INCORPORATION OF ADVANCED NUMERICAL FIELD ANALYSIS TECHNIQUES IN THE INDUSTRIAL TRANSFORMER DESIGN PROCESS

INCORPORATION OF ADVANCED NUMERICAL FIELD ANALYSIS TECHNIQUES IN THE INDUSTRIAL TRANSFORMER DESIGN PROCESS M A Tsili 1, A G Kladas 1, P S Geogilakis 2, A T Souflais 3 and D G Papaigas 3 1 National Technical Univesity of Athens, GR-15780, Athens, Geece, (e-mail: kladasel@cental.ntua.g) 2 Technical Univesity of Cete, GR-73100, Chania, Geece (e-mail: pgeog@dpem.tuc.g). 3 Schneide Electic AE, Elvim Plant, GR-32011, Inofyta, Viotia, Geece, (e-mail: dimitis_papaigas@mail.schneide.f) ABSTRACT The pesent pape descibes the incopoation of finite element method (FEM) fo the calculation of tansfome equivalent cicuit paametes (leakage inductance, shot-cicuit impedance) in the existing design pocess of a manufactuing industy. The benefits of the application of FEM ae extensively analysed, consisting mainly in the accomplishment of high accuacy in the pediction of tansfome chaacteistics, eduction of the industial cycle and the oveall poduction cost. 1. INTRODUCTION In the context of a highly competitive enegy maket, the need fo decease of delivey time is of pimay impotance fo a tansfome industial plant, [1]. On the othe hand, the quality of the poduced tansfomes must not be compomised since high-quality, low-cost poducts ae the key to suvival, [2]. Decease of the tansfome delivey time can be accomplished by eduction of the study-design-poduction time (industial cycle), while tansfome eliability is impoved by accuate estimation of its chaacteistics (shot-cicuit impedance, no load losses, load losses). These objectives can only be achieved by the adoption of tansfome study methods incopoable to an automated design pocess, able to povide accuate esults. Numeical modeling techniques ae now-a-days well established fo powe tansfome analysis and enable epesentation of all impotant featues of these devices. Techniques based on finite elements pesent inteesting advantages fo nonlinea chaacteistics simulation. Key woks adopting this appoach ae povided next. In [3], eddy cuent loss in tansfome tank walls is analyzed and in [4] finite element models with vaying degees of complexity ae used fo the computation of shot-cicuit foces in single phase shell type powe tansfomes. A finite element model is used to simulate foil windings of a thee-phase coe type tansfome in [5], while in [6] minimized magnetic enegy and voltage equilibium ae combined with the finite element method fo the calculation of leakage field poblems coupled with an unknown ampee-tun distibution. In [7], two-dimensional (2D) and thee-dimensional (3D) finite element analysis is conducted in thee-phase shell type tansfome fo leakage flux and foce calculation. Othe woks in this categoy popose the finite diffeence method as a means of leakage field calculation as in [8] whee this method is applied to one-phase and thee-phase coe type tansfomes. In the pesent pape, a paticula 3D scala potential fomulation is adopted fo the development of a FEM model fo thee-phase, wound coe, distibution tansfomes. The method is used fo the calculation of the tansfome leakage field and shot-cicuit impedance. The model is incopoated to the automated design pocess of a tansfome manufactuing industy, inceasing the accuacy in the pediction of the tansfome opeational chaacteistics and educing the oveall industial cycle. The pape is oganized as follows: Section 2 descibes the mathematical fomulation of the 3D FEM fomulation used fo the tansfome leakage field evaluation along with the developed 3D FEM model. Section 3 descibes the tansfome industial cycle and the integation of the FEM model to the existing design pocess. In Section 4, the benefits fom the adoption of the numeical model ae analyzed. Finally, Section 5 concludes the pape. 2. TRANSFORMER MODELING WITH THE FINITE ELEMENT METHOD 2.1 Mathematical fomulation The finite element method is a numeical technique fo the solution of poblems descibed by patial diffeential equations. The consideed field is epesented by a goup of finite elements. The space discetization is ealized by tiangles o tetaheda if the poblem is two o thee-dimensional espectively. Theefoe, a continuous physical poblem is conveted into a discete poblem of finite elements with unknown field values in thei vetices nodes. The solution of such a poblem educes into a system of algebaic equations and the field values inside the elements can be etieved with the use of calculated

