Design and simulation of turbo-alternators using coupled permeance network model

Transcription

1 Deign and imulation of turbo-alternator uing coupled permeance network model Dmitry Petrichenko, Michel Hecquet, Pacal Brochet, Vyachelav uznetov, Daniel Laloy To cite thi verion: Dmitry Petrichenko, Michel Hecquet, Pacal Brochet, Vyachelav uznetov, Daniel Laloy. Deign and imulation of turbo-alternator uing coupled permeance network model. IEEE Tranaction on Magnetic, Intitute of Electrical and Electronic Engineer, 6. <hal > HAL Id: hal Submitted on Feb 18 HAL i a multi-diciplinary open acce archive for the depoit and diemination of cientific reearch document, whether they are publihed or not. The document may come from teaching and reearch intitution in France or abroad, or from public or private reearch center. L archive ouverte pluridiciplinaire HAL, et detinée au dépôt et à la diffuion de document cientifique de niveau recherche, publié ou non, émanant de établiement d eneignement et de recherche françai ou étranger, de laboratoire public ou privé.

2 Deign and imulation of turbo-alternator uing coupled permeance network model Dmitry Petrichenko, Michel Hecquet, Pacal Brochet, Vyachelav uznetov, Daniel Laloy Abtract The modelling of a turbo-alternator uing permeance network i decribed. Thi approach allow implementing electrical and magnetic coupling a well a mechanical coupling. Such procee a aturation, movement, 3D effect are be taken into account. The aim of thi tudy i to et up a deign model of 1 to 1 MW turboalternator. The method of taking into account of 3D effect i decribed. The firt reult of imulation were obtained. The experimental meaurement validate the model. ey word CAD application, reluctance network, magnetic circuit, magnetic field, air-gap permeance, automatic generation of the permeance network. I. INTRODUCTION The recent high growth of the power of the computer ytem, development of the oftware to olve complicated problem made it poible to ue precie method of calculation in electric machinery to obtain the magnetic field analyi. The mot pread nowaday finite element method till demand too much computing power to obtain the reult in a hort time. Thu in the application of optimization, where the calculation time i very important, one hould ue method maybe a little bit le precie than FEM but more quick and effective. Being baed on a permeance network method [1], [] Tooth Contour Method (TCM) [3] give one fat calculation of magnetic circuit and, therefore, high performance calculation of teady-tate and dynamic characteritic and tranient analyi. Thi feature allow TCM to be ued in CAD ytem. The peculiarity of the method i in pecial air-gap permeance calculation and the electrical-magnetic coupling treatment. A oftware implementation of the method realize an automatic parameterized permeance generation. A ame circuit decription tool can generate both electric and magnetic network, providing then the calculation of the machine coupled with electrical part. In the firt part, the bai of the Tooth Contour Method i given and the mathematical model of turbo alternator i preented. Then, the calculation trategy i given and alo the tructure of the oftware TurboTCM. Manucript received June 5. Thi work wa upported by C.N.R.T. Réeaux et Machine Electrique du Futur (Projet Archimed ) and JEUMONT SA (Framatome). D. Petrichenko i with LEP, Ecole Centrale de Lille, Cite cientifique, BP48, Villeneuve d Acq Cedex, France (phone: ; Dimitry.Petrichenko@ec-lille.fr) M. Hecquet i with LEP, Ecole Centrale de Lille, Cite cientifique, BP48, Villeneuve d Acq Cedex, France ( Michel.Hecquet@ec-lille.fr) P. Brochet i with LEP, Ecole Centrale de Lille, Cite cientifique, BP48, Villeneuve d Acq Cedex, France ( Pacal.Brochet@ec-lille.fr) V. uznetov i with Mocow Power Engineering Intitute (MPEI), Dep. of Electromechanic; ranokazarmennaja, 13, Mocow, 1115, Ruia ( uznetovva@mpei.ru) D. Laloy i with JEUMONT SA (Framatome), 7 Rue de l Indutrie, BP189, 59573, Jeumont Cedex, France II. PERMEANCE NETWOR AND TOOTH CONTOUR METHOD Different method uing magnetic equivalent circuit to repreent the field inide the electrical machine are detailed in [3], [4]. The main advantage of thi approach i a good compromie between the accuracy of field calculation and the computing time. In thi method, the 3D effect of a field in the electrical machine are eaily taken into account with accuracy enough for practical purpoe [4]. The Tooth Contour Method repreent one approach of permeance network. It i baed on theoretically validated repreentation of the total magnetic field in the air-gap a the um of local magnetic field of the particular element of the o-called tooth contour [5]. Uually the tooth contour i conidered to be an element formed by the conductor located in adjacent lot, but it may be alo repreented a any part of the core urface e.g., the pole-hoe may be divided into everal "tooth" contour (Fig. 1). (b) FIG. 1 TOOTH CONTOUR REPRESENTATION The local magnetic field of tooth contour are to be calculated under the artificial boundary condition, called the Special Boundary Condition (SBC), uppoing that the permeability both of tator and rotor iron i infinitely large. Thi pecial field i localized in a mall region, which uually doe not exceed three or four tooth pitche and o it could be eaily and quickly calculated. A a reult, a mutual permeance between excited contour of a tator and one of a non-excited rotor contour r are obtained a a function of their relative poition r (b r ), a hown on Fig.1. b

