3rd Harmonic Reduction

8/8/2019 3rd Harmonic Reduction

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Reduction Hethod of High Harmonic Currents onthe AC Side of the Diode Rectifier Circuits

i n the AC Electric Railways

Tokio Matsuhashi, Kazutaka Itako,Takeaki Moriand Susumu Ohya

Non-member,IEEENihon UniversityKohri yama, Fukushima,963,Japan.

AlrPtract-We propose the method which is able to suppress the gen-eration of the high harmonic currents on t h e AC side of th e dioderectifier circuits i n the AC electric railways by connccting the Utseries circuit i n parallel with the load on the BC side. From theexperimental and theo reti cal res ult s, it is confirmed that t h i smethod produces the desirable ef fe ct for the reduction of highharmonics and the improvement of the power characte rist ics.

I . mRomIaIn the AC electric ra ilways, the s ingle phase re c t i f ie r

c i r c u i t s p la ce di n the car generate high harmonic currentson the AC side.The lower order components of th e genera tedharmonics may cause breakdown and overh eating of t hepowersource transformer and the Power Factor improvement capac-itor etc.. Also,the higher order components cause inductiveinte rfer enc e t o neighboring communicationl i n e s and thet ra in cont ro l infornat ionetc..

A a countermeasure, the AC f i l te r to reduce harmoniccurrents on theAC si d e has been adoptedCllC21, buti t doesnot have much effect[3][4]. Also, p roblemC 51 such a sincrease in the size of capacitor kVA acconpanied by funda-mental harmonic current inflow arise.

Then, we propose the new redu ct ion method[61[7]C8] of th ehigh harmonic currents in thecar using the d iode rec t i f ie rc i r c u i t s . I t is able t o s u p p r e s s the generationof the highharmonic currents on the AC si de by connecting theCRseries c i r c u i t in parallel with the load on theDC s ide oft h e r e c t i f i e r circuits.

In th is paper, the the ore tic al analysisC91 of the sin glephase re c t i f ie r c i rc ui t adopted th is methodis pre8ented.Int h i s ana l y s i s , we separat e in to two operatingnodes andcarry out the circuit analys is foreach d e . Furthermore,we make ca lc ula tio ns and experim ents onthe condition ofelectric railways, and then indicate thepower charac ter i s -tics and the reduction ef fe ct s of high harmoniccurrents.And, it is c l a r i f i ed t ha t adopt ingthis method t o th ecarusing the d iode rec t i f ie r circuits produces the des i rableef fe ct s fo r reduction of the high harmonics andthe powerc ha rac t e r i s t i c s .

The equivalentcircuit configuration of a tap cont rolcaris shown with a so li d line in Fig .1 . In th i s c i r cui t , Xpand Rp showthe resul tant reac tandinductance Lplandtheresistance on the AC power sourc e si de . Xd and Rd showthe

Member, IEEEKanagawa Institute of TechnologyAtsug i ,kanagawa, 243-02,Japan.

e a

R P XP

.......

d

Rd

I id2Xd

Fig.1 . Equivalent ci rcu it of ele ctr ic rai lway

applied this method.

resultant reactance(inductanceM) nd resistance of the DCseries motor and smoothing reactoretc..

Genera l ly, the equivalent c i rcu i t on theUC motor side isexpressed in an alternat ing equivalent resi sta nceRt,react-ance Xd and a const ant counter e.m.fE. In t h i s analysis,wesubs t i t u t e a DC equivalent resistance Re for a countere.n.f E. Then, i n Fig.1, Rd showsRt+Re. The influence oft h i s treatment is discussed i n the la ter chapter.

Fir.P (a) shows th e volta ge andcurrent waveforms on theAC s ide of this ci rcui t conf igura t ion .In this figure, ACs ide cu r r en t i p con ta in sthe high harmonicsbased on theinductive load.

