The influence of magnetic saturation of iron-core on the performance of thyristor phase control circuit with series RLC elements is described. The circuit is analyzed by applying an approximate model of three straight lines to the flux Φ vs. current i curve of the iron-core reactor. And the influence on waveforms, r.m.s. values, power factor and response are discussed

Funabiki, Shigeyuki

Himei, Toyoji

Nakanishi, Sen-ichiro

English

Okayama University Scientific Achievement Repository

Memoirs of the School of Engineering. Okayama University. Vol. 16·2. March 1982Influence of Magnetic Saturation of Iron-Coreon Performance of Thyristor Phase Control CircuitToyoji HIMEI~ Sen-ichiro NAKANISHI*and Shigeyuki FUNABIKI*(Received February 5. 1982)SynopsisThe influence of magnetic saturation of iron-coreon the performance of thyristor phase control circuitwith series RLC elements is described. The circuit isanalyzed by applying an approximate model of threestraight lines to the flux cjl vs. current i curve ofthe iron-core reactor. And the influence on waveforms,r.m.s. values, power factor and response are discussed.1. IntroductionThe AC power control circuits of inverse parallel thyristor pairare widely available for the reasons of simplicity of circuitconfiguration and easy controllability, etc. l )2) In most case, theload has an iron-core reactor, which has non-linear characteristicssuch as hysteresis or magnetic saturation3)4) . So, the iron-corereactors are designed and/or used usually under the condition of no-influence by the non-linear characteristics at a given supply voltage.However, when the thyristor phase control circuit has series RLCelements, it may cause an abnormal phenomenon such as extraordinarilyhigh voltage and heavy currentS). Furthermore, if there is an iron-corereactor in the above circuit and it's flux lebel comes up to saturation,the phenomenon is more complicatedly and inscrutable affected by thenon-linear characteristics of an iron-core. Therefore, it is necessaryto make clear this influences of non-linear characteristics, especialy* Department of Electrical Engineering.3132 Toyoji HIMEL Sen-ichiro NAKANISHI and Shigeyuki FUNABIKImagnetic saturation, on the performance for the security of powersystem connected to the AC power control circuit and the selection ofthyristor rate.Thus, the authors analyze the circuit by applying an approximatemodel of three straight lines to the flux ~ vs. current i curve ofthe iron-core reactor. And the influences on current and capacitorvoltage waveforms, r.m.s. vlaues of current and voltage, power factorand transient response are discussed in detail.Fig.l. Phase control circuitwith an iron-corereactor.RiLlSCR~ ir---------l - _f-----------,1 ~I($J .=E",si'l wIIIL2.1 Circuit and Assumption2. Analysis of Circuit PerformanceThe thyristor phase controlcircuit with an iron-core reactorwhich has a magnetic saturation isshown in Fig.l.Now, we introduce the followingassumptions into this analysis.(1) The thyristor is an idealswitching element and fired symmetri-cally in each half~cycle.(2) The source voltage waveform issinusoidal, and its impedance isnegligible.(3) The magnetization curve ofreactor is approximated by thethree straight lines as shown inFig.2. In this figure, ~ is the8flux when the reactance changesfrom L1 to L 2 , and ~m is themaximum flux, in the circuit wherethe reactor of L(~) is replaced toa linear reactor with inductanceL 1 and the thyristors are shorted.Fig.2. Approximate model ofreactor magnetization.Influence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Cireuit 332.2 Characteristics EquationsWhen the thyristor is conducting in Fig.l, the circuit equation isdiL (4)) + Ri + qdt a E sin(wt+a.) ,m (1)where, 1) mode Iif 14>1<4>s2) mode IT.if 4» 4>= sif 4><-4>= sthenthenthenL(4)) = L 1 '4> = L1 i ,} (2)(3)(4)Eq. (1) is solved under the condition of eqs. (2)~(4). Then, for thepurpose of making clear the influences of magnetic saturation, twofollowing parameters are introduced.