cascade multilevel static synchronous compensator

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Published in IET Power ElectronicsReceived on 15th March 2010Revised on 28th August 2010doi: 10.1049/iet-pel.2010.0095

ISSN 1755-4535

Cascade multilevel static synchronous compensatorconfiguration for wind farmsS.D.G. Jayasingha1 D.M. Vilathgamuwa1 U.K. Madawala2

1School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore2Department of Electrical and Computer Engineering, University of Auckland, Auckland 1142, New ZealandE-mail: [email protected]

Abstract: Modulation and control of a cascade multilevel static synchronous compensator (STATCOM) configuration to improvethe quality of voltage generated by wind power systems are presented. The proposed STATCOM configuration needs only fourdc-link capacitors and 24 switches to synthesise nine-level operation. In addition to that, switching losses are further reduced bysplitting the voltage source inverter of the STATCOM into two units called the ‘bulk inverter’ and the ‘conditioning inverter’. Thehigh-power bulk inverter is operated at low frequency whereas the low-power conditioning inverter is operated at high frequencyto suppress harmonics produced by the bulk inverter. Fluctuations at the point of common coupling voltage, caused by suddenwind changes, are suppressed by controlling reactive power of the STATCOM. Simulation and experimental results are presentedto verify the efficacy of the proposed modulation and control techniques used in the STATCOM.

1 Introduction

The static synchronous compensator (STATCOM) is aflexible ac transmission system (FACTS) device that hasbeen used to provide both VAR compensation and voltageregulation in power industry for the past three decades. Fastdynamic response of STATCOMs makes them suitable formitigating potential short-term voltage fluctuations that lastfor few hundreds of milliseconds, particularly in windgeneration systems. Furthermore, in comparison to theconventional static var compensators, STATCOMs generateless harmonics and require a much smaller reactor. In thesimplest form, STATCOMs employ two-level voltagesource converters (VSCs) for power processing. However, amultilevel configuration is preferable to achieve higherac-side voltage levels and improved waveforms withreduced harmonic distortion. Multilevel convertertopologies such as diode-clamped converter, flying-capacitor converter and cascading converter have beensuccessfully implemented in STATCOM [1–11].

Cascaded multilevel converter (CMC) topologies haverecently become a popular choice for the implementation ofhigh power STATCOM systems. Among these topologies,the CMC with separate dc sources can be regarded as themost popular owing to its modularity and flexibility [12].However, the need for large number of separate dcsources, which is usually supplied with capacitors inSTATCOM applications, makes this STATCOM bulkyand less reliable. To overcome this limitation, a STATCOMwith the combined converter topology, which is formedby cascading two three-level diode clamped convertersthrough a coupling transformer, is proposed in thispaper. This cascaded topology needs only four dc-link

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& The Institution of Engineering and Technology 2011

capacitors and 24 switches to synthesise the nine-leveloperation [13].

Fig. 1 shows the schematic of the proposed STATCOM inwhich the two inverters, ‘bulk inverter’ and ‘conditioninginverter’ are connected at the ends of a couplingtransformer secondary winding. The bulk inverter operatesat a low frequency producing square-wave output, whereashigh-frequency low-power conditioning inverter is used tomake the output waveform smooth and closer to sinusoidalin shape. As the high-power bulk inverter operates at alower frequency, it can be constructed using devices likeGTOs, ETOs or IGCTs to reduce switching losses. On theother hand, the conditioning inverter, which acts tocompensate low-order harmonics produced by the bulkinverter, can be constructed using more commonly availabledevices like insulated gated bipolar transistors (IGBTs).This particular power and frequency splitting arrangementhelps to reduce switching losses of the inverter [13–15].

The proposed STATCOM can support wind powergeneration in numerous ways [16–18]. As wind is randomin nature, the power output of wind generators are expectedto have short-term and long-term fluctuations. In particular,short-term fluctuations of the wind power output can causevoltage variations at the point of common coupling (PCC).Such voltage variations can effectively be compensatedwith the appropriate injection of reactive power from theSTATCOM. Furthermore, if properly controlled, a storageelement connected at the dc-link of the STATCOM in theform of battery or super capacitor can also help alleviatingsuch short-term power oscillations.

