The a-c voltage control circuit, composed of parallel connection of a SCR and a reactor, gives the similar performance as the control circuit of a back to back SCR pair. However, the control characteristics of this circuit is affected by magnetizing characteristics of reactor. In this paper, the circuit with the resistive load has been analyzed by using the approximated models of hysteresis loop of core materials, where the SCR's forward voltage drop is taken into account. The results of the analysis have revealed the facts as follows, I) The control characteristics of the a-c voltage in average value is independent on the magnetizing characteristics of reactors except in the vicinity of minimum output point. But, in effective value, it is not valid. 2) A SCR's forward voltage drop results in the reduction of not only SCR's current but also reactor's current. 3) The a-c output current does not include the d-c component, if the winding resistance of the reactor is negligible

Fujitsuka, Takeshi

Himei, Toyoji

Inoue, Jyunichi

Wakabayashi, Jiro

Okayama University Scientific Achievement Repository

MEMOIRS OF THE SCHOOL OF ENGINEERIKG OKAYAMA UNIVERSITY, Vo!. 3, Ko. I, SEPTEMBER, 1968Analysis of the A-C Voltage Control Circuit with ParallelConnection of SCR and Reactor"Toyoji HIMEl, Takeshi FUJITSUKA, Jyunichi INOUEDepartment of Electrical Engineeringand Jiro WAKABAYASHIEngineering Research Institute Kyoto University(Received March 15, 1968)The a-c voltage control circuit, composed of parallel connection of a SCRand a reactor, gives the similar performance as the control circuit of a backto back SCR pair. However, the control characteristics of this circuit isaffected by magnetizing characteristics of reactor. In this paper, the circuitwith the resistive load has been analyzed by using tbe approximated modelsof hysteresis loop of core materials, where the SCR's forward voltage dropis taken into account.The results of the analysis have revealed the facts as follows,I) The control characteristics of the a-c voltage in average value is inde-pendent on the magnetizing characteristics of reactors except in tl:e vicinityof minimum output roint. But, in effective value, it is not valid.2) A SCR's forward voltage drop results in the reduction of not onlySCR's current but also reactor's current.3) The a-c output current does not include the doc component, if thewinding resistance of the reactor is negligible.§ 1. IntroductionThe silicon controlled rectifier (SCR) is a sortof synchronous switch and the circuit of aback to back SCR pair in parallel is an a-cvoltage control circuit. On the other hand,the circuit with saturable reactors i. e., a mag-netic amplifier, is too a similar a-c voltagecontrol circuit. The circuit introduced in thispaper is a new type of the a-c voltage controlcircuit that, though composed of parallel con-nection of a SCR and a reactor, has the similarcontrol characteristics.Here, in order to investigate the dependenceof the control characteristics upon the magne-tizing characteristics of reactor, the circuitwith the resistive load has been analyzed byusing the four models of hysteresis loop,where the SCR's voltage drop in conducting istaken into account.§ 2. PerforIllance of the CircuitThe circuit is shown in Fig. 1. To illustrate* Presented at the Annual Meeting of I. E. E. ofJapan, Kansai District, Oct. (1963), Chugo:w District,Nov. (1963).Fig. I, Circuit diagram.the performance of the circuit, it is assumedthat the reactor has the ideal magnetizing cha-racteristics, as shown in Fig. 3 (a). First, in thehalf-cycle in which the a-c source voltage ap-plies across the SCR in forward direction, untilthe SCR is fired by the gate input, the fullvoltage appears across the reactor and the fluxlevel of reactor will be moved toward the posi-tive saturation level. In this period, the loadcurrent is negligible. Once, the SCR is turnedon, the load current is flowed through the SCRand the source voltage es appears across theload, and the flux level 01 reactor stays stillsince the reactor voltage is negligible.Second, in the succeeding half cycle, thesource voltage e, in turn, appears across theSCR in the backward direction and the load131132 T. HIMEl, T. FUJITSUKA, ]. INOUE and ]. WAKABAYASHI (Vol. 3,From the last equation, it is clear that itzdepend on it, which is controlled by the gateinput to the SCR.Mode Dnonconductingforward I backwa~blocking blocking---A--I--C---DMode BBClassification of circuit modes.conductingMode AMode CFig. 2~ SCRreact~--~~saturated I~~rated !where L: inductance of reactor.