Then,we proposethe new method that the CR series circuit(shown a dotted linei n Fig.l)is connectedi n pa ra l l e l w i t hthe load on the DC side. Iherefore,DC sidecircuit cons i s t s

of the pa ra l l e l circuit of the load and theCR seriesc i r cu i t . Then, i f t he r e l a t i onof the c i rcui t cons tants onthe DC s i d e ca n be maintained as follows

impedance of the DC si de can be considered to be apureres is tance .

Fig.2(b) shows the voltag e and cu rr en t waveform on th eAC si de under the condition of t he equation (l).TheAC s i d e

XdXc=Rd2=R2(constant res is tance condi t ion1, (1)

(a) General waveforms. ( b ) Waveforms applied th i s method.

Pig.2. Voltage a n d current waveforms on the AC s i d e .

0-7803-0634-1/92$03.OO IEEE 1343

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current i p beco rn a si ne wave which does not conta in t hehigh harno nic components.Also, th e AC side impedance hasef fe ct only on Power Factor and thecurrent magnitude onth e AC s i de .

Thus , when the load constant values ar e given, the moatdesirable values of the CR ci rc ui t fo r high harmonicsreduction canbe determined bythe equation (1). But , i npractice, the conditionis not always aa t i s f i ed for reasonof the load f luc tua t ion . In th iscase, t h e ACside inpedanceh a s an effect on theACcur rent waveform. Therefore, in t hearea that the equation (1)is not s a t i s f i e d , t he cha r ac t e r-istics of high harmonics reduction and effi cien cy have t obe investigated.

In order to carry out tba above-mentioned investigation,analysis method ofthe r e c t i f i e r circuit w i t h t h e CR seriesci rcui t on theDCs ide is described in the next chapter.

1. ANALYSIS OF WBPBCTIMER CIRCUITY I T Um CR SRRIB CIRCUIT

In the r e c t i f i e r c i r c u i t w ith t heCR s e r i e s circuit onthe DC si de , commutation cond itionca n be divided into twomodes i n coapliance with ci rc ui t constan t conditions.

(1) There is commutation s t a t e . ( d e1)(2) There is no commutation state.(mode2)

And constant resistance conditionis located i n boundary ofmodes 1 and 2.

A . Aoalysis of .bde 1

In t h e CR series circuit, whenC is small or R is l a rgein comparison w i t h the CR const ant valuea given by thee q . ( l ) , t he r e is commutation state.

1 1 I-4 - -----I

Pig.3. Voltage and cur ren t wavef orm( mode1 ) .

Pig.3 shows th e voltage and curr ent waveform int h i scondition.Each symbol corresponhto Fig. 1 For the analys isof the c i r cu i t i n Fig.1, commutation s t a r t anglea , hecurrent s of each par t i n commutation and re cti fi ca ti ons t a t e s h av e t obe calculated.

(a) Commutation start anglea

Commutation start angle is rec t i f ica t ion end phase inwhich terminal voltage of rectifiercircuit becomes zero.Hereafter,v.b andvd in Fir.1 keep zero,because a l lrecti-f i e r elements a r e i n shor t s ta te . Hence , c i r cui t equationsa r e given in the fo l lowing d i ffe ren t ia l equations;

where each in it ia l cu rrent a t commutation st a rt anglea isi p = - i c d , i d i = i c d i , d 2 = i c d 2 and iCd=ie*i*icd2. Therefore,t he s t a r t ang l e a of commutationstate is

a=sin-I C (X,(Xc i cdi/R+Ra i az/Xa)(8)R P ( i d i + i cd2)) /EJ

(b) Couutationstate ( a 4 8 5 a + U

In the commutation state,the AC s i d e circuit and the DCs id e c i r cui t respective ly behave as independentcircuit,because th e terminal voltages of re ct if ie rcircuit are inshor t s ta te.By the so lu t io ns ofthe equations (2)-(5) eachi is shown in the following equations;

where Zl= (RP2+Xp2) $l=tan-l(X,/R,) and the in it ia lcurrent s a t commutationstart angle a a r e i p = - i c d , i d i = i c d i ,i d 2 = i c d 2 and i d = i c d 1 + i c d 2 . Commutationstate ends, when i,becomes equal to i d .