Section 2 of this paper presents a description and analysison the modulation and control strategy of the proposedcascaded multilevel inverter. Dc-link capacitor voltage

IET Power Electron., 2011, Vol. 4, Iss. 5, pp. 548–556doi: 10.1049/iet-pel.2010.0095

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balancing is discussed in Section 3. The STATCOMcontroller that is proposed to mitigate potential voltagevariations in a permanent magnet synchronous generator(PMSG)-based wind energy conversion system is discussedin Section 4. The PMSG controller, used in simulations isexplained in Section 5. Both simulation and experimentalresults are presented in Sections 6 and 7 to verify thepractical viability of the proposed system, which, accordingto the results, is suitable for wind power generation systems.

2 Modulation and control of the inverter

For the cascade inverter shown in Fig. 1, line-to-groundvoltages of the bulk and conditioning inverters can bederived from the switching states by (1) and (2),respectively. In (1), Sa, Sb and Sc are the switching states ofthe bulk inverter while Sax, Sbx and Scx of (2) representsswitching states of the conditioning inverter. They can takevalues of 0, 1 or 2. It is assumed in (1) and (2) that thecapacitor voltages in the inverter dc-links are balanced.

vag vbg vcg

[ ]T= sa sb sc

[ ]Tvdc

2(1)

vagx vbgx vcgx

[ ]T= sax sbx scx

[ ]Tvdc x

2(2)

Phase voltages of the coupling transformer secondarywinding can be calculated using (3). However, on theprimary side of the transformer that is connected to thePCC, the interest is on line voltages which are related to theprimary phase voltages by (4). Here the transformer turnsratio is taken as 1:1.

vas

vbs

vcs

⎡⎣

⎤⎦ = 1

3

2 −1 −1−1 2 −1−1 −1 2

⎡⎣

⎤⎦ vag − vagx

vbg − vbgx

vcg − vcgx

⎡⎣

⎤⎦ (3)

vabn

vbcn

vcan

⎡⎣

⎤⎦ =

1 −1 00 1 −1−1 0 1

⎡⎣

⎤⎦ vas

vbs

vcs

⎡⎣

⎤⎦ (4)

Fig. 1 Schematic of the proposed STATCOM


Space vector plot of the inverter is shown in Fig. 2, which isobtained by transforming phase voltages of (3) into d–qcomponents using Park’s transformation [K ] in (5).

vds vqs V0

[ ]T= [K] vas vbs vcs

[ ]T(5)

Darker dots in the space vector diagram show the switchingstates of the bulk inverter and are known as ‘bulk vectors’.They can be categorised into five groups. (i) Large vectors200, 220, 020, 022, 002 and 202; (ii) Medium vectors 210,120, 021, 012, 102 and 201; (iii) Negative small vectors100, 110, 010 011, 001 and 101; (iv) Positive small vectors211, 221, 121, 122, 112 and 212 and (v) Zero vectors 000,111 and 222. Therefore altogether there are 27 bulk vectorsmarked by darker dots. Each darker dot is the origin ofanother smaller hexagonal pattern which represents theswitching states of the conditioning inverter. They are thevectors of the conditioning inverter and are simply known as‘conditioning vectors’. These small hexagons also have thesame vector pattern as the bulk inverter. As a result of this,27 × 27 different vectors can be identified for this cascade-3/3 inverter. But some of them overlap as shown in Fig. 2reducing the number of effective vectors. The darker dots aremarked with corresponding switching states. The switchingstate ‘2’ means both upper switches of the correspondinginverter leg are turned on. Similarly, the switching state ‘1’means middle two switches are turned on and the switchingstate ‘0’ means the lower two switches are turned on.

