Fig. 3 b).

6.45 6.5 6.55 6.6 6.65 6.7 6.75 6.8-1.5

-1

-0.5

0

0.5

1

1.5x 10

5

t [s]

T[Nm]

a)

10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

6

7

x 104

f [Hz]

T[Nm]

b)

Figure 3. Torque transients upon short circuiting statorterminals.

a) time domainb) frequency domain

The next step was to investigate a voltage sagdown to 10%. A field component at grid


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frequency with 10% of the nominal amplituderemains as opposed to the case of the shortcircuit. The remaining 90% of the stator fieldbecome stationary and decay as describedabove. The rotating stator field component andthe field component that is stationary with

respect to the rotor form the third torquecomponent at slip frequency.Simulation results confirm these theoreticalconsiderations (see Fig. 4). Fourier analysis ofthe torque yields three components: a smalldirect torque component, one component atangular frequency of the rotor, and a thirdcomponent at slip frequency

HzHzfZfHzf slippmechgrid 1022050 +=+== (3)

where Zp is the number of pole pairs.

6.45 6.5 6.55 6.6 6.65 6.7 6.75 6.8-1.5

-1

-0.5

0

0.5

1

1.5x 10

5

t [s]

T[Nm]

a)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

3.5

4

x 104

t [s]

T[Nm]

fmech.*Zp

fslip

b)

Figure 4. Torque transients after a voltage sag of 90%a) time domainb) frequency domain

The voltage induced in the rotor windings has avery high magnitude. Therefore, it is necessaryto protect the rotor side converter by using a

crow bar circuit. Torque amplitudes are veryhigh, and may become critical for gear boxes.

V. Summary

Grid codes have emerged in many countries,

requiring the ride through capability for windplants. This is very demanding for wind plantswith doubly-fed induction generators because oftransients that occur after voltage sags.

High voltages are induced in the rotor windings.They are dangerous for the rotor side converter.Thus, a crow bar circuit is used for protection.The inherent torque pulsations may reachsignificant amplitudes and are dangerous for thegear box. Torque transients were investigatedand explained in a comprehensible way bydecomposing the field into rotating and stationary

components. The presented simulation resultsconfirm the theoretical predictions.

References

[1] Bolik, S. M.: Grid requirements challengesfor wind turbines. Fourth InternationalWorkshop on Large-scale Integration ofWind Power and Transmission Networksfor Offshore Wind Farms, 20.21.10.2003,Billund, Denmark

[2] Franko, S.: More Sequrity AgainstBlackout (in German: Mehr Sicherheitgegen Blackout). Sonne Wind & Wrme6/2004, S. 80-82

[3] Hartmann, E.: Realisation of Grid CodeRules for Wind Power Plants (in German:Umsetzung von Netzanschlussregeln frWindenergieanlagen). ErneuerbareEnergien 5/2002, S. 34-36

[4] Hartge, S.; Fischer, F.: Wind Power Parkswith Power Plants Qualitys (in German:Windparks mit Kraftwerkeigenschaften).Erneuerbare Energien 6/2004, S. 31-33

[5] Hennechen, N.: Staying Connected to theGrid Upon Voltage Sags (in German: Am

Netz bleiben, wenn die Spannungeinbricht). Erneuerbare Energien 9/2002,S. 38

[6] Miller, N. W.: Power system dynamicperformance improvements fromadvanced control of wind turbinegenerators. Fourth Int. Workshop onLarge-scale Integration of Wind Power andTransmission Networks for Offshore WindFarms, 20.21.10.2003, Billund, Denmark

[7] Stiebler, M.: Lecture notes Dynamics ofelectrical machines, TU Berlin, Germany

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