(c) Rect i f ica t ion s ta te( a + U S 6 5 1~ + a 1

In the rec t i f i ca t ion s ta te , the equivalentcircuit isc o n p o d of the AC s ide c i r cui t and theDC s ide circuit.Hence, the ci r cui t equat ions are g iven i n the followingdifferent ia l equat ions ;

By the so lu t i onsof these equations eachi is as fo llows;



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where the in i t i a l va lues a t re c t i f ica t ion s t ar t anglea + Ua r e i d l = i R l d l , i d 2 = i ~ l d 2 nd q=qR.In these equations,Zl-ZT,$2 ,Tn and K, are constants and are showni n appendix. V I

V I

- i I ~ I

(d) Flowchart of calculation

In the case of node1,the flowchart of each currentca lcula t ion u s i n g the above-mentioned equationsis shown i nFig.4.

B . Analysis of rode 2

In th e CR s e r i e s circuit,when C i s l a rge or R is small i ncomparison wi th th e CR constant values given by the

equat ion ( l ) , thereis no commutation st at e. And the ci rc ui tgives rise t o the s t a t e ( I n t e r rup t i on s t a t e ) i n which nocurrent flowsi n any diode.

Fig.5 shows the voltage and cur ren t waveformi n thisnode. When t h e c i r cu i t i n t h i s node is analyzed, rec t i f i - (a ) Rect i f ica t ion s t ar t angle8 1ca t io n s t a r t a n g le B 1 and currents of each part i n r e c t i -f ica t io n and in ter rupt ion s ta t es have t o be ca lcula ted .

Pig.5. Voltage and cur ren t waveform( mode2 )

Rec t i fi c a t ion s t a r t ang leP i s interruption end angle

Therefore, B i is shown i n the following equation;a t which vat,(=ea)is equal to vd .

~ . _ _ _ _ _ _ _ _ _

~ s . ( 7 ) , ( 8 ) , ( 1 0 ) a n d ( l l )

harmonic analysiscalculation of K.F,P.F aid J P

Fig.4. Flowchart of calc ula tio n( mode1 ).

where current and charge at p i a r e i d l = i R Z d i and q=qR2.Hence, from eq. (191, equation (20) is obtained;

81=sin-' ( ( R i 2 d i + o X, qRZ) /Em) . (20)

(b) Rect i f ica t ion s ta te( Bid 0 B2)

The current i n the r e c t i f i c a t i o n s t a t e a r egiven bysubs t i t u t i ng f l1 f o r a + U i n the eqs. (16)-(18);

where the i n i t i a l va lue s a t r e c t i f i c a t i on s t a r t ang le8 1a r e i d l = i R 2 d2 , i d 2 = h Z d l and q = q R 2 . When i d 2 is equal tocapacitor discharge currenti d 1 , ec t i f i c a t i on s t a t e ends .

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The constants i n the eqs.(21)-(23) are equal to thevalues( appendix) which ar e obtained by sub stit utin g,respect ive ly, in i t ia l va lues8 1 , i R 2 d 1 , - i R 2 d 2 and q R 2 f o ra + u , i R l d l , i R l d 2 and q R 1 .

(c) In ter rupt ion s t a t e( B 2 5 0 S ?c + B 1 )

In the in ter rupt ion s ta te , the charged energy i ncapacitor i s supplied to the load andthe c i r c u i t i scomposed of the closed circuit onthe DC s ide .

