00052680 - A Detecting Method for Active-Reactive- Negative-Sequence Powers and Its Application

7/28/2019 00052680 - A Detecting Method for Active-Reactive- Negative-Sequence Powers and Its Application

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IEEE TRANSACTIONS ON INDUSTRY APPLICATION S. VOL. 26 . NO . I , J A N U A R Y / FEB R U A R Y 1990 9 9

A Detecting Method for Active-Reactive-Negative-Sequence Powers andIts ApplicationMIKIHIKO MATSUI A N D TADASHI FUKAO

Abstract-A s imple but qu i te usefu l detec t ing method for the power o fthe three-phase circuit i s proposed. The detected power i s decomposedinto fou r com ponents o f the fundamenta l pow er , i .e ., ac tive power ,react ive pow er, and two co mpo nents of negat ive-sequence pow er on theor thogonal coord inates . Based on these fou r com ponen ts, the reversecalculat ion s of the f ir in g angles for the thyr istors become simple and easyto implement . A t yp ica l app l icat ion to the feedforward power cont ro lo f a h igh- f requency ( H F ) cycloc onverter to stabi l ize the H F outputvoltage against sudden load changes i s shown to prove the va l id i t y o fth is method.

I. INTRODUCTIONTHE MAJOR applications of static power converters,I"he detection of power is an essential problem because it di-

rectly affects system performance such as the response andthe accuracy of the control. For this reason, a number ofpower detecting methods have been investigated, especiallyin the field of reactive power compensation of the varyingload [1]-[5]. Amo ng these methods is a general theory basedon the instantaneous real power and imaginary power [p, q ]proposed by Akagi et al. [4] which gives a good insight incontrolling an active filter with instantaneous current control-lability. On the other hand, in the case of line-commutatedconv erters that cannot control the instantaneous curren t, suchas phase-controlled thyristor bridges and thyristor-controlledreactors (TCR's), the method based on [p, q ] cannot be read-ily applied. For such converters, the problem is how to detectthe power consumed by the load and how to implement theon-line calculation of the control angles for the thyristors.In this paper, a solution especially suitable for the controlof TCR's under unsymmetrical control is given. The proposedscheme has the following features.

1) The detected power is decomposed into four compo-nents of the fundamental power. They are active and reactivepositive-sequence components P an d Q and the two compo-nents of the negative-sequence power on the rotating orthog-onal coordinates, S D an d S Q .2) Th e detection of these powers an d the reverse calculationof the firing angles are simple and quite easy to implementcompared with conventional methods.

Paper IPC SD 89-2 , approved by the Static Power Converter C omm itteeof the IEEE Industry Applications Society for presentation at the 1987 In-dustry Applications Society Annual Meeting, Atlanta, GA. October 19-23.Manuscript released for publication April 17 , 1989.The authors are w ith the Department of Electrical and Electronic Engineer-ing, Tokyo Institute of Technology, 2-1 2- 1 0-Okayama Meguro-ku, Tokyo152, Japan.IEEE Log Num ber 8931468.

The scheme is applied to the feedforward power controlof a high-frequency (HF) cycloconverter [6], [ 7 ] , in whichthe behavior of i ts circulating current is treated as an equiv-alent TCR, to stabilize the output load voltage deviation un-der sudden load changes. Experimental results with a labora-tory system prove both the availability of the proposed detect-ing method and the validity of the feedforward power controlscheme.