3 Air-gap permeance To calculate the air-gap permeance one ha to calculate the magnetic field in the air-gap region. The field calculation can be performed by many different method. Here an analytical method of calculation i given [5]. The curvilinear air-gap i tranformed into the plane uing conformal tranform function. The following aumption are applied: the lot form i not taken into account, they are conidered to be rectangular with the width equal to the width of the lit; the field i conidered to be D; The method hown above ha been validated for a mall region uing OPERA [ The reult can be found in [6]. Magnetic ytem permeance The permeance network of the magnetic ytem of tator and rotor i generated automatically baed on parameter of the geometry. The general tructure of the permeance network of the tator i preented on the Fig.. FIG. STATOR EQUIVALENT CIRCUIT The number of layer in the tator yoke and number of layer in the teeth zone i variable. That variable influence both on the calculation accuracy and time. The rotor of a turboalternator can have rather ophiticated tructure and geometry, a different dimenion of the lot and teeth, etc. The oftware under development generate the equivalent circuit completely automatically taking all thee difficultie into account. The oftware analyze the geometry of the inter-lot pace and generate the circuit for the particular zone automatically. The uer can define the number of layer (which affect the accuracy of calculation). The ource of MMF are ituated in the horizontal branche and are not preented on Fig. and Fig. 3. Taking into account 3D effect In modern turboalternator of high power tator and/or rotor have radial ventilation duct which hould affect a lot on the magnetic permeance network of the model. Beide, tator uually i made of laminated teel with it filling factor. All thoe fact how that pure D repreentation of the field in an electrical machine i not correct; pure croection without taking into account the axial heterogeneity of the machine i impoible. To take into account thee effect in the permeance network the permeance mut be modified in order to reflect axial effect in the network. Taking into account the reduction of the axial length of teel caued by the exitence of radial ventilation duct and teel filling factor i rather imple. The magnetic field calculation in two-dimenional repreentation one hould perform not for a real magnetization curve B(H) but for the one with the reduced component B in the following proportion: the axial teel length by full axial length of the core including the length of the ventilation duct. For the flux denitie exceeding T another correction hould be added to the curve obtained, caued by the flux bulging into the inter-heet non-magnetic pace in the teel packet. The gap between the heet being determined by the thickne of the inulation layer uually doen t exceed 1-15% of the thickne of the heet itelf. Thu, the flux bulging play a noticeable role only in the zone of high aturation. It can be calculated uing the ame method a one to obtain a new magnetizing characteritic of teeth with flux bulging into lot uppoing that the magnetic flux line are parallel inide a tooth and a lot. That formula i well-known a can be found in the book of electrical machine deign. Other area where the correction of the permeance hould be applied are the one with air. Thee zone are the lot of tator and rotor and the air-gap, the lat one having the mot influence of duct both on tator and on rotor. Slot leakage flux b t d b d L FIG. 3 ROTOR EQUIVALENT CIRCUIT Fig. 3 how the equivalent circuit of one tooth of the rotor where the height of the adjacent lot are different. FIG. 4 SLOTS AND DUCTS REPRESENTATION The influence of ventilation duct in lot zone i very important for the lot top leakage. The cro-ection of a

4 lot on ome radiu i hown on Fig. 4, where: b lot width, b d duct width, t d duct pitch, L - core length in axial direction. To obtain correct value of permeance in thee zone a modification of zone permeability hould be applied, which would reflect the axial heterogeneity of the core. Since the air zone in machine contain only linear element, the modification of the permeability can be achieved by correcting the effective length of the zone. In imple cae, a well-known Carter factor can be ued. Thi factor reflect the influence of core aliency on the air-gap. A modified Carter factor calculation i hown below: b d b b lot td td (1) bd 5 b where: b =.5b half of the lot width. Thi factor i applied to the length of the lot zone for the whole lot if the lot i rectangular. It may vary from layer to layer if the lot i trapezoidal or ha any other form. The obtained length i: 1 L b L () eff lot In formula () an additional length equal to b i added to the core length L in order to take into account the edge effect. By mean of (1) and () the modified zone length are obtained for tator and rotor core. The ame method i ued to determine the influence of the duct on the permeance of air-gap except that tator and rotor may have both different length and different number of duct with different ize a hown on Fig. 5. L 1 bdr r tdr tdr (4) bdr 5 The length of the air-gap will be influenced both by (3) and (4): max L, L Leff r r (5) Actually, formula (5) contain both the influence of ventilation duct and the edge effect. III. CALCULATIONS AND SOFTWARE REALIZATION The oftware ha been deigned to perform the calculation both in dynamic and teady-tate mode. The dynamic algorithm i rather imple and conit of calculating the ytem of equation uing regular timetepping method. The teady-tate calculation algorithm with fixed rotor ha been implemented for teady-tate mode characteritic calculation. The oftware (TurboTCM) implementation of the method decribed earlier conit of everal layer. A an input data one ha a full pecification of the turboalternator: tator and rotor ize, number of tator and rotor lot, their dimenion, inulation, full decription of the tator and excitation winding, characteritic of the material, pecification of the electrical part, etc. Fig. 6 preent one of the input window. Baed on that information, the oftware automatically generate the parameterized magnetic equivalent circuit, electric circuit and coupling equation. Stator t d b d Air-gap b dк L r t dк FIG. 5 DUCTS AND AIR-GAP ZONE In thi cae the Carter factor i conidered a following: bd td td (3) bd 5 1 Rotor FIG. 6 TURBOTCM: SLOT PARAMETERS INPUT DIALOG TurboTCM ha been implemented in Matlab and ued Component Object Model (COM) technology. To take into account the aturation a well-known Newton-Raphon algorithm ha been ued. IV. SIMULATION RESULTS AND COMPARISONS WITH EXPERIMENTS In firt time, TurboTCM ha been experimented on a claical machine. Obtained reult and their comparion with the finite element imulation have been preented in [6], [7]. The gain of time calculation in TurboTCM comparing with the field method wa 6 time. The experimental reult were obtained for a -pole turboalternator, which cro-ection i preented on Fig. 7.