A given reference voltage vector can be synthesised bycombining a bulk vector and three conditioning vectors [19].As mentioned in the introduction, the bulk inverter producessquare-wave outputs by switching from one bulk vector toanother slowly. In this process, depending on the amplitudeof the reference voltage (0 , Am , 8), different bulk vectortraversal patterns have to be used, as shown in Fig. 3.However, owing to operational limitations caused by theabsence of an active power source at the conditioninginverter, the upper limit of Am for steady-state operation isreduced to 6. When Am . 4.58, the bulk vector traversalpattern consists of large and medium bulk vectors, as shownin Fig. 3a. Sub-hexagonal vector patterns are omitted inthese diagrams as the focus at this point is only on bulkvectors. Bulk inverter output voltage for this range takes theshape as in Fig. 3b. For 3.60 , Am , 4.58, medium andsmall bulk vectors are alternatively used as in Fig. 3c and thecorresponding bulk inverter output voltage waveform isshown in Fig. 3d. For the range 1.73 , Am , 3.60, onlysmall bulk vectors are used as in Fig. 3e. In that case

Fig. 2 Cascade inverter space vector diagram for (Vdc:Vdcx ¼ 3:1)

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Fig. 3 Bulk vector traversal patterns

a Am . 4.58b, d, f are corresponding bulk inverter output voltage waveformsc 3.60 , Am , 4.58e 1.73 , Am , 3.60g Bulk vector timingh Effect of the conditioning inverter

number of levels in the bulk inverter output voltage is reducedas seen in Fig. 3f. However, in the STATCOM operation thisrange is hardly used. When Am , 1.73, the bulk inverter isturned off and only the conditioning inverter continues itsoperation. This region is never used in the proposedSTATCOM. The time spent on each bulk vector is afunction of Am, which varies as depicted in Fig. 3g.

As mentioned above, bulk inverter produces square-waveoutputs, whereas the conditioning inverter is used tosuppress its harmonics. Fig. 3h illustrates this combinedoperation where the conditioning inverter is purposelyturned off until 30 ms. Harmonic distortion of the outputvoltage is quite high under this operation. After 30 ms,conditioning inverter is turned on and consequently theoutput voltage becomes smooth with a low harmonicdistortion. Therefore one can consider the conditioninginverter as an active filter. In the case of harmonic filters,the given waveform is subtracted from the ideal waveformand then the difference is compensated. The same idea isused in the proposed modulation method.

Fig. 4 shows the bulk inverter vector diagram with threeaxes va, vb and vc which correspond to relevant phasevoltages vas, vbs and vcs. Available bulk inverter phasevoltage levels are marked on the respective axes. For agiven amplitude Am, corresponding bulk inverter phasevoltage levels can be found in Table 1. A plot of theselevels and the reference is shown in Fig. 5a. Differencebetween them varies as in Fig. 5b. This difference is thevoltage which should be supplied by the conditioning

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inverter as the compensation voltage. Subsequently, it ispulse-width modulated (PWM) using two triangularwaveforms as shown in Fig. 5c. A low-frequency carrier isused here for clarity. The corresponding switching signalfor the leg ‘a ’ of the conditioning inverter is shown in Fig. 5d.

Fig. 6 shows the block diagram of the combined invertercontroller, where the square-wave generator produces bulkinverter switching states Sa, Sb and Sc. Rest of the controllergenerates suitable conditioning inverter switching states Sax,Sbx and Scx based on the above harmonic filtering technique.

Fig. 4 Phase voltage levels of the bulk inverter


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Fig. 5 Modulation technique

a Reference voltage and square wave output of the bulk inverterb Difference between the square wave output and the referencec PWM with two triangular carrier waveformsd Switching signals for the leg ‘a’ of the conditioning inverter

Table 1 Bulk inverter phase voltage levels for different ranges of Am

Range of Am Bulk inverter phase voltage levels Vas, bulk

4.58 , Am , 6 26 24.5 23 0 3 4.5 6

3.60 , Am , 4.58 24.5 23 21.5 0 1.5 3 4.5

1.73 , Am , 3.60 23 21.5 0 1.5 3 – –

A proportional integral (PI) controller is used to regulate theconditioning inverter dc-link voltage to one-third of the bulkinverter dc-link voltage. This is required for the nine-leveloperation of the combined inverter. PI controller adds a smalldelay angle da to the conditioning inverter phase anglewhich in turn draws some active current from the bulkinverter to charge conditioning inverter dc-link capacitors[13]. Fig. 7 illustrates this lagging operation on the spacevector diagram. The redundant state selection (RSS)algorithm, followed by the PWM process, is used to balancecapacitor voltages. A detailed analysis on RSS and capacitorvoltage balancing is given in the next section.