(5)z4>mEmL1/IR2+(WL1-1/WC) 2wL1-l/wCtan- 1R(6)Where, k is a parameter which indicates the mode changing point in thereactor model approximated by three straight lines, that is, therelation between the source voltage and the flux in which may saturate.Also, Z is another parameter which indicates the ratio of inductanceL1 , in mode I to L 2 in mode IT •2.3 Numerical AnalysisThe characteristics equations mentioned in previous section aresolved in each mode, by using the regula falsi method. The computerprogram reads r.m.s. values of supply voltage E, resistance R, displace-ment angle of load ¢1' a damping factor 81 (=R/2.;C/L1 ), Z, and k asdata and gives the steady state performance and the transient performance,34 Toyoj i HIMEL Sen-i chi ro NAKANISHI and Shigeyuki FUNABIKIe.g. waveforms, r.m.s. valuesand harmonics of current and eCt)voltage.In the following analysis, bothE and R are set to unity for nor-malization, and particularly theeffects of parameters k and Z onthe circuit performance are dis- VLcussed. Fig.3 shows the calculatedwaveforms.3. Influences of Magnetic Satura-tion on Circuit Performance3.1 Influence on Current andvoltage Waveforms Fig.3. Waveforms.The current and capacitor voltage waveforms in the thyristor phasecontrol circuit shown in Fig.l are illustrated in Fig.4(a). The wave-forms with a load composed of linear elements are shown in Fig.4(b).Provided that the-load has a saturable reactor, a cornu waveform ofcurrent flows. Namely, when the reactor operates in the saturationstate, the current waveform becomes salient with a large peak, asshown in Fig.4(a). The waveform of capacitor voltage is also distortedmore notably compared with that with a linear load.Therefore, we clarify how the peak values of current and capacitorvoltage are effected by the magnetic saturation. The variation ofpeak value of current is shown in Fig.5. As Z is smaller, shown inthis figure, the peak value of current becomes larger. For example,this value with Z=O.Ol and u=40o is 12.7 times as large as one withthyristor shorted and about twice as large as one with a linear load.Namely, as k is larger, the period when the reactor operates in mode ITbecomes shorter, because the reactor can be regarded as a linearelement and then a current waveform is not a salient one. On the otherhand, as k is smaller, the period when operates in mode IT becomeslonger. Especially in case of k=O, the reactor can be regarded as alinear reactor of inductance L 2 • Thus the peak value of current isdependent on the parameter Z.Next, the variation of peak value of capacitor voltage is shown inInfluence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Circuit 35(A)-6.0(a) load with a saturable reactor(¢1=-80o, 01=0.1, k=S.O, Z=O.Ol).(A)3.0-2.0-3.0(b) linear load(¢=-80o, 0=0.1).Fig.4. Current and capacitor voltage waveforms.Fig.S. Peak value of current.36 Toyoji HIMEL Sen-i chi ro NAKANISHI and Shigeyuki FUNABIKIFig.G. As k and Z are smaller, the ratio of the peak value of capacitorvoltage with phase control to that with thyristor shorted becomes largercompared with that with "a linear load. For example, the ratios are about0.77 and 0.3 at k=5.0, Z=O.Ol, a=40o, and k=l.O, Z=O.Ol, a=40o, respec-tively.Fig.G. Peak value of capacitor voltage.1.0-- : linear6---6 : ~ =0.6ll----.... : ! =0.10-0: ! =0.011.0-- : linear0-0: ~ =3.0)(----ooc: ~ =1.06---6: It =0.50.5-80 0 80 160phase control angle a(DEGS)-80 0 80 160phase control angle a(DEGS)Fig. 7. I/IHn2.Influence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Circuit 37G --: linear~ A---6 : ~ = 0.6~ ,,---..,x : ~ = 0.10-0: ~ =0.0150-80 0 80 160phase control angle a(DEGS)--: linear0-0: k = 3.0,,----x : ,= 1.0A---A : Ie =0.550-80 0 80. 160phase control angle a(DEGS)(b) ~1=-80o, 01=0.1, Z=O.Ol.Fig.8. Conduction angle.It is well known that the waveforms are distorted by a thyristorswitching in thyristor phase control circuit. And also, as mentionedabove, the current waveform is a more distorted and salient one witha non-linear load having a saturable reactor. Then, from the pointaimed at clarifing these effects, the variation of I 1 /ILInz (I1 :r.m.s.value of fundamental current, I :r.m.s. value of nth harmonic current)nis shown in Fig.7. From this figure, the ratio of fundamental componentto r.m.s. value of current with a linear load decreases as the phasecontrol angle becomes lagger. But, provided that a load is composedof a saturable reactor, the ratio becomes very small as the reactorsaturates. As k and Z are smaller, the influence on them becomesremarkable. For example, the value of I1/~ is 0.885 at a=40owith a linear load, while it is 0.47 at k=l.O, Z=O.Ol, and a=40o witha load composed of a saturable reactor.Next, the variation of thyristor conduction angle vs. the phasecontrol angle is shown in Fig.B. The conduction angle with a linearload decreases monotonously with an increase of phase control angle.On the other hand, it does not decrease monotonously with a non-linearload. In that case the conduction angle decreases till the phase controlangle increases to a certain value and then increases till the phasecontrol angle at which the curve agrees with that with a linear load.38 Toyoji HIMEL Sen-i chiro NAKANISHI and Shigeyuki FUNABIKI3.2 Influence on Steady State