Improved modeling of new three-phase high voltage transformer with magnetic shunts

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1 ACHIVES OF ELECTICAL ENGINEEING VOL. 64(1), pp (015) DOI /aee Improved modelig of ew three-phase high voltage trasformer with magetic shuts M. CHAYGANE 1, N. EL GHAZAL 1, M. FADEL 1, B. BAHANI 1, A. BELHAIBA 1, M. FEFA, M. BASSOUI 1 High School of Techology, MSTI Laboratory, Ibou Zohr Uiversity, Agadir-Morocco m.elghazal@gmail.com Mohammadia s School of Egieers, esearch Team i Electrical Eergy & Cotrol Mohamed V Uiversity, abat-morocco elghazal@ymail.com (eceived: , revised: ) Abstract: This origial paper deals with a ew approach for the study of behavior i oliear regime of a ew three-phase high voltage power supply for magetros, used for the microwave geerators i idustrial applicatios. The desig of this system is composed of a ew three-phase leakage flux trasformer supplyig by phase a cell, composed of a capacitor ad a diode, which multiplies the voltage ad stabilizes the curret. Each cell. i tur, supplies a sigle magetro. A equivalet model of this trasformer is developed takig ito accout the saturatio pheomeo ad the stabilizatio process of each magetro. Each iductace of the model is characterized by a o liear relatio betwee flux ad curret. This model was tested by EMTP software ear the omial state. The theoretical results were compared to experimetal measuremets with a good agreemet. elative to the curret device, the ew systemprovides gais of size, volume, cost of implemetatio ad maiteace which make it more ecoomical. Key words: trasformer, three-phase, modelig, EMTP, microwaves, power supply 1. Itroductio Figure 1 shows the scheme of the ew three-phase HV power supply for N magetro, used as a microwave eergy source (treated case: N = 1 magetro per phase). A ew threephase magetic leakage trasformer, ot yet so far modeled or maufactured, is the basic elemet of this ew power supply. The ew trasformer supplies by phase a voltage doubler ad a curret stabilizer cell. This special trasformer with shuts esures the aodic curret stabilizatio i each magetro by saturatio of its magetic circuit. The characteristics of the magetro [1-7] as well that these limit values impose a proper desig of its power supply. Ulike the covetioal trasformer, the leakage flux i the shut is of the same order as both the primary ad secodary fluxes. Thus, the theory of classical trasformers does ot apply i the case of the trasformer with shuts. O the other had, the desig ad optimizatio of such Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

2 158 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg. devices ca be facilitated usig simulatio tools takig ito accout the geometry ad the o liear magetic properties of materials. I this article, we itroduce a equivalet circuit of the ew trasformer that meets these coditios. Itegrated ito a overall scheme of the ew HV power supply for a sigle magetro by phase, it is adapted to the modelig of the assembly by a umerical calculatio of trasiet electrical circuits EMTP (Electro Magetic Trasiets Program). Experimetal measuremets, obtaied for a sigle-phase trasformer with shuts, used to validate the simulated results of this model. The paper is orgaized as follows: firstly, the mathematical equatios characterizig this ew special trasformer are described i order to drive a ew equivalet model. Secodly, a implemetatio of obtaied model usig EMTP software was preseted. The obtaied results were compared with those already foud i feasibility study already doe [ ], ad experimetal measuremets for the classical power supply for a sigle magetro [1-7].. The modelig priciple The ew trasformer caot be separated from the exteral circuits, icludig each of the three magetros, because the equivalet diagram must reflects the behavior of the whole. It is therefore ecessary to fid a formulatio that will allow the simultaeous resolutio of the electric ad magetic equatios of the etire system. Too complex to be solvedaalytically, the solutio ca be oly umerical usig suitable software. I additio, the choice of materials ad dimesios of the ew trasformer should be possible, with a view to a possible optimizatio. A simple model of represetatio is ot sufficiet, because its parameters must be able to be extracted directly. To accout for the stabilizig effect of the ew power supply of magetros, it is ecessary to cosider the oliearities of the system. As well, the EMTP software accepts the data relatig to the oliear saturable iductaces ad the global model used operates this facility. Takig all these cosideratios ito accout, the developmet equatios caot be that particular to adapt to the costraits of the used EMTP code ad the lik of the equivalet circuit with the costructio parameters. 3. Theoretical study of the ew three-phase trasformer with shuts I the proposed study, the ew three-phase trasformer is cosidered without iro losses (hysteresis ad Foucault currets). The leakages that exist are oly chaeled i the shuts. The leakage of air dispersio is egligible. Oly the saturatio pheomeo is take ito cosideratio Descriptio The magetic circuit of the ew three-phase trasformer is of the type tetrahedro (Fig. 1). Each phase has three colums, a cetral core receives the widigs ad the others at the eds are used to close the magetic circuit. Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