{}: arc tan wL/R.Mode A of operation continues until theTable I Classification of modes of operation.forms of output voltage eR and reactor voltageeSR are schematically illustrated too.Here, the following analysis will be carriedout only with regard to the B-H loop in Fig.3 Id), because the analysis of the others in Fig.3, (a), (b) and (c), is contained in this example.Mode D j of operation; When the phase angleof the source voltage is zero, i. e., ilJt = 0, theoperating point of reactor is supposed to be onthe point (0), the intersection of the negativesaturation level - (j)s and the vertical axis. Theperiod from point (0) to point (1) is mode D.The phase angle of source voltage wt = $1when the operating point comes to the point(1) is given byt11 ~~ sin-1 101 RjEm (4)Mode A of operation; At (ot = $" the modeA of operation starts, because the reactor be-comes unsaturated and the SCR is blocked inforward direction. The load current iR is ex-pressed as follows.i R ~~ ';R~?;;}j) {sin(wt-o)_R(t_ 1l1 ) • }. _R(t_ 131 ) (5)-c L w Smeaj-O) -i-IJlc L w(3)(2)(1)where N: number of turns of reactor.ilJ: angular velocity of source voltage.itl: firing angle of SCRitz: firing angle of reactor.es : source voltage in instantaneousvalue.From Eq. 1, the following relation betweenitl and itz may be obtained.3) The resistance of windings of reactor isnegligible.4) The load is pure resistance.5) The approximated magnetizing charac-teristics of reactor are indicated in Fig. 3 (a),(b), (C) and (d).3.2 Equivalent circuits. The modes of ope-ration in a cycle may be classified into (A), (B),(C) and (D), as shown in Table I. The equi-valent circuits corresponding to each modesare shown in Fig. 2.3.3 Boundary conditions and behaviors ofmodes of operation. The four approximatedmodels of B-H loops of the reactor utilized inthis analysis are shown in Fig. 3 and the wave§3. Analysis of the Circuit3.1 The assumptions. To simplify thecircuit analysis, the following assumptions areintroduced.1) The leakage current of the SCR is negli-gible and the SCR has the constant voltagedrop ESCR when conducting.2) The source voltage es is expressed by Eq.(3).current is blocked. In turn, the source voltageacross the reactor cause the flux level to movetoward the negative saturation. When the fluxlevel of the reactor reaches to the negativesaturation level, the load current begins toflow through the reactor in the reverse direc-tion.Since, in steady state, the flux change of thereactor during one half cycle, must be equalthat during the succeeding one half cycle, thefollowing equation will be valid.1 )"1 1 ~"2-N.- esd«(()t) + N.-- es d«(()t)=O0) 0 (V .1t1968) Analysis of the a-c Voltage Control Circuit 133_("t(b)-L 10". ¢"Fig. 3¢. Ii~-A+B -+- C-+-,-D~,'-'"1~:}7~"--",:: A,~\, _("t'"(c)Models of approximated B-H loops,The phase angle w{ = S2, when the SCRturns off, is obtained from the relation of Ep.(12)(14)Mode AI of operation; After S2, the circuitcondition is mode Al of operation similar tomode A of operation. The load current iR andthe reactor voltage eSR are given in Eq. s (5)and (6) by substituting S2 for SJ and also iSR2 atS2 for lui. The boundary point S3 between thismode and the succeeding, is determined byeSR = O. The operating point of reactor is thenat (4) in Fig. 3(d).Mode D 2 and D J of operation; After Sa, theoperating point moves into the inner of theB-H loop. At (JJ{ = IT, the operating point ison the vertical axis and at w{ = S4, reachesto the left side of the B-H loop. The durationfrom [3, to IT corresponds to mode D2, and theduration from 'Tr to [34 does to mode Dc. St is asfollows.') • -1 R (. 