CharacteristicsThe influence on r.m.s. values of current and capacitor voltage,fundamental power factor, and input power factor are investigated.To begin with, the variation of r.m.s. value of current is shownin Fig.9. Further the variation of r.m.s. value of capacitor voltageis shown in Fig.lO. Though the peak value of current becomes very-- : linear0_. : ,,= 3.0,,----l< : " = 1.01'1 =0.56.0--; linear/1---/1 : l! =0.6x-----x : Do =0.10_0: Q. =0.0160-80 0 80 160 -80 0 80 160phase control angle a(DEGS) phase control angle a(DEGS)(a) <1>1=-80°, °1=0.1, k=5.0. (b) <1>1=-80°, °1=0.1, l=O.O1.Fig.9. r.m.s. value of current.6.0-- : linear6---A : Q. =0.6)<----"1< : a=0.10-0: Il. =0.01--: linear0-0: k=3.0,,----x : ~ = 1.011---/1 : h = 0.5-80 0 80 160 -80 0 80 160phase control angle a(DEGS) phase control angle a(DEGS)(a) <1>1=-80°, °1=0.1, k=5.0. (b) <1>1=-80°, °1=0.1, l=O.Ol.Fig.lO. r.m.s. value of capacitor voltage.Influence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Circuit 39'\\, .\\, \\\\\,.\\'\-80 0 80 160phase control angle a(DEGS)(b) <P 1= - 8 0 0, ° 1= 0 •1, Z= 0 • 01'.--linear~--' linear §; -: ~ =3.0l/l0 4-. .........4: t=0.6 l/l ,..---.. : 11. = 10u ~ =0.1 0w-----« : U.6---4 : ,,= 0.5""---<>: R. =0.01-80 0 80 160phase control angle a(DEGS)(a) ¢1=-80 o , 01=0.1, k=5.0.Fig.ll. Fundamental power factor.linear linearu..: /1---/1 ~ = 0.6 LL 0--0: 11. = 30a: )C---- x.0.=01 a: >(-----)( : 11. = 101.00-0 1=0.01 10 Ii---Ii : fI. = 0.5-80 0 80 160 -80 0 80 160phase control angle a(DEGS) phase control angle a(DEGS)(a) ¢1=-80 o , °1=0.1, k=5.0. (b) <P 1=-80o, °1=0.1, Z=O.01.Fig.12. Input power factor.large due to the magnetic saturation, the r.m.s. value decreases inopposition. Also the r.m.s. value of capacitor voltage decreases aswell as its peak value. As k and Z are smaller, the influence is moreremarkable.In the next, the variation of fundamental power factor is shown inFig.ll. The current waveform as mentioned in previous section isdistorted to be salient by the magnetic saturation, so that the angle,at which the current waveform has a peak value, is shifted to leading40 Toyoji HIMEL Sen-ichiro NAKANISHI and Shigeyuki FUNABIKIdirection of conduction angle. For that reason, the phase control angle,at which the fundamental power factor equals to unity,becomes lag.Thus, the influence of magnetic saturation is more remarkable withsmaller values of k and Z.The variation of input power factor is shown in Fig.12. ~~ere, theinput power factor is expressed as follows:(7)Fig.13. Transient waveforms.COs~l;fundamental power factor.That is, the input pwer factor can be expressed as the product ofIl/~ in Fig.7 by the fundamental power factor in Fig.ll. Then theninput power factor is poor because of the distorted waveform of currentcompared with that with a linear load. For example. the power factoris 0.9 at u=40o with a linear load, but it is 0.47 at k=I.O, Z=O.OI,and u=40o. And also, the phase control angle, at which the fundamentalpower factor is equal to unity, is lagger. Therefore, the phase controlangle, at which the input power factor is best, becomes lagger comparedwith that with a linear load.3.3 Influence on Transient CharacteristicsIn case of thyristor phase control circuit with linear seriesRLC elements, the time delay appears owing to an electrostatic storedenergy in capacitor which is a energy storage element. In this section,the influence of magnetic saturation on the time delay is discussed.At first, the transient response waveform is shown in Fig.13. Now,we assume that the initial value of capacitor voltage is zero at theinstance when the powersource is switched on.As soon as a power sourceis switched on and athyristor is trigered,the thyristor burst intoconduction and the currentbegins to flow. In thefirst few half-cycles, thecircuit operation issimilar to that withInfluence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Circuit 41II(%)!linearl' 01l' 0.01linear11= 50fF3,01< =101e- (.' /'_.--=-;:.;-;------------.//,;:100" .'7"--_--:::::..---------,.:' /:,' /'I,' ,:/h.'20 half-cycleO.~_--,----__ ---'---------l.__-----l. _1 5 10 1520 half-cycle15J~-L-_-'----L--.......:...