11. PRINCIPLEF POWERETECTIONIn this chapter, a simple and quick detecting method for the

componen ts of the fundamental power P , Q , S O , an d S Q isproposed.A . Definition and Properties of Quantities sd and sq

In the three-phase ac system, transformation of the instan-taneous phase voltages and the currents into a-0 orthogonalcoordinates yields following expressions:

Then the four electrical quantities [p, q , S d , sq ] can be de -fined by

(4 )

where p and q are the instantaneous real and imaginary powersdefined by Akagi et al. [4], respectively, while s d an d sq arethe newly defined quantities in this paper. Since

( 5 )2 + q 2 = s i +si,0093-9994/90/01OO-OO99$01OO 0 990 IEEE


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IEEE TRANSACTIONS O N INDUSTRY APPLICATIONS. VO L 26. NO . I, JANUARYIFEBRUARY 1990

the degree of freedom among these four quantities isthree. Therefore, it is impossible to calculate the values

The physical meaning of each quantity is considered as fol-lows. p is the total sum of the instantaneous power suppliedto the a an d f i phases, because u,i, an d ugig are the prod-ucts of voltage and current in the same phase, and s d is thedifference of the instantaneous power v,i, an d ugig .

On the contrary, q an d s, each have no meaning of in-stantaneous power, because u,ig and upi, are the productsof voltage and current in different phases. They do not havean obvious physical meaning but are the quantities defined forconvenience.

In the case of a voltage source system, since U, an d ug arethe known variables, i, an d ig can be reversely calculateduniquely from [p, q ] o r [ s d , s,]:

[U,, u g , i,, i p l uniquely from [p, q , s d , s,I.

How ever, the other kinds of combinations of the instantaneouspowers, such as [P, sdl, [p,s,I, tq , sdl, or [ q , ql , annotb e of use because the voltage matrices may not always beregular.

When the above transformations are applied to , say, an ac-tive filter for calculating the current reference, the problem ishow to determine the power reference on the right-hand side.

In (6), we can determine [p, q ] based on the controllaw-e.g. , p an d q supplied from the source should holdp + onstant, q+ -which is previously settled from apoint of view of desirable energy flow between the ac sourceand the load. That is because the control o f pmeans the controlof energy flow itself. Giving the control law in (7), however,is more puzzling because the desirable ene rgy flow cannot bestated with only s d an d s q .Thus it is concluded that there are no merits to introducing[ s d , s q ] n addition to [p, q ] egarding the instantaneous cur-rent control. Even so, for the control of TCRs or other line-commutated converters that cannot control the instantaneouscurrent, the method based on [p, q ] cannot readily be ap-plied, and the electrical quantities based on the average valueconcept should be used instead. In such a case, introducing[ s d , s q ] is highly advantageous, as will be described.Assuming that the three-phase voltages are the balancedcosine waves and the currents ar e the arbitrary repetitive ones,[P, q ] n (4) re given as follows:

The first terms of the right-hand side, the dc componentswhich involve the information of the am plitude and the ar-gument of the positive-sequence current, present the so-calledfundamental active and reactive powers P an d Q. The secondterms present the ac comp onen ts having 2w ang ular frequencywhich involve the amplitude and the argument of the negative-sequence current. The third terms present the sum of the har-monic powers. As is well-known, P an d Q can be detectedby separating the first terms by applying adequate low-passfilters. On the contrary, detecting I b an d +t, is troublesomebecause further calculations are needed to separate them a s dcsignals.

However, by introducing [ s d , s,], as follows, the troubleof additional calculations is solved with ease:7 D I

The first terms of the right-hand side present the fundamen-tal average powers genera ted by the assumed negative-sequence voltage [U,, - u p ] and the actual negative-sequence current [i,, ig], i .e. , the two components of thenegative-sequence power. In this paper, they are defined asSD and S Q . The second terms are the 2w ac components in-volving the information of the positive-sequence power, andthe third terms are the sum of the harmonic powers. HenceSO an d S Q can be easily separated by using low-pass filters.