Hence, the c ir cu it equations aregiven i n the followingdifferent ia l equat ions ;

calculationof rectificationstar1 angle 81 eq.(20)

calculationof rectificationI

By the solutio ns of the equations (2)-(5) eachi and v a reshown i n the following equations;

where the condition of the ci rc ui t constantsi s i n thevibratory case. Then,

And, i n i t i a l va lues a t in ter rupt ion s t ar t angle8 2 a r e i d 1= - i d 2 = i 1 d 1 and q = q I . When vab(= ea) becomes equal toV d,in ter rupt ion s ta te ends .

(d) Flowchart of calculation

In the case of mode2, flowchart of each current calcula-t ion using the equations given above are showni n Fig.6.

IV. ANALYSIS RESULTSAND CONSIDERATION

By us ing th e an al ys is way showni n the former chapter,the analys is res ul t s consideredthe condi t ion of e lec t r icrailway are showni n the following.

A . Circuit condition and wavefom of voltage and current

In the elec t r ic ra i lway, the constant values of thepopular DC motor MT-52 i n the rated load condition areR=0 .394R, X=1.49652 and E=675.8V( equivalent res is tance

Re=1.185R 1. Including the impedance of smoothing reactor,their values[lO] ar e Rt=O.415R and Xd=2.28R a s the valu escorresponding t o the c i r cu i t conf igura tion .

c s t a r t )~

I assumption of initial values 1

calculationof interruption=end values st at e eqs. (27), (28)and(29)

,. .,

I vI I end va lue s in i t i a l

calculationof K.F,P.F and Jp

Fig.6. Flowchartof calculation( mode2 ) .

For example, i n the ED75 systeo[11][12], their constantsvariable limits owing to change of the load cu rrent valuea r e R t =0.385-0.555R and Xd=2.08-5.56R .Also, impedanceratios among the constantsi n t h e e l e c t r i c r a ilway c i r c u i tar e Kd=Xd/Rt=5-15, KL=Xp/Xd=0.05-0.3 andKR=Rp/Rt=O.1-0.3, and, the t u r n r a t i o n[12] of the main transformeri sn=ls.O,etc..The rate d capa city of themain transformer usedi n the

experiment is 200VA. Rated primary voltage is 100V(f=80Hz)and rated secondary voltageis 15V. Turn r a t i o n=Ni /N2+6.67. Secondary leakage reactanceis 0.0314R .Each circuitconstant value usedi n the experimentsi s about s i x timeslarger than practic al values owing t othe res t r ic t ion ofthe experiment system. Then, th e im pedances onthe AC s i d econverted int o secondary si de are Rp=0.74Q and Lp 3. 6d .Assuming that the constant values ofthe motor i n the ra tedcondition are maximum load constants, values ofR t , Re andLd ar e 2.5 R, 7.OR and 36mH.Also, because the values ofimpedance ratioKD, KLand KRare 5.4, 0.1 and 0.3, t h e yare w i t h i n the range of the practice example.

Pigs .7(a) , (b) show examples of the voltage and curren twaveforms i n the experiments. Pig.7 (a) shows waveformsi nthe case of the CR ser ies c i r cu i t non- inser tion . P ig.7(b)shows waveforms i n the case of the CR s e r i e s circuit

inser t ion(C=400pP,R=9.5R) and the ir values sa ti sf yn e a r l ythe constant resistance condition. Each symbol correspondsto Pig.1. In the waveforms of Fig.7(a),ip shows change likea square uave i n the neighborhood of phase angle zero and

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I - .'-r ---I,---,---

I O V/ d i v

0 . 5 i \ / d i v

ZOV/div1 . i \ / t l i v

(30)(31)

Klirr Factor K. F = I h / I .Total Power Factor P . F = I I/ .cos+ 1

k = l k 1

n = 2 k - 1 , m = 2 k + l9 i =phase difference between the fundamental harmonic

I I effective value of the fundamental harmonic current.voltage and current.