----] 5 10Fig.14. Response time.a linear load because the reactor is not saturated. After then, thereactor is saturated so that the current becomes a salient waveformand reaches a steady state.In the next, the influence of magnetic saturation of the reactoron the transient response time, that is, the time delay is mentioned.The response time in half-cycle is shown in Fig.14. In consequence,as k and Z are smaller, the transient response time becomes shorter.It is considered to be due to the cause that the electrostatic energyin capacitor is limited by the magnetic saturation and the dampingfactor of load is larger with the reactor saturation.4. Discussion(1) The current waveform becomes a salient one due to the magneticsaturation, and the peak value of current with ¢1=-80o, 01=0.1, k=5.0,Z=O.Ol, and a=40o is 12.6 times as large as that with thyristorshorted and twice as large as that with a linear load. On the otherhand, the capacitor voltage waveform is distorted notably and itspeak value is lower compared with a linear load. Then, the conductionangle decreases. The most noteworthy influence appears in the distor-tion and the peak value of current waveform. Therefore, it is necessaryto consider them carefully on the selection of thyristor devices andthe influence on a power source.(2) The r.m.s. values of current and capacitor voltage are decreaseddue to the magnetic saturation of reactor. That is, the power into42 Toyoji HIMEL Sen-ichiro NAKANISHI and Shigeyuki FUNABIKIa load decreases and the input power factor becomes poor. Because theangle, at which the current waveform has a peak value, is shifted toleading derection and the conduction angle d~creases, the phase controlangle, at which the fundamental power factor equals to unity, becomeslagger.If active power, reactive power, harmonic power, and apparent powerare represented as P, PR, PH' and PA respectively, P/PA , PR/PA , andPH/PA with ~=-80o, 8=0.1, and a=40 o are 0.9, 0.0, and 0.44 witha linear load respectively. While, in the case which a load hasa saturable reactor and k=l.O and l=O.Ol, P/PA , PR/P A, and PH/PA are0.47, -0.21, and 0.86, respectively. The rate of harmonic power contentbecomes great and the reactive power is leading. It is consideredthat the decrease of input power factor is mainly due to the increaseof harmonics.(3) The transient response time on saturating of reactor decreasesbecause the electrostatic energy is kept lower and the dampingfactor increases.5. ConclusionsThe influences of magnetic saturation of iron-core reactor onthe performance of the thyristor phase control circuit with seriesRLC elements are analytically made clear by the numerical calculationusing a simplified three straight lines approximate model. The resultsobtained are sammarized as follows:(1) The peak value of current waveform becomes larger. On the otherhand, the peak value of capacitor voltage decreases. Furthermore,the conduction angle decreases.(2) The r.m.s. values of current and capacitor voltage decrease.(3) The phase control angle at which the fundamental power factorequals to unity becomes lag. The input power factor becomes lower andthe phase control angle at the maximum input power factor becomesalso lag.(4) The transient response time becomes smaller.Influence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Circuit 43References1) W. Shepherdi"Steady-State Analysis of the Series Resistance-Inductance Circuit Controlled by Silicon Controlled Rectifiers",IEEE Trans. Industr. Gen. Applic., Vol.IGA-l, No.4, p.259, 1965.2) B. W. Linger, R. W. Johnson and W. Shepherdi"Steady-StatePerformance and Analysis of the Series Resistance-CapacitanceCircuit with Control by Adjustable Thyristor Triggering", IEEETrans. Industr. Gen. Applic., Vol.IGA-4, No.6, p.644, 1968.3) T. Himei, S. Nakanishi and S. Funabiki;"The Influence of MagneticSaturation of Iron Core in Thyristor Phase Control Circuit",1977-Chugoku Branch Conv. Four Insts. Elec. Engrs., Japan, No.40504(in Japanese) •4) T. Himei, S. Nakanishi and S. Funabiki;"The Influence of MagneticSaturation of Iron Core in Thyristor Phase Control Circuit (PartII: )",1978-Chugoku Branch Conv. Four Insts. Elec. Engrs., Japan,No.40514 (in Japanese).5) T. Himei, J. Inouye, S. Nakanishi and I. Ukita;"A Step-upPhenomenon of the Thyristor Control Circuit with Series RLCElements", IEEE Trans. Industr. Applic., Vol. lA-II, No.5, p.53l,1975.

Funabiki;&quot;The Influence of Magnetic Saturation of Iron Core in Thyristor Phase Control Circuit&quot;,1977-Chugoku Branch Conv. Four Insts.

Shepherdi&quot;Steady-State Analysis of the Series ResistanceInductance Circuit Controlled by Silicon Controlled Rectifiers&quot;,

Shepherdi&quot;Steady-State Performance and Analysis of the Series Resistance-Capacitance Circuit with Control by Adjustable Thyristor Triggering&quot;,

Step-up Phenomenon of the Thyristor Control Circuit with Series RLC Elements&quot;,

Influence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Circuit

Influence of Magnetic Saturation of Iron-Core on Performance of Thyristor Phase Control Circuit

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