Simulation of CMV-minimized Direct Power Control forDoubly Fed Induction Generators

B. Rueckert, W. HofmannDresden University of Technology

Department of Electrical Machines and DrivesHelmholtzstr. 9, 01069 Dresden, Germany

Phone: +49 (0) 351-463 39298Fax: +49 (0) 351-463 33655

Email: bastian.rueckert@tu-dresden.deURL: http://tu-dresden.de/et/ema

Keywords

<<Common mode voltage»>, < <Direct Power Control»>, < <Doubly fed induction generator»>

AbstractNowadays the doubly fed induction machine is often used as generator in high power windenergy sys-tems. Because of the use of two converters in the generator's rotor circuit bearing damages can occurespecially for this type of machine. So the aim is to reduce the common mode voltage as one cause ofbearing currents. Instead of a classic space vector modulation this paper presents the simulation of anenhanced direct power control.

IntroductionDue to the current debate on climate protection the interest in renewable energy is growing to reduce boththe C02-emissions as well as the dependence on fossil energy sources. A major contribution is madeby wind power. In the last few years the installed power is continuously increasing. Nowadays severaltypes of generators for converting the mechanical power into electrical power are used. Widespread isthe doubly fed induction generator (DFIG) for high power wind turbines. The stator is connected directlyto the grid and the rotor is fed by a back-to-back converter. The advantages of the DFIG are on the onehand the relatively small size of the inverters, which must deal only the slip power, and on the other handthe four-quadrant active and reactive power capabilities [4].Well known, but unfortunately often underestimated problems with converter fed machines are the oc-curring bearing damages in consequence of bearing currents. The causes of bearing currents are theswitching frequencies of the converter and the common mode voltage. The latter can be reduced bychoosing capable pulse pattern [7]. The use of two converters in the rotor circuit of a DFIG can achievemuch more critical states of the common mode voltage.Instead of using a modified space vector modulation this paper presents a direct control, in particular thedirect power control (DPC) which is based on the direct self control [2] and the direct torque control [5],respectially, in order to minimize bearing currents by using only active vectors.

System OverviewFor high power wind turbines the doubly fed induction generator is an interesting concept with a signifi-cant market potential. The advantages of such a system with variable speed are increased energy output,improved power quality as well as a reduced mechanical stress compared to fixed speed wind turbines.The stator is connected directly to the grid. The rotor-side back-to-back converter can be divided into

f0qg - PPgrS d, rf q,e

Figure 1: Complete schematics of doubly fed induction generator with direct power control

grid-side and rotor-side converter. Latter controlled the active and reactive power of the stator. The grid-side converter controls the dc-link voltage and ensures an operation at unity power factor. The completeschematics is shown in figure 1.

Modeling of the DFIG

Under the conditions and assumptions of a symmetrical design of the windings and no influence of ironlosses and saturation the voltage equations were obtained in a general reference frame using direct (d)and quadrature (q) axis representation as

dUs = Rs&s+ dtiVs +IOkNf (1

J~~~~~

LLr=Rrir+ dt Ui{r +j((k-(o)NJrand the flux equations as

vN= Lsls+Lhir]_s_ (2)

Summarizing the equation system (1) - (2) yields the following state space model for the DFIG

[Lr]JL TrGs TrG J(°:)k -))[Ur]'Jjand

02~~~~~~~q.e 6dc re qs t]ma(

where

TsGw= ,vTrG= and k = L, kr= 1 and 6G=lIkskr. (5)

At last the electromagnetic torque can be expressed with Zp as number of pol-pairs as

3m=-is sown in).g(6)

Modeling of the Main-Side Converter

The equivalent circuit shown in figure 2 yields

di dig [fal -1/3 (2sa -Sb-sc)]L- u= L-U+ftUd- with 97: [j ['-/3(2sL-sa j)

with s, as the switching state and Udc the dc-link voltage. The coherency between the grid current Lg andthe dc-link voltage Udc is given by the kirchhoff's law and can be expressed as

dudcCdc dt =Saga + b_gb + ScLgc - iload (8)

As well as the DFIG model the equations of the grid-side converter can be expressed in the state spacesystem:

[iga 1 I/L 0 0 fa/L] [iga] Uga

d igb 0 I/L 0 fb/L| igb| + Ugb| (9)dt igc - ° ° I-1L fc/L igc ugc

_Udc- Sa/L Sb/L SC/L ° IUdc- 'iload

5,S~~~~S. 1~~~load

0O* ~ ~ ~ ~ -

Figure 2: Schematic of the grid-side converter

Direct Power Control

The intention of the direct power control is to push the state ofthe system in each sampling time towards the reference value Lz, Lby evaluating the best suited voltage vector (available at theconverter output). A hysteresis regulator is used as a controller u;< u ()lufor the instantaneous power that selects the appropriate voltagevector from a lookup table [3], [6].Based on the equivalent ciruit shown in figure 3 the voltage Figure 3: Equivalent ciruit of the grid-sideequation can be transformed into converter based on space vectors

ALg ~JjA (ug-u5)bdt (10)

where Ts is the sampling time. The equivalent circuit is composed of the grid voltage ug followed by thegrid-filter and the voltage of the converter. This voltage is obtained from the switching states 5a,b,c andthe dc-link voltage.The instantaneous active and reactive power [1] is calculated by

q~~~~~ ~~~UaUf3ci-U a i

Thitetin f hediec p 1e [-to s ops hesaeo

where u' is 900 lag of ua. By changing into the new c43-reference frame, which is oriented with the gridvoltage vector (thus u = 0), the change of instantaneous active and reactive power can be expressed as

Ap UocAi, and Aq -uO /Aip . (12)

The space vector diagram in figure 4 shows the change ofcurrent vector for all six switching states of the converter

A2 ulfor one possible system state. As descriped in equa-tion (12) the ct-component of current will vary the active4: 3 2

Ai6 Ai5 power. And the 3-component will vary the inverse reac-tive power. With this knowledge the pq-axis can be draw

Y3 u// Ulmo wSw 8Sr Aat the current space vector position to see the change ofAl the instantaneous power for all six states. For the derive

\ /,4 *Ai of the switching table the c43-frame is devided into 12equal sectors. The resulting switching table is shown in

64-_ table I. For example to increase the active and reactivepower when the voltage vector is located in sector 4 youhave to use the converter state U2.

U5 'U6 A closer look at the equation (10) shows a dependence4: Space vector diagram: change of current of the dc-link voltage Udc on the current change Ai. The

Figre difference between grid and dc-link voltage influence thesize and direction of the current change. For a healthymode of operation for the control it is important that a

change of active and reactive power in any direction is available at any time. Hence follows a minimumdc-link voltage of double value from the grid voltage vector.

Ap Aq k=1 2 3 4 5 6 7 8 9 10 1 1 12> 0 > 0 ul LU U2 -U2 U-3 Lu3 U-4 m-4 UL5 Lu5 UL6 46> 0 < ° U2 U2 -U3 LU3 U-4 m4 Us5 U5Us 6 -U6 uILI< 0 >0 L5 u6 U-6 LUI UI 2 U-2 LU3 1U3 m4 U4 U5< 0 <0 u3 m-4 U-4 -U5 _U5 -U6 U-6 LUI LUI 2 U-2 LU3

Table I: Switching table for 12 sectors (k)

Simulation ResultsThe simulation was done in MATLAB/SIMULINKusing the parameters shown in table II. The grid-side and the rotor-side converter were simulated sep- Filter inductance 7.2mHarately to reduce model complexity and simulation Filter resistance 0.5Qtime. DC-link capacitor 1470,FThe grid-side converter is connected to a reduced DC-link voltage 600Vvoltage system in order to reduce the maximum nominal power of DFIG 4kWdc-link voltage as descriped in the previous sec- sampling time 5,pstion. The dc-link was loaded with a variable current average switching frequency 4kHzwhich change from negative to positive values. The Table II: Parameters used in the simulationresults are shown in figure 5.The rotor-side converter is connected to a constant dc-link voltage and the active power on the stator ofthe machine is changed from negative (generator) to positive (motor) values. Figure 6 shows the results.