3 Capacitor voltage balancing

The proposed modulation method equally generates bothpositive and negative small conditioning vectors. Therefore

Fig. 6 Conditioning inverter controller block diagram


for a given constant amplitude Am, conditioning invertercapacitors get charged or discharged equally. In otherwords, they tend to maintain their initial conditions as longas Am is constant. Owing to this open-loop-like control,small ripples appear on capacitor voltages as shown inFig. 8a. However, they are negligible in comparison todeviations which occur at transitions of Am. The suddenchange of the amplitude at t ¼ 0.2 s, creates a short-termimbalance in the capacitor charging and discharging pattern.

Fig. 7 Delay angle da

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Consequently, one voltage goes up while the other goesdown. But owing to the tight voltage regulation of theconditioning inverter dc-link voltage, their addition remainsconstant. As Fig. 8 illustrates, the proposed modulationmethod itself is not capable of balancing capacitor voltages,especially in dynamic situations. To overcome this issue,the authors have proposed a RSS-based capacitor voltagebalancing method in [19]. Simulation results in Fig. 9 showthe efficacy of the above method on capacitor voltagebalancing, without ripples, even under dynamic situations.

The same capacitor voltage balancing method can beapplied for the bulk inverter by reversing current directions.However, it is valid only for the range of 1.73 ,Am , 4.58, where small bulk vectors are available. ForAm . 4.58, only medium and large bulk vectors areavailable; this makes capacitor voltage correctionsimpossible. Large bulk vectors do not change capacitorvoltage, since they have no connection to the middle point.But medium bulk vectors do have a single connection tothe midpoint, whereas the other two ends are connected tothe upper and lower points. Because of that, significantripples can appear on capacitor voltages under unbalancedloads. Even for balanced loads, ripples occur as shown inFig. 10. But usually they are negligible.

4 STATCOM controller

Fig. 11 shows the controller block diagram of the STATCOMthat controls the active and reactive power transfer betweenthe grid and the STATCOM. The measured PCC voltage Vd

in synchronous reference frame is compared with thereference V∗

d and the error signal produced is then fed into aPI controller that generates a current reference i∗q for theinner current controller loop. The STATCOM’s ac-side

Fig. 8 Natural balancing of conditioning inverter capacitor voltages

a–b Conditioning inverter capacitor voltagec Amplitude of the reference voltage vector

Fig. 9 Forced balancing of conditioning inverter capacitor voltages

a–b Conditioning inverter capacitor voltages

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currents are measured and transferred to the synchronousreference frame in the form of direct and quadraturecomponents. The direct component is related to the realpower exchange, whereas the quadrature component isrelated to the reactive power exchange. Therefore the bulkinverter dc-link voltage Vdc can be regulated by controllingthe direct component of the STATCOM current. To regulatethe grid voltage, the quadrature component of theSTATCOM current is controlled [20]. The current controlleroutputs, v∗ds and v∗qs are the reference voltages for the inverter.

With the above reference values, amplitude Am and thephase angle am of the STATCOM output voltage arecalculated using (6) and (7). Consequently, the STATCOMinverter controller generates output voltages with therequired amplitude and phase. The instantaneous angle u, ofthe phase voltage vector, is obtained through a phaselocked loop.

Am = 9

Vdc

��v∗2

ds + v∗2qs

√(6)

am = tan−1 v∗qs

v∗ds

( )+ u (7)

Fig. 10 Bulk inverter capacitor voltages with self-balancing

a–b Bulk inverter capacitor voltagesc Amplitude of the reference voltage vector

Fig. 11 Schematic control diagram of the STATCOM connected ina wind generator system


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5 PMSG controller

PMSGs have been gaining acceptance in direct-coupled low-speed wind generation applications as they are highly efficientand relatively small in diameter [21]. Therefore to test theability of the proposed STATCOM to mitigate potentialvoltage variations caused by sudden wind changes, aPMSG-based wind energy conversion system is used.Equations (8)–(12) describe the mathematical model of thePMSG used in this study.