0. Srnsldiv( a CR series circuit non-insertion

-

( b ) CRser ies c i rcui t inser t ion .o . m s / t ' "

Fig.7. Experimentalwaveformsof voltage and current.

pai. Therefore, i p contains a larg e quan ti ty of h ighharmonics. Also, the r e c t i f i e r c i r c u i t g e t s i n t othe s t a t ethat instantaneouse value of vdi s zero(commutation state).And, the ri pp le of id2 is low due t o the load reactance.In the waveforms of Fig .7(b), accompanied by in ser tio n ofthe CR c i r c u i t , i p approaches a sine waveform. Id2 showschange very l i t t l e by i n s e r t in g the CR c i r c u i t . I d ireiterates charge and discharge in the twotimes frequencyof the power sourcei n accordancew i t h magnitude relationbetween vd and capacitor voltage.

From the above-mentioned, i n the constant resistancecondition, i t was made sure t h a t i p approaches a sinewaveform and thati t contains high harmonics very l i t t l e .

B . Characteristics fo r constants change of the CR seriescircuit

In this paragraph, reduction eff ect of th ehigh harmonicsfo r constants change of the CR s e r i e s c i r c u i t is i n v e s t i -gated. Also, it shows considerations for selection of theci rcu it constant values. These investig ations are giveni nthe condition of the load power 21.4W constant.

(a) Efficacy for third harmonic current,Klirr Factor andTotal Power Factor.

The definitionsC131 ofKlirr Factor and Total PowerFactor are showni n the following equations;

t4"

-

Capacitance c( P F)+

Fig.8. Capacitancevs. third harmonic current,Porer Factor andKlirr Factor.

Fig.8 shows the chara cter ist i cs of thir d harmonic curren t,Klirr Factor and Total Power Factor for variation of theCRcircuit constants on the condition that the value ofimpedance on theAC side and the load constant are fixed.Because investigation oft h i s method is aimed at reductionof equivalent disturbing current Jp, the value of theres is tance R fo r C except fo r the constant resistancecondition is selected i n th e condition whichthe value ofJp is the lowest.

The th ird harmonj c c urre nti s regularized by the value ofthir d harmonic curren t13 0 i n C=O. A their results show,th ird harmonic curre nt andKlirr Factor are zeros i n th e

con stant resis tanc e condition and even i fC is small, thee f f e c t is enough.

In Total Power Factor, even i f value ofC i s very small,the e f f e c t is great.The calculationresults agree w i t h th eexperimental results i n Fig.8.

(b) Effect for the equivalent disturbing current Jp andl o s s

Considering the induction obstacle of the communicationl i n e s , it is customary th at the disturbance degreeisevaluated by the equivalent disturbingcurrent. Accordingt o CCITTC141,the d e f i n i t i o n is revealed i n the equation,asfollows;

(321

I ,, : ffec t ive va lue of the n t h harmonicS : oise evaluation coefficient.

J P ~ C(sn n > 2

where

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t

(AC side insertion)counter e . n f E).

S I \

-A- - -* - -

\ onstant resistance condition

FiE.9. Capacitance VS. Jp/Jp,

Pig.9 shows the ch ar ac ter is tic s of Jp, coaparedt h i smethod with the case of inserting the CR c i r c u i t i n t o t h eAC side. The values of the CR c i r cu i t cons t anti n Fig.9 andPig.8 a r e the same. V ertic al ax isis regularized by thevalue(Jp0) of Jpi n C=O.

Experimental results considered the constant e.n.fE a r eshown i n Pig.9. A the result shows, value of C on the DCs id e is eff icac ious i n the value given by the cons tantresistance condition or aore than it . The calculationre su l t s ag r ee with the experimentalresults i n Fig.9. Jp ofAC s i de i n se r t i o n is about ten t in es as la rg e as Jp of theDCs ide inser t ion i n the constant resistance condition.

Therefore, th e reduction eff ec t of theCR ci rc ui t on theDC s i de is good.