3 Vol. 64 (015) Improved modelig of ew three-phase high voltage trasformer with magetic shuts 159 b=60 mm Phase 1 a a.a a a Phase 3 Phase 5.a (a=5mm) Shut Shut B(H): SF19 6.a (a=5mm) Fig. 1. Magetic circuit of type tetrahedro of the ew three-phase trasformer To realize a magetic circuit of the type tetrahedro, three idetical magetic circuits of the sigle-phase trasformer with shuts ca be used. The magetic circuits beig separated, the magetic fluxes i the three circuits are idepedet. Although there is idepedece of fluxes, a three-phase secodary system is obtaied. Figure shows the structure of the ew three-phase trasformer with shuts, ot yet modeled or maufactured, that will be used i the HV power supplies for N magetros per phase (treated case: N = 1 magetro per phase). ϕ 13 J ϕ 13 B ϕ 11 C ϕ 1 G K φ sh 3 ϕ 11 A ϕ 1 ϕ sh 1 ϕ comp D ϕ coms ϕ sh ϕ 1 H L F ϕ 1 E ϕ ϕ I Fig.. Distributio of fluxes i the magetic circuit of the ew three-phase trasformer The magetic shuts are used to deflect a importat part of the flux circulatig betwee the primary ad secodary widig. Takig ito accout the dimesios of residual gaps ad Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

4 160 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg. the saturatio state of materials, the magetic fluxes i the air ca be cosidered egligible compared to the fluxes through the shuts. The three primary widigs costitute a balaced three-phase load give that these three widigs are the same. This meas that the effective values of the three voltages are equal ad the three voltages are shifted relative to it 10 degrees. 3.. Cocept of calculatio The primary quatities are show by r 1i, 1, i 1i, u 1i, (phase i = 1,, 3) ad the secodary quatities are materialized by r i,, i i, u i, (phase i = 1,, 3). The fluxes N 1i, N i, N 3i (phase i = 1,, 3) are respectively: the flux passig through the primary, the secodary ad the shuts of each phase as show i Figure : r 1i : primary widig resistace (phase i); i i : secodary widig resistace (phase i); 1 : umber of turs i the primary coil of each phase; : umber of turs i the secodary coil of each phase; u 1i : voltage of the primary widig (phase i); u i : voltage of the secodary widig. The dimesios i millimeters of the magetic circuit are marked by letters A, B, C, D... L ad are related to the mea force lie flux i the differet portios of the circuit. AB = HG = KJ = DC = *a FA = ED = IH = LK = *a DA = DH = DK =.5*a CB = CJ = CG =.5*a EF = EI = EL =.5*a The electric equatios The goverig electric equatios of the trasformer operatio are obtaied by applicatio of the Ohm geeralized law i primary ad secodary widig of each phase. For the phase 1: For the phase : For the phase 3: u u u u 11 dϕ 11 = r11i11 + 1, (1.1) dϕ 1 1 = r1i1, 1 (.1) dϕ 1 = r1i1 + 1, (1.) dϕ = ri, u 13 (.) dϕ 13 = r13i13 + 1, (1.3) Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

5 Vol. 64 (015) Improved modelig of ew three-phase high voltage trasformer with magetic shuts 161 u dϕ 3 3 = r3i3, (.3) 3... The magetic equatios To have the equatios relatig to the magetic circuit of this trasformer, we apply the formula of magetic circuits to the various cotours of Figure (Hopkiso law). So it comes: For the phase 1: The cotour ABCDA: Posig: Cosiderig: (balaced three-phase load) ϕ comp = ϕ11 + ϕ1 + ϕ13 = 0 (primary side), ϕ coms = ϕ + ϕ + ϕ 0 (secodary side). 1 3 = ϕ The followig equatio is obtaied: The cotour ADEFA: Posig: ϕ sh 11 1 AB ϕ 11 + BC + CDϕ comp + DA = 1i11 FA ϕ BC DA p1 = AB + ; =. p ϕ = 1i11. ϕ ϕ (3.1) ϕ sh EF + DEϕ coms DA = i1 EF = DA + ; = As well for this cotour the followig equatio is obtaied: The cotour BCEFB: DA ϕ (4.1) 1 ϕ = i1. p ϕ 1 = 1i11 i1. ϕ (5.1) The Equatios (3.1), (4.1) ad (5.1) are supplemeted by the additioal relatio reflectig the coservatio of fluxes i the phase 1: ϕ 11 = ϕ 1 + ϕ. (6.1).. Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