1 1e. = Sill E- lSR3 - 01 - (2")mwhere iSR3: reactor current at SJ.Mode C of operation; After S:, the circuitcondition is mode C of operation. The loadcurrent iR and the reactor voltage are ex-pressed in Eq. (5) and (6) by substituting S4 forSI and iSR I for 1..11.At the phase angle a2 when the reactor issaturated, the relation iR = - I. 2 is valid.Further more, since the total flux changesover one cycle in steady state is zero, a2 isgiven by(/',. -1- (j); + (j);' + (j}g = 0 (15)(8)(7)(13)(9)(10)(11 )durationeSR = E SCRiSR = EER(t- :1) + i.SRIThe flux resetting value (j); in theof mode B of operation isd" E SCR (') )'Vr = - -- e2-a jNwwhere ism: Reactor current at al.Mode B of operation; After the SCR turnson, the circuit condition is mode B. The loadvoltage eR, the reactor voltage eSR and thereactor current iSR are given respectively.eR = eS-ESCRpoint (2), aJ, when the SCR turns on by thegate input. The flux change (j}1 (the flux reset-ting value) from the point (1) to (2) is1 )"1(j}r =N.- esd (wt)w /31The correlation of the current and flux givesthe flux resetting value as follows.d 2/Js (. 1'Pr = ~---- ~ lSR1- 01)10,-101134 T. HIMEl, T. FUJITSUKA, J. INOUE and J. WAKABAYASHI (\'01. 3,Fig. 4 Calculated waveforms of reactor voltageand load current.Fig. 5 Calculated control characteristics in effec-tive value (a) and in average value (b).wherc (ft;': Flux resetting value in mode Alof operation.(/)g: Flux gating value in mode C ofoperation, i. e., "flux gatingvalue" means the flux change inthe direction from + (fts to - r/Js•Mode D of operation; After lY2, the circuitcondition is mode D of operation. This modecontinues until OJ! = 2IT. The load current illis eslR.3.4 Control characteristics. As above men-tioned, since boundary conditions and be-haviors of modes of operation over one cycleare determined for any firing angle lYJ, thewave forms of load voltage and therefore thecontrol characteristics are determined for lY"The above analysis of the circuit operationwill be valid to other B-H loops in Fig. 3 byusing the following expressions, that is, I J1 =102 = 0 in Fig. 3 (a), IJI = 102 = I J in Fig. 3 (b), and101 = - 102 = - 1'0 in Fig. 3 (c).3.5 Calculated. According to the analysis,an example has been calculated numerically.Circuit constants and boundary conditions,wave forms and control characteristics areshown in Table 2, Fig. 4 and Fig. 5 respectively.Table 2 Circuit constants and boundary conditions.101 -80mA102 120mAL 5HR 100Em 141.4Vf 60£8('1/ IVPI -3"'I 90°,92 180° - 0.56°/33 180° - 0.22°(34 190 0 + 1.4]0a:2 180 0 + 95°The calculated in the case of idealized B-Hloop, is also shown with dotted line in Fig. 5for comparison.§ 4. Experirrlents resultsIn order to investigate experimentally thedependence of the control characteristics uponthe magnetizing characteristics of reactors, themeasurement are carried out used with fourreactors, that is, Fe 50 %-Ni 50 % oriented(V)10C(V)100e,t10090~ 800~70E-7.~ 60un::~ 50e::0s 40x~~ 302010010090G 800~b 70z~u 60n::~e:: 500S 40x~IJ30201002"'x,0-\ ~\\\\\\,,\\\\30 60 90 I~U l')U 180"1 [DEGREES)(a)-0- parallel quadrilateralB-B characteristics- - }<. - - Ideal rectangularB·H characteristics,,,,'>\.30 60 90 120 150 180"1 (DEGREES)(b)1968) Analysis of the a-c Voltage Control Circuit 135Fig. 6 Observed B- H loops (a), miner loops (b), reactor voltage wave forms (c, upperside) and load current wave forms (c, lower side).( i) Fe 50%-Ni 50% oriented core. (ii) oriented silicon steel core.