S i g n a is nuch the saneresult a s s i g n 0 subs t i tu ted theresistance for the constant counter e.m.fE. Hence, i t wasnade sure tha t subs t i tu t ingthe res is tance is per t inent .

According to the reports ofUIC the f i f t h s t ee r in gc o r n i tt e e , e l e c t r i f i c a t i on s ec t iona lmeeting and WG-5-A-22,the reduction ef fe ct of Jpi n former method inserted theACt u ned f i l t e r is about V3.7 i n the examinationresults by

the car of Sweden National Railways. Also, according tothemeasurenent examples used the 951t y p e examination car ofJR, i t is reported th at Jp becomes w i t h i n the range ofV1.04-111.78.

The red uction ef fe ct ofthis method i s very good a scontrasted w i t h these resul t s .

Next, Pig.10 shows increase r at e( (I pc R- Ip )/I F 100) ofACcurrent and power loss( PcR/P,X~DO ) of the CR seriesc i r cu i t f o r v a r i a ti on ofthe capacitance as contrastedw i t hth e AC s i de i n s e rt i onwhere

I, : ffective value of the current on the AC s i d ei n the case of the CR ci r cui t non-inser t ion

I,CR : effec t ive va lue of the current on the AC s i d ei n the case of th e CR c i r cu i t i n se r t i on

PCR

Pa : ota l e ffec t ive power.

: effective power ofthe CR circuit

The cond ition s of Fig.10 and Fig.9 ar e the same.A showni n Pig.10, i n the constant resistance condition of theDCs ide inser t ion , increase ra te of th e AC current becomes

increase rate CR c i r cu i t(DC side inser t ion)

T !

/ measured:calculated

counter e.m.f E ) .

(AC side inser t ion)measured

, L

A

Capacitance C ( c r F ) +

Fig.10. Capacitancevs . increase rateof I Ccurrent and powerloss of CR s e r i e s c i r cu i t .

maxinun value(about 13%).Likewise,in th e AC s ide i n se r t i on ,i t becones about IO$.Also,inthe r e c t i f i e r circuit inser tedthe CR c i r c u i t i n to t he CC si de , no na tt er how muchthe Cincreases, I, does not increase. But , i n the r e c t i f i e rc i r cu i t i n se r t ed the CR c i r c u i t i n t o t h eAC side, the more

C increases, the morei, increases, becausethe fundamentalharmonic current flows into theCR c i r cu i t on the AC s ide .I n the AC s ide inser t ion , naximun value of the CR c i r c u i tl o s s is about 24%,andi n th e DC s ide inser t ion , i t s maximumvalue is about 13%.

I t is evident from the above-mentioned th at connectingthe CR c i r c u i t with th e DC s ide is a p rof itab le method.

(c) Effect for Jp ofthe inductive reactance onthe AC s ide .

In order to know the eff ec t for Jp of the induct ivereactance on theAC s ide , ca lcula t ionresults of the Jp/Jp,for the CR ci rcui t t ime cons tant with the parameter of theinductive reactance on theAC side are showni n Fig.11.

I t canres is tance

is 3 7 8 9 ~ s

t,

sY

be seen from the r e s u l t s t h a t i n t h e constantcondition ( C=8 8.89p F, R=9.5R, Time cons tant

), s t r i k i n g reduction effect can be got and the

.n

Y

-ElY

6 0 . 5 -

Y

r

Z U O U 4 0 U U 6000 8000 l U U 0 0 12000

Tine constant of CR s e r i e s c i r cu i t ( p s )+

Fig.11. Tine constantof CR ser ies c i rcui tvs. Jp/Jpn.

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value is 516 as contrasted with Jp ofthe CR circuit non-inse rtio n. Further, Jp showsminimumpoint without referenceto magnitude of the indu ctive reactance onthe AC s ide .Also,in the case of (C=200/1F,time cons tant 130 0ps)and(C=BOOpP, t ime constant6 0 0 0 ~I, their cha rac t e r i s t i c s a r es im i l ar t o the above-mentioned one. When th e more di ff er en t

th e time constant i s from optimum point,the greater thee ff e c t f o r J p of the inductive reactance onthe AC s ide is .And, the smal ler L, is , the higher the relative value of Jpis .