TSR = rvm

vw

(8)

vref =TSRopt

r∗ vw (9)

Pm = 0.5rACpv3w (10)

Tm = Pm

vm

(11)

Tm − TLoad − Tf = Jdvm

dt(12)

where r, vm and vw represent the turbine radius, mechanicalangular frequency of the generator and wind speed,respectively. vref is the reference angular frequencygenerated by the turbine model. In (10), Pm denotes theoutput mechanical power of the wind turbine. r and A areair density and the area swept by the blades, respectively.For simulations, the optimum tip speed ratio (TSRopt)corresponding to maximum power point and powercoefficient (Cp) were taken as TSRopt ¼ 5.09 andCp ¼ 0.42. With these values, mechanical torque Tm can be

Fig. 12 Equivalent circuit of the PMSG, rectifier and inverter

Fig. 13 PMSG controller block diagram


calculated using (11). In (12), TLoad is the electric torqueproduced by the generator, Tf is the friction and J is themoment of inertia of the turbine.

Fig. 14 Dynamic behaviour of the system for step changes in windspeed

a Wind speedb PCC voltage restoration in synchronous reference framec STATCOM active and reactive current componentsd STATCOM current of phase ‘a’e STATCOM output voltage vabn

f line voltage vab at PCCg Bulk inverter capacitor voltagesh Conditioning inverter capacitor voltages

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Fig. 12 shows the per-phase equivalent circuit of the PMSGand the rectifier is used to convert generated ac voltage to a dcvoltage. The phase electromagnetic force E of a non-salientpole PMSG is proportional to the generator speed and canbe expressed as

E = Kevm (13)

where Ke is related to the magnetic flux linkage and can beconsidered as a constant. Voltage equations can be given asfollows.

E2 = (Vs + Rpip)2 + (Xpip)2 (14)

Vdc =3

��3

√ ��2

√Vs

( )p

(15)

From (8) to (15), it can be seen that random fluctuations of thewind speed can propagate through power conversion stagesand can affect the voltage at PCC. According to (12),inertia of the turbine and blades can suppress high-frequency variations of the rotor speed caused by suddenwind changes. But still there can be variations which lastfor few hundred milliseconds causing voltage fluctuations atthe PCC [22]. Fig. 13 shows the controller block diagramof PMSG. For maximum power-point tracking, the windturbine model in the controller generates a reference speedfor the PMSG using the measured wind speed and theoptimum tip speed ratio of the turbine. The difference ofthe actual speed and its reference is then fed into a speed

Fig. 15 Experimental setup

a Schematic diagramb Photograph of the experimental setup

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regulator. As the speed is controlled by regulating theelectrical torque, the currents of the grid interfacing inverterare controlled in a manner that the torque indirectly tracksthe optimal speed of the PMSG.

6 Simulation results

Fig. 14 shows the dynamic behaviour of a 5MVA STATCOMfor two-step change in wind speed. As shown in Fig. 14a,wind speed is changed from 9.3 to 6.3 ms21 at t ¼ 300 msand again it is changed to 8.1 ms21 at t ¼ 700 ms. Thesetwo sudden variations make the voltage at PCC to deviatefrom its set value as shown by the dashed line in Fig. 14bwhen the STATCOM is not connected. With theSTATCOM connected, it detects those deviations andinjects appropriate amount of reactive power to bring thevoltage to the set value. The results of these voltagerestoration attempts are shown in Fig. 14b by thecontinuous line. Without the STATCOM being connected,magnitude and duration of voltage variations would wellexceed acceptable levels. Therefore it can be seen that fastacting STATCOMs can effectively mitigate voltagefluctuations caused by sudden wind changes in windgeneration systems. Fig. 14c shows the variation of thereactive current reference i∗q and the actual reactive currentiq of the STATCOM. The reactive current iq follows thereference with a little delay. There is a small active current

Fig. 16 Dynamic response of the system for step changes inreactive power command

a Reactive current command and the responseb Bulk inverter capacitor voltagesc Auxiliary inverter capacitor voltagesd Inverter output voltage of the ‘a ’ phase


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id drawn from the grid to compensate switching losses in theSTATCOM and to maintain the bulk inverter dc-link voltage.Fig. 14d shows variation of the STATCOM phase ‘a’ current.STATCOM output voltage and the line voltage at PCC areshown in Figs. 14e and f, respectively. The bulk inverterand conditioning inverter dc-link voltage regulation isshown in Figs. 14g and h, respectively. Note that theconditioning inverter voltage is maintained at one-third ofthe bulk inverter dc-link voltage for nine-level operation.The results show a good performance of the proposedPMSG and STATCOM control systems.