The relationship between [p, q ] an d [ s d , s,] becomes moreclear by considering the instantaneous power vectors c j nd bon the complex plane defined by the following expressions:f A p + j q

b A sd + s ,

where S f an d s b present the amplitude of the positive- andnegative-sequence surface powers and their arguments are pre-sented by 4j and & . The subscripts f an d b correspond tothe positive- and negative-sequence components, respectively.Fig. 1 shows these two power vectors. So long as the balancedcosine wave voltages are assumed. the following relationshir,


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M A TSU I A N D FU K A O : D ETEC TIN G M ETH O D FO R A C TI V E- REA C TI V E- N EG A TI V ESEQ U EN C E PO WER S 101

(a ) (b )I pFig. 1. Loci of power vectors on complex plane. ( a) Locus of vector ,I, (b)Locus of vector b.

UAdditional part

Fig. 2. Block diagram of power detection circuit.holds:

3 x qeJ*a'. (12)This means that detecting the first term S b . e C J@ b of 3 in(11) equals separating the second term of 1 in (10) as dccompone nts by ap plying a coordinate transformationB . Power Detecting Circuit

Fig. 2 shows the block diagram for detecting P , Q, S D ,an d S Q . It can be realized simply by adding two sets of anadder and a fi l ter, shown surrounded by the dotted lines, tothe conventional circuit for detecting P an d Q. However, thefollowing problems arise.

How is the detected amplitude of SO an d SQ affected byHow ca n we realize a low-pass filter with both a sufficient

Effect of Voltage Unbalance or Distortion on Detect-ing Error fo r SD an d SQ : Assume that both the three-phasevoltages and the currents are the arbitrary repetit ive waves.Then the detecting error for S D an d S Q can be estimated asfollows. [ S o , SQ ], the dc components of [ sd , s q ] , are givenby (see the Appendix)

the existence of voltage distortion?attenuating characteristic and a small time delay?

(;;) =v 5V f n I b n co s (6, - b n ) f v b n l n cos ( 6 b n - f n )V f n I b n sin ( O f n - b n ) - b n l f n sin ( O b , - f n )

(13)

where 0 an d 4 are the arguments of voltage and current, re-spectively. The subscript n means the nth-order component.Rearranging (13) into the vector form yields

where O f l =0 is assumed. The first term of the right-handside is the objective fundamental negative-sequence powervector, and the remainder are regard ed as error vectors. Hencedetecting error er is defined as

where carets indicate the normalized values, as

Consequently, the condition to repress the er ror er under thedesired value E; is given by

f l # l

In the case I b l =E T = 10 percent and no harmonics areassumed to be contained in the voltages, the permitted max-imum of V ~ Is one percent. Therefore, the unbalance or thedistortion of the voltage signals should be eliminated suf-ficiently by using adequate filters. Utilizing the outputs of athree-phase sine wave oscillator, which are synchronized tothe actual voltage waveforms, as the reference voltage signalsmay be an another solution.Characteristics of Low-Pa ss Filter: The low-pass filtersfor the average power detection are required to meet the fol-lowing specifications.

1) The main ac 2w component should be completely atten-uated.

2) The ac w component, which remains due to the maincircuit unbalanced or control circuit offset, etc., should alsobe attenuate below 1/10.3) Th e time delay should be minimized.

The combination of a delay-circuit bucket brigade device(BBD) and a two-pole Butterworth filter has been used forthose purposes [3]. The block diagram with its transfer func-tions and the attenuation characteristics are shown in Fig. 3.By setting the delay time 7 to be a quarter of the fundamentalperiod of the input voltage or current signals, the 2w compo-nent and its odd multiples can be eliminated. Fig. 4shows theinput and output waveforms of the BBD stage only. Since T is


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1 0 2

ButterworthLPF (fc=250Hz)

IEEE TR A N SA C TI O N S ON IN D U S T R Y APPLICATIONS, V O L . 26. NO. I , J A N U A R Y IF E B R U A R Y 1990-irst stage Second stage I I I

1 1 11+1 . 2 (s /wc) +( s/wc )2l+exp(-ST)}/2

(a )I 2nd stage with LPF 1st stage with BBD

1 OkFrequency(Hz)(b)

Fig. 3 . Low-pass filter using delay circuit. ( a) Block diagra m and transferfunction. (b) Attenuation characteristics.