In the diagram, i n the absence of the impedance on theACs ide , sign I is the time constant i n th e minimum val ue of Jp.In the presence of the impedance on theAC s ide , t h i s timeconstant is approximately same valuei n comparisonwi th it .Therefore, when the load constants are given, the bestCRci rc ui t constants can be determined without reference tothe impedance on theAC s ide .

C. Mfect for Jp of the load variatim(coddering theinductive reactance variation w the AC side)

In this paragraph, assuming a tap co ntrol car,the char-

ac t er i s t ic s of Jp for the load var ia t ion are inves t iga tedon the assumption thatload current is constant control andtha t t u r n ra ti o of the main transformer is ~ 1 6 . 0 n t h emaximum load condition.In the inves t iga t ion of t h i s para-graph , he load variation means variation ofthe constantcounter e.m.f E accompanied by a speed control.

In t h i s investigation, becausethe constant counter e.m.fE is es tin at ed as Re=7.0R in the maximum load cond ition,Fig. 12 shows the cha rac ter ist i cs of Jp calculated bychanging the value of Re fromOR t o 7 .OR. However, theload current id:! is 1.5A con sta nt. Jpis obtained fromvalues converted in to primary side by computing theturnra ti o for each secondary voltage.In addition, constantvalues of the CR ci rc ui t are selecte d under the conditionthat Jp becomesminimumv a l u e i n the maximum load condition.A the results show, i t can be seen th at Jpi s great ly

suppressed for increase of the loadaverage power i n eachcapacitor. Also, i n the case of the CR c i r c u i t i n se r t i on,when t h e inductivity reactance onthe AC s ide increases ,

M

cs Load average wwer P,(W)-+ naximun load w wer

Fig.12. load average power YS . JP/JPQ

the value of Jp becomes relativelylow l i k e i n the case ofthe CR c i r c u i t non -in ser t ion .

From t h e above-m entioned, i t i s confirmed that if bestvalue of the CR circuit constants is selected i n themaximum load condition,the circuit can always maintainlowvalue of Jp.

v . CaNCLuSIOw

The prop osed method i n t h i s paper can make the highharwnic currents on the AC si de reduce by gett ing thecorrect harmonic distribution onthe DC si de by connectingth e CR ci rcui t wi th theDC s ide .

The inves t iga t ion results of a tap control car appliedt h i s method can be summed upas follows.

1) The best value of the CR circuit constants i s given i nthe constant resistance condition and even ifthe value ofC i s a l i t t l e differ ent f romthe condition, the eff ect isgreat . Fur ther, thebest value of res ista nce R f o r t h evarious C may be se lec ted wi thout reference to theimpedance on th eAC s i d e i n the e l ec t r i c r ai lway c i r cu i tcondition.

2) In the constant resistance condition, the value of theequivalent disturbingcurrent Jp is 5$ a s cont ras ted wi thth e CR ci rcui t non- inser t ion .3) The effects forKlirr Factor and third harmonic current

ar e gre at too. Andi t can be s a id t ha t much hope is foundi n the reducing thir d harmonic curren t a tthe inside of thecar.

4) Increase i n s iz e of capaci torkVA accompanied by thefundamental harmonic current inflowis small and thereduction effect of h igh harmonic currentsi s great too .Furth er, To tal Power Factor a ls o can be improved.5) Jp is low w i t h i n the wide rangeof the load variation

and even maximum valueis about 2%. There fore, by usingth is method, i t becomes pos sib le t o narrow a gener ationarea of the induction obstacle.

From these results, it is confirmed that t h i s method hasmuch effec t on the reduction of h igh harmonic currents andimprovement of Power Factor.