5 U, V U, V Line voltage, V of 36 tr/min (6 Hz) and nominal excitation current of 5 A. The reult are preented on Fig. 1. Calculation time i 77.9 ec. x 14 No load line voltage, V FIG. 7 TURBOALTERNATOR CROSS-SECTION The turboalternator ha 48 lot on tator and 8 lot on rotor. The tator ha a double braid winding with the tep y = 5/6. The peculiarity of thi machine i that the rotor lot are not evenly ditributed and have different height. Steady-tate analyi The teady-tate analye have been performed uing the method with fixed rotor, which wa decribed in [6]. The reult are hown on the Fig. 5. The experiment and imulation reult are quite cloe. The maximal error i 6.58 %. For the excitation current equal to nominal, error i.86 % No load characteritic (line voltage) Experiment TurboTCM If, A FIG. 8 NO-LOAD CHARACTERISTIC COMPARISON Fig. 6 how the comparion of no-load curve depending on different number of layer in tator and in rotor No-load characteritic, U(If) 4 layer on tator and rotor 6 layer on tator and rotor 8 layer on tator and rotor If, A FIG. 9 NO-LOAD CHARACTERISTICS DEPENDING ON LAYERS The greater the number of layer, the more precie calculation of aturated part i. However, the difference between 6 and 8 layer i negligible and in mot cae 5-6 layer i ufficient enough for practical ue. Dynamic analye The dynamic analyi ha been performed for no-load cae on a full period of 36 with the tep of for a peed Rotor angle, deg. FIG. 1 LINE VOLTAGES OBTAINED BY TURBOTCM The RMS value of line voltage i 1385 V while in experiment 1383 V i obtained. The error i.16 %. Table 1 preent the harmonic level in percent of the firt harmonic for the imulation reult. TABLE 1 COMPARISON OF HARMONIC LEVELS OF STATOR VOLTAGE Line voltage, % Harmonic level TurboTCM V. CONCLUSION In thi work the model of a ynchronou machine baed on a tooth contour method wa preented along with the oftware TurboTCM. The method of taking into account the 3D effect wa decribed. The firt reult of imulation were compared and validated with thoe of experiment for no-load cae. The comparion how good correpondence between the calculation reult and the experimental data. While realizing a good compromie between accuracy and computing time, thi model open the way to optimal deign of turbo-alternator. REFERENCES [1] Otovic V., Dynamic of aturated machine, Springer-Verlag, [] Worotynki J., Turowki M., and Mendrela E.A., "The accuracy of calculation of magnetic field, inductance and force in electromagnetic device uing the reluctance network method", Proc.ISEF 93, Waraw, pp159-16, [3] uznetov V., Brochet P., A general numerical modelling of electromagnetic proce in electromechanical ytem, The International Journal for Computation and Mathematic in Electrical and Electronic Engineering (COMPEL), Vol., No. 4, pp , 3. [4] Hecquet M., Brochet P., Time variation force in a ynchronou machine uing electric coupled network model, IEEE Tran. On Magnetic, Vol. 34, No 5, pp , September [5] Ivanov-Smolenkii A. and author, Univeral Method of Electromagnetic Procee Calculation in Electrical Machine, Energoatomizdat, 1986, Mocow, Ruia. [6] D. Petrichenko, Michel Hecquet, Pacal Brochet, Vyachelav uznetov, Daniel Laloy, Numerical modelling of a turboalternator uing Tooth Contour Method: CAD application, ICEM 4, CD- Rom, Cracovie, 5-7 Oct. 4. [7] D. Petrichenko, M. Hecquet, P. Brochet, V. uznetov, D. Laloy, Development of the turboalternator imulation oftware, ELECTRIMACS 5, CD-ROM, Hammamet, Tuniia, 17- April, 5.