0.5mSOut put -

Input -

(b)input. (b ) A C ( 3 kHz) plus dc input.Fig. 4. Transient response of first stage in Fig. 3 . (a) AC ( 1 kHz) plus dc

selected to be 0.5 ms, the components of 1, 3 , 5 , 7 kHz, etc. ,are canceled within 0.5 ms. The settling time of the secondstage low-pass filter under the indicia1 respon se is 1 .9 ms.Therefore, the total delay time of the power detection in Fig.2 is about 2.4 ms, which corresponds to 1.2 cycles of theinput signals.

111. APPLICATIONO FEED-FORWARDOWER ONTROLFHIGH-FREQUENCYYCLOCONVERTER

In this section, the proposed power detecting method isapplied to the feedforward power control of a high-frequencycycloc onver ter to show its availability.A . HF CycloconverterSystem Outline: Fig. 5 shows the main circuit of the HFcycloconverter, which was proposed previously by the authorsfor linking commercial and 500-Hz distribution lines in a fac-tory or a chemical plant [6], [7]. It is composed of a six-pulsebridge cycloconverter and H F capacitors to provide vars forboth the conv erter and the load. Fig. 6shows the typical oper-ating waveforms unde r balanced resistive load. It is an obviousmerit that both the input current and the output HF voltagecan be made quasi-sinusoidal.

Thou gh the basic idea of this sort of power conversion tech-nique is based on the static frequency ch anger with a H Fbase proposed by Gyugyi e f a l. [8], this system has follow-ing peculiar features.

1) Th e HF base that provides the commutation voltage forthe cycloconverter is composed of only capacitors (not LCtank circuits), and the circulating current of the cyclocon-verter is utilized instead of reactors. Since the reactive powerbalance is maintained by the controllable circulating current,the voltage and the frequency of the HF side can be kept con-stant regardless of the power factor on commercial line sideor the load conditions.2) The cycloconverter is operated in a discontinuous cir-culating current mode, which utilizes the reactive power dueto only the ripple current. Since the independent control ofeach line-to-line circulating current viewed from the HF sideis available in this mode, the behavior of the circulating cur-rent i,, can be modeled as an equivalent TCR so far as thefundamental component is concerned [9]. As mentioned later,this property enables the compensation of the unbalanced loadon H F s ide.Necessity of Feedforward Power Control: The voltagewaveforms established at the HF terminals should be stableenough from the viewpoint of supplying power with goodquality to the load and ensuring the commutation voltage forthe thyristors. How ever, a deviation or an unbalance of the H Fline voltage may occur when the load condition changes sud-denly or unbalanced load is applied. Therefore, to maintain astable voltage waveform regardless of the load, it is requiredto detect the load consumed po wer continuously and to controlboth the comm ercial l ine current is and the circulating currenti,, so that the cycloconverter may provide the required powerfor the load at any instant. To meet this requirement, a feed-forward technique is introduced to the power control systemin the following.B . Feedforward Power ControlSystem Configuration: Fig. 7shows the configuration ofthe prototype power control system. Th e main circuit cyclo-converter operating in discontinuous i,, mode can be treatedas an ice-free cycloconverter combined with a TCR . Th e loadpower is detected and utilized for the control of i s an d i ce

A cosine crossing scheme is used to generate the gatingpulses. However, the cosine reference signal is synchronizedwith neither comme rcial nor H F lines, but is provided by athree-ph ase voltage-controlled oscillator (VCO).

Fig. 8 shows the block diagram to calculate the controlreferences for i, an d i,,. The control system is divided intotwo blocks according to the functions.Feedforward (FF) block: By detecting the load power,control references for i s an d i,, to maintain the power equi-librium on the HF side are generated.

Feedback (FB) block: Control errors of the FF blockare compensated; 1) the voltage unbalance is completely elim-inated, 2) the angular phase difference 8 between uoSc an d U his kept at zero, and 3 ) the line voltage I / h is adjusted to meetits reference V i .