A t the present t ime, the devices used the re c t i f ie rc i r c u i t s are on the inc rea se year by year. Hence,i t mayappear th at the reduction countermeasureof high harmoniccurrents generated from the devicesw i l l be investigated i nfu ture .

The au th or s thank Prof .Sat oru Sone of Tokyo Un ive rsi tyand Prof .Tadashi Pukao of Tokyo Technical Uni versit y f o rthe i r ins t ruc t ive advices .

REWENCIS

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c11 T.Hongo: On the Higher Harmonic Curren tsi n AC Side of theSingle Phase Full-Wave Rectifier Circuitw i t h th e AC Fi l t e r (1nNo-Grid Control ) .Jour.IEE of Japan 79,722 (1959-9)

C21 T.Ilongo: On the Higher Harmonic Curren tsi n AC Side of t heSingle Phase Full-Wave Rectifier Circuitw i t h th e A CFil ter (1nGrid Control).Jour.IEEof Japan 80,35 (1960-1)

C31 Special steerin g committee for induction reserch: The NewestTrend and Theme for the Kagnetic Induclion.Jour.IEE of Japan (1979)

[41 Railway Electrification Society:Reserchof Various Problems i nthe Thyr is tor Appl ica t ion car. (1968)

C51 Railway Electrification Society: Reserch Steering Commitleeofnon-contact control car. (1970)

C61 T.K ats uh ash i and Y.Anemiya: The Nois e Reductio n Method of th eDevices Containing R ect ifi ers .Pa ten t number 696027(1973) Japan

C71 T. natsuhashi, . Uatahiki,S . Shirai and T. Tani no: Experiments fo rReduction of High llarmonic Curr ent s on th eAC Sid e by th eFi l ter on the DCSide.The national conference of IEE of Japan (1973)

High Harmonic Currents on theAC Side by the F il te r onSide i n t h e R ec t i f i e r C i r cu i t .The northeast branch conferenceof IEE of Japan(1983)

C9l K.Itak o and T.Katsuhashi: The Reductionof th e High HarmonicCurrents i n the Rectifier Circuit-In the Case of Counter e.m.f

Non-consideration-.The national conferenceof IEE of Japan (1990)

Single Phase Rectifier Circuit Usedi n the Electric Railway.Jour.IEE of Japan 87,539(1967-3)

t i f i e r c i r c u i t u sed i n the Elect r ic Rai lway.ibid. 87,2232(1967-11)

cl21 Railway Elec tri fic ati on Society: Basic Studyof Non-contactControl Car. (1970-3)

C131 T.Pukao: Ef fec tiv e Power and Rea cti ve Power. (st ud ent column)Jour.IEE of Japan (1981)

Cl41 CCITT: D ire cti ves (1963)

C81 T.Ueda,T.Matsuhashi and T.llongo: Th e Reduction of theAC Sideth e DC

cl01 N.Irie,T.Kawazoe and T.Kawamura: Ca ra ct er is ti c Calculat,ionof

C111 N.Irie and Y.Yamazaki: Normalized Characteristicof Phase Rec-

K3 = CqRi Z 3 2 + Z 4 2 ) - n E, ( Z ss in ( a + u+ d 2) - Zrcos (a + U + $2)) / 01 /( z 3 z+ 242)+ ( ( T 2 - T i ) - ( P i - P z ) ) /A

A = ( T - T 2 ) ( Pi - P 3 1 ( T 3-T 1 P 2 - P 3 1P i . P 2 and P 3 are root of the character is t ic equat ion

and their values are showni n the following;

PI=- x - y - zP 2 = - 0 x - w 2 y - zP3=- 0 2 x - w y - z

wherea = ( Rd R p + X c X p + X d ) + R ( R p + R d ) ) X P &b = X , ( R p + R a ) / X pxda=(- * & / 2

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3rd Harmonic Reduction

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