6 16 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg New trasformer equivalet model circuit To study the operatio of the ew trasformer model usig the EMTP code, it is coveiet to brig its equivalet three-phase circuit to the secodary. To do this, each phase equivalet scheme will be treated: Phase 1. Multiplyig by / 1 ad puttig the quatity N 11 i the form p1 ϕ11 p1, it comes: The quatities d p1 u11 = r11 i11 + ϕ 11. p1 p 1 ad p 1ϕ 11 are respectively the dimesios of a iductace ad a electric curret which we may call L p1 ad i p1, which allows writig the above equatio i the form: d u 11 = r 11 i 11 + { L p1 i p1 }. Usig the Equatio (6.1) ad by writig that: It comes: ϕ ϕ ϕ 1 11 = = = p1 p1 ϕ = L i 1 ϕ 11 = L ϕ = L, i. p1 p1 d d d p1 p1 By expressig the quatity N 1 the Equatio (.1) also becomes: With: { L i } = { L i } + { L i } u d { L i } r. 1 = 1i1 i, Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

7 Vol. 64 (015) Improved modelig of ew three-phase high voltage trasformer with magetic shuts 163 L = O the other had, multiplyig by / 1 the curret expressio i 11 as a fuctio of N 11 ad N, extract from the Equatios (3.1), (4.1) ad (5.1), the followig equatio is obtaied: This equatio ca be writte i the form: 1 i 11 = p1 p1. ϕ 11+ i = i p + i 11 1 sh Usig the Equatio (4.1), (5.1) ad (6.1), the followig expressio is obtaied: This expressio ca be writte i the form: So, 1. ϕ 1 = ϕ 1 + sh i i = i s + i 1 1 sh i 1. sh 1 = i + i1. ϕ 1. The followig complete system of electric ad magetic equatios is obtaied: d u 11 = r11 i11 + { L p 1 i p1}, (7.1) u d = { L i } r, (8.1) i 11 = i p 1 + i, (9.1) 1 1i1 i (10.1) sh 1 = i + i1, d d d ϕ = ϕ + ϕ (11.1) This equatio system respods to the equivalet diagram i the first phase of the ew three-phase trasformer with magetic shuts. By perfectly similar calculatios, the equatio system which respods to the equivalet diagram of the phase ad 3 permits to fid the models idicated i Figures 4 ad 5. The model elemets icludig the iductaces are ot the same. It is possible to decompose shi (i = phase 1,, 3) to highlight the costat overall reluctace shi of air gaps betwee shuts ad cores, i parallel with shi relative to correspod e f largest part of the path i each phase etirely ferromagetic eviromets. Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

8 164 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg. Fig. 3. Equivalet model of the phase 1 of the ew three-phase trasformer with shuts brought back to the secodary Fig. 4. Phase of the ew three-phase trasformer: equivalet model Fig. 5. Phase 3 of the ew three-phase trasformer: equivalet model L e shi ( i = phase 1,, K 3) = e shi is equivalet to the correspodig costat iductace i parallel o L f shi = e shi Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

9 Vol. 64 (015) Improved modelig of ew three-phase high voltage trasformer with magetic shuts 165 hece the equivalet diagram see from the secodary of the ew trasformer which will be used i power supplies for magetros. Fig. 6. New model of the ew three-phase trasformer with magetic shuts 4. Validatio of the model of the ew power supply The advatage of this ew model is part of its equivalet circuit which seems more coveiet to study the operatio of the ew trasformer usig the EMTP code. The immediate iterest of this model is to be able to assig to each iductace a o liear relatio betwee Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