In the above system, uosc is applied for the power calcula-


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MATSUI AND FUKAO: DETECTING METHOD FOR ACTIVE-REACTIVE-NEGATIVE-SEQUENCE POWERS 103C o m m e r c i a l - l i n e ( 50Hz)

Fig. 5. High-frequency cycloconverter for 5 w - H ~ istribution system.vr /vh = 107 Vi160 v , r =TV,/3Vh =0.7; L , =3 .3mH X 3 ( 0 . 1 0 ~ ~ ) ,L C c= 3 . 5 m H x 6 ( 0 . 1 1 p u ) , C = 6 0 p F x 3 ( 1 . 4 8 p u ).

(b )Fig. 6 . Input/output operating waveforms. ( a) Input (USL,:107 Vidiv.i s u : 1 2 A l d i u ) . (b) Output ( u o : 80 Vidiv, iho: 16A ldiu) .

rn C o m e r c i a l - l i n e ( 5 0 H z )

G a t i n g i s c o n t r o l P o w e rp u l s e t d e t e c t i n ggen. c i r c u i tCR c o n t r o l C=

cFig. 7. System configuration.

tion instead of the actual HF voltage uh for the following tworeasons.

In the steady state, the power detection errors due tothe voltage distortion or unbalance can be avoided. (I nthe FB block, negative-sequence powers drawn from thecapacitor S D ~ ~ ~nd S Q ~ ~ ~annot be detected from U han d i c a p . )In a transient such as a sudden load cha nge, the calculatedpowers become estimates, assuming no voltage devi-ation occurs, and are more suitable as the feedforwardpower references.

Determination of Power References: In Fig. 7, the allot-ment of supply power is determined based on the followingideas.

The active power demanded by the load is supplied fromThe reactive power of the TCR is chosen to satisfy the

. he two components of the negative-sequence power arethe comm ercial line through the cycloconverter.reactive power equilibrium on the HF side.supplied from the TCR.

Thus the feedforward power references are given as

where the coefficient p relates the active load power P L an dthe reactive power due to P L genera ted by the cycloconverter .Assuming that the output voltage ratio is r = 0.7 and thedisplacement factor on the commercial line side is unity, pequals 0.674 [7].After adding the FB components to the above F F ones, thecontrol references for i s an d i,, are reversely calculated. Theeffective value of is is given by

if =P:/3Vs. (19)By the instantaneous current control loop, quasi-sinusoidal iswaveform is achieved as shown in Fig. 6(a).Control of TCR: Fig. 9shows the equivalent TCR m odelof the circulating current concerning to its fundamental com-pone nt, in which the existenc e of the harmonics in the line-to-line arm current is ignored. Each arm current is a function ofthe control angle A6 which adjusts the conduction ang le of thediscontinuous circulating current [SI. Assuming the balancedsinusoidal terminal voltages, i.e.,


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1 0 4 IE E E TRANSACTIONS ON IN D l lS T R Y APPLICATIONS. V O L . 26. NO. I , A N U A R Y I F E B R U A R Y 1990

1 ps* - PS* ( FF)A:(Is* -~

c a l c u . e q . ( 1 8 )- Q T C R * ( F F ) :zi:r

SD TC R * ( FF) c a l c u .-X sQTCR*(FF)

~ L - L o a d II Three- a l c u . I * phaseIDL

- ( 4 ) &+ L:Load-QL + LPF.c : F i g . 3 c u r r e n t1e q . ( 1 ) I s i nwaveos c

the line currents are presented by using the control coefficientskl , kZ, k3 for each arm:

(23) yields

0 5 k l , kz, k j 5 1. (21 )From (20) and (21), [ s d , s q ] becomes

The first terms are the dc components corresponding to thenegative-sequence power vector SjTCR,nd the second termsare the 20 ac components corresponding to the positive-sequen ce reactive p ower vector QTCR. Fig. 10is the schematicexpression of the above equations. Defining new referenceaxes as i l lustrated, STCRs given by the sum of the thre e vec-tors on each axis, i .e. , the vector sum. The amplitude ofQTCRs given by the sum of the amplitude of three vectors,i .e. . the scalar sum:

QTCR =v h I m ( k i + k 2 + k 3 ) . (23)The refor e, the possible existing region of QTCR s given by ahexagon as illustrated in Fig. 10. Rearranging the (22) and

Once the references of the power on the left-hand side aregiven, k,(i = 1, 2 , 3) are easily obtained by the reverse cal-culation as follows:

Then the control angles A s, can be obtained by using a non-linear function shown in Fig. 9 (b).C . Exper imental Resul ts

Fig. 11 shows the experimental results of the transient re-sponse when the 1.2-kW single-phase resistive load (whichcorresponds to 0.37 pu of the maximum conversion power3.2 kW with balanced three-phase load, or 0.85 pu of thepermitted maximum single-phase load 1.4-kW) is connectedto the HF side.In case 1 with only the feedback control being applied,about 30 percent deviation in the HF terminal voltage ampli-tude is observed at the step load chang e. The amplitude of thecommercial line input current increases gradually to replen-ish the required active power. At the same time, the voltageunbalance is compensated by the equivalent TCR (circulat-ing currents). It takes about 20 0 ms (10 0 HF voltage cycles)before the transient is over.On the other hand, in case 2 with the feedforward control


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MATSUI AND FUKA O: DETECTING METHO D FOR ACTIVE-REACTIVE-NEGATIVE-SEQUENCE OWERS 105

(a ) (b)Fig. 9. Equivalent T C R model of circulating current. (a ) Idealized model of T C R . (b) A 6 - characteristic.

43

a x i m u m e x i s t i n gk 2 - a x i s S I k; I=k;VhIm

Fig. 10. Negative-sequence power vector S,,, of TC R on compex polane.

applied, the step load change is detected immediately, andhence the transient is settled-within a few H F voltage cycles.

the control of a general thyristor-controlled reactors connectedto the com mercial ac system lines.

Clearly, the proposed scheme is valid for stabilizing the HFvoltage against the sudden load change.

IV . CONCLUSION1) A detecting method for active, reactive, and two compo-nents of negative-sequence power on the rotating orthogonal

coordinates, i .e. , [P, , S D , S Q ] s proposed.Two electrical quantities s d an d s q are newly defined,which are available for detecting the average powers SOan d S Q .In designing the low-pass filter for detecting the averagepower, combining a delay circuit (BBD) with a Butter-worth filter enab les large attenuation and small time delay(1.2 cycles of the input signals).

2) As a typical application of the proposed power detect-ing method , a feedforward p ower control of a high-frequencycycloconverter has been investigated.

APPENDIXD E R I V A T I O NF (13)

The arbitrary repetitive voltages and currents presented ina-/3 orthogonal coordinates are given by

Based on the four components [P ,Q, S D , Q ] , he de-tection of the load power and the reverse calculation ofthe thyristor firing angles become simple and easy to im-plement.

V f n COS ( n o t +6 +V b n COS ( n o t +-Ob,,)V f , sin (not+Of,) - b n sin (not+ b, )

(26)The proposed feedforward power control scheme is suc-cessful for stabilizing the output terminal voltage wave- I f n co s ( n o t +4 f n ) + b n cos ( n o t +4 b n )forms against sudden load change.