7 Experimental results

7.1 Experimental setup

The schematic diagram and photograph of the experimentalsetup are shown in Figs. 15a and b, respectively.Exaggerated views of both bulk and conditioning invertermodules are also shown in the bottom right corner of thephotograph in Fig. 15b. In this experiment both inverterswere built using IGBTs. But in practice the bulk invertercan be built using slow devices, as mentioned in theintroduction. The MATLAB/SIMULINK software platformand the dSPACE hardware interface are used to control theproposed STATCOM. A variable ac source is used tosynthesise the PMSG-based wind energy conversionsystem. Reactive power control and voltage regulation


performances of the overall system shown in Fig. 15b weretested and the corresponding results are given in theSections 7.2 and 7.3, respectively. System parameters ofthe experimental setup and controller gains are given in theAppendix.

7.2 Reactive power control

Three step changes were applied to the reactive currentreference, iq

∗, as shown in Fig. 16a. The correspondingdynamic response of the STATCOM reactive current isshown in the same figure with the graph marked as iq.Fig. 16b shows the bulk inverter dc-link capacitor voltageswhich are stable and equal in spite of transients in theSTATCOM currents. Similarly, the controller regulatesconditioning inverter dc-link capacitor voltages as shown inFig. 16c. An expanded view of the inverter output voltageis shown in Fig. 16d.

7.3 Voltage regulation

The ac source is programmed to generate three step changesin the PCC voltage as shown in Fig. 17a. At the beginningof this process the system of Fig. 15 is at steady-stateand the d-axis component of the PCC voltage Vd is atits nominal value. Therefore reactive power injection isnot required. Once a change in voltage Vd is sensedthe controller starts to inject reactive power as shown in

Fig. 17 Experimental results showing voltage regulation

a PCC voltage without STATCOMb PCC voltage with STATCOMc Injected reactive currentd STATCOM output current of the ‘a’ phase, ias

e Amplitude of the reference voltage vector, Am

f Power angleg Active current drawn by the STATCOM, idh Bulk and conditioning inverter dc-link voltages

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Fig. 17c to bring Vd back to the nominal value. The result ofthis voltage restoration attempt is shown in Fig. 17b.Corresponding variations of the STATCOM output currentsis shown in Fig. 17d. The variation of modulation index Am

and the power angle are shown in Figs. 17e and f,respectively. Apart from that, a small amount of activecurrent, id, is drawn from the grid as shown in Fig. 17gto maintain capacitor voltages and replenish power lossdue to switching and resistive components of thecoupling transformer. The resulting dc-link capacitorvoltage variations are shown in Fig. 17h. It can be seenfrom these results that the proposed cascade multilevelSTATCOM and the controllers perform well in transientand steady-state conditions.

8 Conclusion

The proposed STATCOM configuration provides highvoltage and power ratings. In addition to that, the hybridstructure of the VSC limits the dc-link capacitor count to 4.As a result, it has a high potential of being implemented infuture high capacity wind farms for both active and reactivepower compensation. The simulation and experimentalresults show good dynamic responses of the STATCOM forvoltage variations caused by sudden wind changes. Theseresults indicate that the proposed cascade multilevelSTATCOM is capable of suppressing voltage fluctuations atthe PCC caused by random wind changes.

9 Acknowledgment

An earlier version of this paper was presented at the IEEEInternational Conference on Power Electronics and DriveSystems (PEDS), Taipei, Taiwan, 2–5 November 2009.