10 166 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg. the flux ad the curret i the form N(i), from the geometrical parameters of the ew trasformer magetic circuit. To traslate the variatio law of total flux N(i) i terms of i of each iductace, the magetizatio curve B(H) of the material ca be used, usig the relatios: N = B.S ad i = l*h/. Fig. 7. Experimetal B (H) for each sectio of the studied magetic circuit The model of the ew trasformer is itegrated i the ew HV power supply circuit from the source to the magetros. Each tube microwave is represeted by a equivalet diagram deduced from its electrical characteristics which is formally similar to that of a diode with dyamic resistace = 350 Ohms ad threshold voltage E 3800 Volts. Exploitig the EMTP code, the electric behavior of the HV circuit of the ew three-phase power supply with sigle magetro per phase is simulated (Fig. 8). The waveforms obtaied from this simulatio are show i Figure 10. This figure shows that i omial operatio (U 11 = U 1 = U 13 = 0 V ad f = 50 Hz) the results of simulatio by EMTP of the ew device, i o liear regime, cofirm the results obtaied durig a feasibility study already doe. The relative differeces will ever exceed 6%. η = ((exp) theo). ((exp) + theo) These sigals have the same form as those of a classical HV power supply usig a trasformer for a sigle magetro. The phase shift of 10 degrees betwee them cofirms the absece of iteractio betwee magetros. Takig ito accout the accuracy of the various data ad of the permissible toleraces acceptable o the operatio of the magetro, the modelig was deemed satisfactory. Ecouraged by the successful results, a ew structure of the magetic circuit has bee udertake. I the core of commo retur of the three circuits (the primary side (also secodary)), the total flux the is cosidered zero. Therefore, the core returig i the two primary ad secodary sides has o iterest (Fig. 9). The ew power supply will be cosidered therefore a differet versio of the sigle-phase model curretly maufactures amog the maufacturers of domestic or idustrial microwave oves. Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

11 Vol. 64 (015) Improved modelig of ew three-phase high voltage trasformer with magetic shuts 167 Fig. 8. a) Modelig of the ew three-phase trasformer with magetic shuts usig the EMTP code; b) simulated model with EMTP of the ew three phase power supply Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

12 168 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg. Fig. 9. New type of magetic circuit of the ew three-phase trasformer with magetic shut Fig. 10. Simulatio results: currets ad voltages waveforms of the ew three-phase power supply usig EMTP code (omial mode) Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

13 Vol. 64 (015) Improved modelig of ew three-phase high voltage trasformer with magetic shuts 169 Fig. 11. Experimeatl results: currets ad voltages waveforms of the sigle-phase power supply (omial mode) 5. Verificatio of the regulatig process of a magetro curret Durig the simulatio of the model usig the EMTP code, we maaged to observe the stability of the magetro curret variatios with respect to the mais voltage. Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

14 170 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg. Figures 11 ad 1 show the waveform of the curret magetro i the respective cases 00 V ad 40 V (±10% of the rated voltage). We ote that the maximum amplitude of the curret ever exceeds the permissible limit valuerecommeded by the maufacturer (I max = 1. A). We ca say that with this model, the stabilizatio process of the magetro curret is completely recovered. Fig. 1. Waveforms of the curret magetro for U 11 = U 1 = U 13 = 00 V ad U 11 = U 1 = U 13 = 40 V 6. Coclusio I this article, a ew origial model able to represet the best possible characteristics of saturatio of a ew three-phase trasformer with magetic shuts, ot yet so far modeled or made, was cocluded. Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