Common Mode VoltageThe common mode voltage of a converter can be calculated as

11cmv =1/3 (Ua + Ub + Uc~) (13)

80 20 900 T 90056

> 40 2\ gridv i ephase 600 -0

_ 600

. 300 ~ oe g300o 20 /0 ~ ~ ~~~~00 0

7: 74:T:/:::0:\::: 1 > -300 l-300 .

gri c rrent ig9 -600 -*, , -600-60 - -15 active power pg-80 -20 -900 -900

0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80time in ms time in ms

Figure 5: Simulation of the grid-side converter

400 20 4 _ _ 4

> 200 gridv e phase / 10 200!/=,1 X reactivepowerq1

_ -100 S 12 c0 0 o0

too-0 -15 -3 -3

-400 2i0 -20 -40 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80

time in ms time in ms

Figure 6: Simulation of the rotor-side converter, showing the stator-side values

where Ua,b,c are the output voltages. For an applied zero vector the CMV reaches the maximim amplitude.This value is half of dc-link voltage, when the middle of the dc-link is connected to ground. The classicspace vector modulation needs zero vectors. Whose common mode voltage is shown in the left diagramof figure 7. By contrast, the proposed enhanced DPC uses only active vectors. Therefore the maximumamplitude can be reduced to one third with respect to the dc-link, as you can see in the right diagram offigure 7.

classic space vector modulation enhanced direct power control

0.8_.__._08;- 0.6_ __ _0.

ct .4-- -0o0.202

" 0

E -0.6 -0.2 Eo oo -0.8 _ _ _ -0.8

-1 -10 5 10 15 20 5 10 15 20

time in ms time in ms

Figure 7: CMV of grid-side converter for classic SVM (left) and enhanced DPC (right)

FFT Analysis of Current

0.1 t--------

-I-0. 1- --

.0 ------

.0 ~~~~0.1 ----------------I------------------

0.01

0- --.0 1-500- 1000-- -1500 2000- -2500 3000- -3500--- 4000 --4500-- --- 5000 --5500-- ---6000

fre in---H

Figure 8: FF -ocurrent fo te -lasi SV (bottom) and- the- enanedDP (top)

Because~~~~~~~~~~~~~~~~~--------------of-the non-constant swchig-rquny -hFF of current showsin- figue 8 widspread-frqec petu oatdaon heaeaeswthn reunyo kHz.In--comparison- tothe--- FFT

ofacretwthcascS Mte aiu mltde fteDCcurn r oe. utemr hlo c------- ts--- are------ ---sm aller.-------- ---------------------------7-

lu io n~~~~~~~------- ---------------------------------------------

Theproposed CMV~~~~~~--minimized------ DPC---shows----a--different-----way---to--control---a--------doubly----- fed-- idctasion genraorWith the enhanched------ switching----table----it--is-- possible-----to--reduce----the--common----mode---voltage----in--compa-----son--to

the classic space~~~~~-----vecor- oduatin.-the-adantge of-------------the----------------DPC----------- are------- the------- simple----- algorithm------with--- less-computation time-------as---well-----as---a--very----fast----dynamic-------behaviour.--------Furthermore--------a---low---harmonic------- distortion--------of-

current is obtained.~~-The-----------aveageswtchngfreueny-s-eua to--------------------------------- the----- one of a------ SVM------- but---produces----a--wide-frqun y p ct u w t only small -------------------low------------harm o n ics.---------------

-- --

[1] Afonso, J.;Freitas, M.; Martins, J.: p-q Theory power components calculations. IEEE International Sympo-~--------------siumonIndustrial Electronics, 2003, 1, 385-390~~~~~~~~~~~~~~~~~~~~--------------------------[2]Depenbrock, M.:Direct~~~~----------- self------control--------------(DSC)-----------of---invrte-fd-iducio mahie IEEE--- Transactionson-----------Power--

le tro ic s, 3,~~~----------- -4 ---[3] Malinowski,~~~~~~~M.;-------Kaziekowki-M.-Hnsn,-.;BlabjrgF.;--------------------------------------MaqusG.:----- irtual----flux---based---direct-power control~~~~~~~-----othe-phase--PWM--rectifiers.--IEEE-Transactions on Inusr Aplctos 2001,- 37,---------------1019---------1027~ ~~ ~~~~~~~~~--------

[4] Stupin,P.; Kuehnel, S.: Doppeltspeisende~~~~~~~~~~~---------Asynchrongeneratoren----bi 5, MWfue die Windenergie.----------Etz--- 2005--.7

[5] Takahashi,I.; Ohmori, Y: High-performance direct torque control of an induction motor IEEE Transactions---on Industry Applications, 1989, 25, 257-264~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- -------------I-[6] Xu, L.; Cartwright,P.: Direct Active and Reactive Power Control of DFIG for Wind EnergyGeneration.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~----------

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