10 References

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2 Singh, B., Saha, R., Chandra, A., Al-Haddad, K.: ‘Static synchronouscompensators (STATCOM): a review’, IET Trans. Power Electron.,2009, 2, (4), pp. 297–324

3 Saeedifard, M., Iravani, R., Pou, J.: ‘Control and DC-capacitor voltagebalancing of a space vector-modulated five-level STATCOM’, IETTrans. Power Electron., 2009, 2, (3), pp. 203–215

4 Ronner, B., Maibach, P., Thurnherr, T.: ‘Operational experiences ofSTATCOMs for wind parks’, IET Trans. Renew. Power Gener., 2009,3, (3), pp. 349–357

5 Kincic, S., Chandra, A., Babic, S.: ‘Five level diode clamped voltagesource inverter and its application in reactive power compensation’.Proc. IEEE-LESCOPE, 2002, pp. 86–92

6 Liu, Y., Luo, F.L.: ‘Trinary hybrid multilevel inverter used inSTATCOM with unbalanced voltages’, Proc. IEE Electr. PowerAppl., 2005, 152, (5), pp. 1203–1222

7 Saha, R., Singh, B.: ‘Improved 48-pulse static synchronous compensatorfor high-voltage applications’, IET Trans. Power Electron., 2010, 3, (3),pp. 355–368

8 Chatterjee, K., Ghodke, D.V., Chandra, A., Al-Haddad, K.: ‘Simplecontroller for STATCOM-based var generators’, IET Trans. PowerElectron., 2009, 2, (2), pp. 192–202

9 Saeedifard, M., Nikkhajoei, H., Iravani, R.: ‘A space vector modulatedSTATCOM based on a three-level neutral point clamped converter’,IEEE Trans. Power Deliv., 2007, 22, (2), pp. 1029–1039

10 Figarado, S., Sivakumar, K., Ramchand, R., Das, A., Patel, C.,Gopakumar, K.: ‘Five-level inverter scheme for an open-end windinginduction machine with less number of switches’, IET Trans. PowerElectron., 2010, 3, (4), pp. 637–647

11 Luo, A., Shuai, Z., Zhu, W., Shen, Z.J., Tu, C.: ‘Design and applicationof a hybrid active power filter with injection circuit’, IET Trans. PowerElectron., 2010, 3, (1), pp. 54–64

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12 Sirisukprasert, S.: ‘The modeling and control of a cascade multilevelconverter based STATCOM’. PhD thesis, Virginia PolytechnicInstitute, Blacksburg, Virginia, USA, 2004

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14 Corzine, K.A., Wielebsk, W., Peng, F.Z., Wang, J.: ‘Control of cascadedmultilevel inverters’, IEEE Trans. Power Electron., 2004, 19, (3),pp. 732–738

15 Corzine, K.A.: ‘Operation and design of multilevel inverters’, availableat: http://www.motorlab.com, accessed August 2010

16 Qiao, W., Harley, R.G., Venayagamoorthy, G.K.: ‘Effects of FACTSdevices on a power system which includes a large wind farm’. Proc.IEEE Power Systems Conf. and Exposition, November 2006,pp. 2070–2076

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19 Vilathgamuwa, D.M., Jayasinghe, S.D.G., Madawala, U.K.: ‘Spacevector modulated cascade multi-level inverter for PMSG windgeneration systems’. Proc. Industrial Electronics Society Conf.,November 2009, pp. 4636–4641

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11 Appendix

Parameters of the experimental setup and PI controllers aregiven in Tables 2 and 3.

Table 2 System parameters of the experimental setup

fundamental frequency f ¼ 50 Hz

STATCOM interfacing resistance Rf ¼ 0.8 V

STATCOM interfacing inductance Lf ¼ 3 mH

line resistance Rn ¼ 1.1 V

line inductance Ln ¼ 18 mH

load resistance Rl ¼ 17 V

load Inductance Ll ¼ 11 mH

dc-link voltage Vdc ¼ 128 V

dc-link capacitors C1,C2,CX1,CX2 C ¼ 2200 mF

nominal value of d-axis voltage Vd ¼ 90 V

short-circuit impedance of the STATCOM 0.8 + j0.942

Table 3 Parameters of PI controllers

PI controller Control

variable

Proportional gain (KP) Integral gain (KI)

PI 1 id 15 500

PI 2 iq 45 200

PI 3 Vd 20.1 28

PI 4 Vdc 20.2 20.2

PI 5 Vdcx 20.01 20.01


cascade multilevel static synchronous compensator

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