(iii) oriented silicon steel cut core. (iv) silicon steel stack core.E"" -- ~1(1 I VOLTS]30 60 90 120 ISO 180'" (DEGREES](a) __ Fc50C%l-\iSO(%]corc- -----Oricntcd silicon steel core_. - Silicon steel stack core- 0 - Oriented silicon steelClIt core10090&i' 80'"~ 70bZ'" 600'"'" 502:l§ 40X.' .30",I",20100-60-30lOO90&i' 80'"-< 7Dbz'"GO0'"'"50~ 40 ~xJ~ 3020100- 00-60 :-10 60 ~)() 120 l:iU 180(rt DF(;REESJ(b)Fig. 7 Measured control characteristics in effectivevalue (a) and in average value (b).core, oriented silicon steel core, oriented sili-con steel cut-core with air gaps and siliconsteel stack core for power transformer.The B-H loops, the minor loops at QCj = IT /2and the wave forms of the reactor and voltagesat QCj=7l'/2 are shown in Fig.6(a), (b) and (c)respectively. The measured of voltage controlcharacteristics with resistive load are shown inFig. 7, where (a) is in effective value and (b) isIII average.§ 5. DiscussionThough it seems to be the good identifica-tion between the calculated and the measured,the discussion on the foregoing analysis andmeasurements more over reveals some featuresof the control characteristics as follows.5.1 No d-c component in load current. Inevery modes of operation, the following equa-tion is always true.es = e.~R + eR (16)But, in steady state, since the total fluxchanges over one cycle is zero, the followingequation may be obtained.):"eSR d (wt) = 0 (17)From Eq.s (16) and (17),136 T. HIMEl, T. FUJITSUKA, J. brOUE and J. \VAKABAYASHIWhere, if iSlI is negative, the flux resettingvalue (/J;. is increased. (/J;. affects to increase a'2in mode D of operation.And also, in mode D of operation, the loadvoltage ell is['elld(o)t) =, 0 (18)Eq. (18) tells that the d-c component is notincluded in the load current. This fact is goodfor thc case in which the resistance of reactorwindings is negligible.Otherwise, it is not and the following equa-tion have to be taken into account in mode Bof operation.R"R . R --- e.,-i· ,'iIi.(19)(20)exciting current to the load one decreases ex-tremely. Therefore, the forward current ineffective value and also in average value, isindependent on the magnetizing characteris-tics of reactor except in the vicinity of at ~~ {12.And more, the bacdkward load current inaverage value is true, since the load currenthas not doc component. However, the back-ward load current in effectivc value is not,because the backward current waveform is notthc same to the forward one.5.3 Effect of SCR forward voltage drop E,e}/.As the load voltage ell when the SCR is con-ducting is indicated in Fq. (9), and decreasesby E,ell. Further more, Ese }/ resets the flux byf/J;. in Eq. (13), which results in the increaseda2. In other word, E,e}/ results in the reducednot only SCR's but also reactor's current.The increment of a2 and the decrement ofell in mode D of operation result in the exis-tence of doc component in the load current.5.2 Dependence of control characteristicsupon the magnetizing characteristics of reac-tors. As ai approaches to 132, ill decreases andminimized at a, = {h Then, in the case of themagnetizing characteristics in Fig. 3 (a 1, theexciting current of reactor does not flowthrough the load, but, it does in the cases ofFig. 3 (b), (c) and (d).As al decreases and leaves away from {12,the load current flowing through the SCR in-creases, but, in the fOr\vard load current, thatis, the load current in the direction of the SCRcurrent, the component of the exciting currentdecreases, and then, the proportion of the§ 6. ConclusionThe a-c voltage control circuit with a resis-tive load has been analyzed. The results ofanalysis and measurement have revealed thefact as follows.I) The control characteristics of the a-coutput voltage in average value is independenton the magnetizing characteristics of reactorsexcept in the vicinity of minimum outputpoint. But, in effective value, it is not valid.2) A SCR's forward voltage drop results inthe reduction of not only SCR's current butalso reactor's current.3) The a-c output current does not includethe d-c component, if the winding resistanceof the reactor is negligible.

Analysis of the A-C Voltage Control Circuit with ParallelConnection of SCR and Reactor

Abstract

Similar works

Full text

Available Versions

Okayama University Scientific Achievement Repository

Okayama University Digital Information Repository