15 Vol. 64 (015) Improved modelig of ew three-phase high voltage trasformer with magetic shuts 171 After the dimesioig of its ew three-phase flux leakage trasformer, the observatio of the correct fuctioig of various braches of the circuit power was successful. At the ed of simulatio with EMTP code, the regulatio process curret i each magetro ad flow rate of full microwave power was verified. This preserves the protectio of all magetros agaist ay chage i the iput voltage of the three-phase power supply etwork. The results cofirm that there are o iteractios betwee the three magetros. The failure of oe or more magetros does ot affect the operatio of other powered magetros. As perspectives, this study ca be exteded without ay problems i case of operatio of the ew power supply for N > 1 magetros per phase i omial scale. efereces [1] Chraygae M., Ferfra M., El Khouzaï M., Hlimi B., Itude de l état magétique itere global du trasformateurs à shuts d ue alimetatio pour géérateurs micro-odes à magétro destiés aux applicatios idustrielles. Télécom 003 et 3ème JFMMA Marrakech. Commuicatio, pp (003). [] Chraygae M., Ferfra M., Hlimi B., Modélisatio d ue alimetatio haute tesio pour géérateurs micro-odes idustriels à magétro. evue 3EI, 41, pp (005). [3] Chraygae M, Modélisatio avec EMTP d ue ouvelle géératio d alimetatio haute tesio moophasée pour géérateurs microodes à magétros destiés aux applicatios idustrielles. Thèse de doctorat d état, Uiversité Ib Zohr Agadir, Maroc, 113/07 (007). [4] OuldAhmedou M., Chraygae M., Ferfra M., New π Model Validatio Approach to the Leakage Flux Trasformer of a High Voltage Power Supply Used for Magetro for the Idustrial Micro- Waves Geerators 800 Watts-450 MHz. Iteratioal eview of Electrical Egieerig IEE 5(3) (May-Jae 010). [5] Ould.Ahmedou M., Ferfra M., Nouri., Chraygae M., Improved π Model of the Leakage Flux Trasformer Used for Magetros. Iteratioal Coferece o Multimedia Computig ad Systems, IEEE Coferece, Ouarzazat-Morocco (07-09 April 011). [6] Ould Ahmedou M., Ferfra M., El Ghazal N. et al., Implemetatio ad Optimizatio Uder Matlab Code of a HV Power Trasformer For Micowave Geerators Supplyig Tow Magetros, Joural of Theoretical ad Applied Iformatio Techology 33() (30 November 011). [7] Belhaiba A., Chraygae M., OuldAhmedou M., Modélisatio du bila éergétique d u géérateur micro odes idustriel à u seul magétro. Coférece Méditerraéee sur l Igéierie Sûre des Systèmes Complexes, MISC 11 Agadir-Morocco (7-8 Mai 011). [8] El Ghazal N., Chraygae M., OuldAhmedou M., Modélisatio d ue alimetatio haute tesio à caractère triphasé pour géérateurs micro odes idustriels à u magétro par phase. Coférece Méditerraéee sur l Igéierie Sûre des Systèmes Complexes, MISC 11 Agadir-Morocco (7-8 Mai 011). [9] El Ghazal N., OuldAhmedou M., Chraygae M., Optimizatio of High Voltage Power Supply for Idustrial Microwave Geerators for oe Magetro. Joural of Theoretical ad Applied Iformatio Techology 46(1): (01). [10] Belhaiba A., El Ghazal N., Chraygae M., Improved optimizatio of the omial fuctioig of a high voltage power supply for N = magetros for microwave geerators, Iteratioal Joural of Electrical ad Computer Egieerig, IJECE (5): (October 01). [11] Belhaiba A., Chraygae M., El Ghazal N., Modelig the power of microwave geerator for oe magetro by Matlab-simulik. IEEE Iteratioal Coferece o Multimedia Computig ad Systems, ICMCS 1, Tager (10-1 may 01). [1] El Ghazal N., Belhaiba A., Chraygae M. et al., Feasibility study of a ew three-phase HV power supply for microwaves geerators supplyig a oe magetro per phase. Iteratioal Coferece o Multimedia Computig ad Systems, IEEE, /ICMCS , Tager (01). Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM

16 17 M. Chraygae, N. El Ghazal, M. Fadel et al. Arch. Elect. Eg. [13] El Ghazal N., Chraygae M., Belhiba A. et al., Modelig of a New HV Power Supply with a Character Three-Phase for N = Magetros by Phase for Idustrial Micro-wave Geerators, Iteratioal Symposium o Security ad Safety of Complex Systems, Agadir (5-6 may 01). [14] Belhaiba A., Chraygae M., OuldAhmedou M., Modelig the power balace of microwaves geerators for N = magetros. Iteratioal Symposium O Security Ad Safety Of Complex Systems, Agadir (5-6 may 01). [15] Belhiba A., Chraygae M., El Ghazal N., Modelig ad optimizatio of high voltage power supply for magetro, LAP LAMBET Academic Publishig GmbH& Co. KG Heirich-Böckig, pp , Saarbrücke, Germay (013). [16] El Ghazal Naama, Chraygae M., Ferfra M., Modelig of New Three-Phase High Voltage Power Supply For Idustrial Microwave Geerators With Oe Magetro Per Phase, Iteratioal Joural of Electrical ad Computer Egieerig, IJECE 3() (013). [17] Boubker B., Bouzit A., Chraygae M. et at., Modelig of a New Sigle-Phase High Voltage Power Supply for Microwave Geerators with Three Magetros. Iteratioal Joural of Electrical ad Computer Egieerig, IJECE 3() (April 013). [18] El Ghazal N., Chraygae M., Belhaiba A., Power Supplies of Magetros: Modelig, Simulatio &Optimizatio. LAP LAMBET Academic Publishig GmbH&Co. KG Heirich-Böckig, pp 6-8, 6611, Saarbrucke, Germay (013). Brought to you by Biblioteka Glówa Zachodiopomorskiego Uiwersytetu Techologiczego w Szczeciie Autheticated Dowload Date 6/6/15 10:46 AM