Note that the above control scheme is readily applicable to (27)


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1 0 6 IEEE TR A N SA C TI O N S O N I N D U STR Y A PPLI C A TI O N S, V O L. 26, NO . 1, JANUARYIFEBRUARY 1990L o a d c o n n e c t e d Load d i s c o n n e c t e d

111121

[31141

(a )L oa d c o n n e c t e d L o ad d i s c o n n e c t e d

iSU*

i u

: k V A )-:(b )Fig. 11. Transient response under step load change. (Single-phase resistiveload: P =1.4 kW, s b =1.2 kVA). (a) Cas e 1:with feedback power controlonly. (b) Case 2: with both feedforward and feedback power control.

where 8 an d 4 are the arguments of voltage and cur-rent, respectively. Therefore, [ S O , Q ] , he dc component of[ s d , s g ] , is given by

Substituting (26) and (27) into (28) yields (13).ACKNOWLEDGMENT

REFERENCESS . Yokokawa et al . , Application of Fuji static flicker compensator(FSC) , Fuji Elec. J . , vol. 50, no. 9, p . 445, 1977.I. Takahashi et a l . , Universal power compensator of line commu-tated thyristor converters, in Con/. R E . IEEEIIAS Annu. Meeting,1980, p. 858.Y. Yanaura et al ., Reactive power conpensator for flicker suppressionof plural arc furnaces, Nisshin Elec. J. , vol. 26, no. 4, p. 68, 1981.H. Akagi et a l . . Generalized theory of the instananeous reactivepower in three-phase circuits, in Conf.Rec. IEE JapanlIPEC-Tokyo83, p. 1375.M. D. Cox et al. , A new static var compensator for an arc furnace,2EEE Trans. Power Systems, vol. PWRS-1, no. 3, p. 110, 1986.M. Matsui et al ., Loa d chara cteristic s of high-frequency distributionuse cycloconverter, in C o n / . Rec. IEE JapanlAnnual Meeting, no.602, 1983, p. 713.

[7] T. Fukao er a l . , Basic characteristics of cycloconverter for linkingcom merc ial and high-frequency distribution lines, IEEE Trans. Ind.A p p l . , vol. IA-23, no. 5, p. 927, 1987.L. Gyugyi et a/ . The high-frequency link power conversion- A newapproach to static high-power conversion, IEEE Trans. 2nd. App l. ,vol. IA-15, no. 4, p. 420, 1979.S . Seong et al ., Behavior of high-frequency cycloconverter operatingin discontinuous circulating current mode and its control scheme forcirculating current, IEE Japan Trans., vol. D-109, no. 4, p. 243,1989.

[8]

[9]

Mikihiko Matsui (M85) was born in Fukui Pre-fecture, Japan, in 1957. He received the B.S. andM.S . degrees in electrical engineering from NagoyaInstitute of Technology, Nagoya, Japa n, in 1979 and19 81, respectively.Since 1981 he has been with Tokyo Institute ofTechnology as a Research Associate in the Depart-ment of Electrical and Electronic Engineering. Heis engaged in rebearch on the application of high-frequency power conversion, reactive power com-pensation systems, and microprocessor-based con-Mr. Matsui is a member of the Institute of Electrical Engineers of Japan.trol of static power converters and drives.

Tadashi hkao (M85) was born in Shizuoka Pre-fecture, Japan, in 1940. he received the B.S., M . S . ,and Ph.D. degrees in electrical engineering fromthe Tokyo Institute of Technology, Tokyo, Japan, in1964, 1966, and 1969, respectively.From 1968 to 1977 he was with the Tokyo Insti-tute of Technology as a Research Associate; from1977 to 1987 he was an Associate Professor; a ndsince 1986 he has been an Professor in the Depart-ment of Electrical and Electronic Engineering. Heis engaged in research on thvristor control circuits- Iand systems, static var compensators, and microprocessor-based controllersfor static power converters and drives.Dr. Fukao is a member of the Institute of Electrical Engineers of Japan.The authors would like to thank all the members of th elaboratory for their cooperations for this research.

00052680 - A Detecting Method for Active-Reactive- Negative-Sequence Powers and Its Application

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Transcript of 00052680 - A Detecting Method for Active-Reactive- Negative-Sequence Powers and Its Application