values in thei indices. Theefoe, the solution of the 3D magnetostatic poblem descibing the tansfome field educes in to the calculation of the magnetic field density at each vetex node of the tetaheda of its 3D mesh. In most of the developed scala potential fomulations this calculation is ealized with the use of the following equation: H = H s Φ m (1) whee Φ m is the scala magnetic potential satisfying Laplace equation: 2 Φm = 0 (2) and H s is the souce field density given by Biot- Savat s Law: 1 J ( ) Hs = π dv 4 (3) 3 V Howeve, the above calculation pesents the dawback of consideable computational effot, due to the pio souce field calculation with the use of (3). In the pesent pape, a paticula scala potential fomulation is adopted [9]: accoding to this method, the magnetic field stength H is conveniently patitioned to a otational and an iotational pat as follows: H = K - Φ (4) whee Φ is the scala potential extended all ove the solution domain while K is a vecto quantity (fictitious field distibution), defined in a simply connected subdomain compising the conducto, that satisfies Ampee's law and is pependicula on the subdomain bounday. 2.2 Repesentation of the tansfome configuation Fig.1 shows the active pat of the thee-phase, wound coe, distibution tansfome consideed. Its magnetic cicuit is of shell type and is assembled fom two small and two lage wound ion coes. Fig. 2 illustates the pespective view of the one-phase tansfome pat modeled, compising the ion coe, low and high voltage windings. Neumann bounday condition ion coe Diichlet bounday condition High Voltage winding Low Voltage winding Fig. 2. Pespective view of the one phase tansfome pat modeled. The use of this one phase model instead of the whole thee-phase tansfome model was conducted fo the following easons: i) The smalle model size enables the constuction of moe dense tetahedal finite element mesh without geat computational cost (given that the exact epesentation of the tansfome magnetic field equies geat accuacy which is dependent on the mesh density and the total execution time of the finite element calculations). ii) The epesentation of one phase of the active pat does not affect the accuacy of the equivalent cicuit paametes calculation. Due to the symmeties of the poblem, the solution domain was educed to one fouth of the device (although thee is a slight disymmety due to the teminal connections in one side). These symmeties wee taken into account by the imposition of Diichlet bounday condition (Φ=0) along xy-plane and Φ Neumann bounday condition ( =0) along the othe n thee faces of the ai box that suounds the tansfome active pat. Fig. 1. Active pat configuation of the theephase wound coe distibution tansfome consideed. As shown in Fig.2, the High Voltage winding aea is divided into fou subcoils. This division was made in ode to take into consideation the winding connection which gives the second high voltage level (i.e. 15 kv). In paticula, in the case of the fist connection (20 kv) all the subcoils ae consideed to undego the nominal cuent, while in the second one, two of them ae connected in paallel, theefoe half of the nominal cuent flows though them. Each subcoil consists of the espective numbe of tuns which ae given by the manufactue.

The finite element mesh of the tansfome active pat is shown in Fig. 3. The density of the mesh is geate in the windings aea, which is cucial fo the leakage inductance evaluation unde shot-cicuit test. Moeove, special consideation has been given to the homogeneity of the oveall mesh, as it consists an impotant facto fo the accuacy of the finite element calculations. Fig. 3. Thee-dimensional finite element mesh of the tansfome active pat. 3. INCORPORATION OF FINITE ELEMENT METHOD IN THE TRANSFORMER INDUSTRIAL CYCLE 3.1 Desciption of the industial cycle The tansfome industial cycle consists mainly in the study, design and constuction phases, [1]: The tansfome study is implemented, based on data that ae included in the custome specification (ated powe, pimay and seconday voltage, shot-cicuit impedance, losses, equied accessoies). Next, the study data sheets ae ceated using a suitable compute pogam. Afte that, the study data sheets ae send to the Industial Dawings Depatment and this Depatment ceates the tansfome constuctional dawings (using the AUTOCAD envionment) and the bill of mateials. Next, the study data sheets, the constuctional dawings and the bill of mateials ae send a) to the Puchasing Depatment in ode to manage the equied mateials fo the constuction, and b) to the Tansfome Poduction Depatment in ode to poceed to tansfome constuction. Afte the completion of the poduction, the Quality Contol Depatment subjects the tansfomes to vaious tests and, afte confiming that the tansfomes fulfill the specifications, they ae deliveed to the custome. 3.2 Tansfome study pocess 3.2.1 Technical specifications. In the tansfome study phase, the design enginee must satisfy the custome need fo one specific tansfome type, poducing a design that fulfills the custome equiements and the intenational technical specifications. The specifications elated to tansfome manufactuing ae shown in Table 1. These specifications ae elated with the electical chaacteistics and the accessoies of tansfomes. The specification IEC 60076 (1 2 3 5) descibes the electical chaacteistics and the tansfome tests that ae elated with the tansfome dynamic, themal and electical stain. The DIN specification defines the tansfome losses and accessoies, while the CENELEC specification combines data of vaious specifications. Table 2 pesents the toleances accoding to IEC 60076-1 to be applied to cetain ated quantities when they ae the subject of manufactue's guaantees. 3.2.2. Tansfome study softwae. Fo the implementation of the tansfome study phase, the manufactuing industy has developed a compute softwae, using an optimal solution seaching algoithm. The design enginee intoduces the data in the compute pogam and the pogam calculates whethe acceptable solutions can deive fom the specified data. Duing the development of the softwae, special consideation has been given to the data input pocedue. Moe specifically, thee ae seven goups of vaiables fo the design of a thee-phase distibution tansfome: - Desciption vaiables (e.g., ated powe, ated LV and HV, fequency, mateial of LV and HV coil, LV and HV connection, ) - Vaiables that aely change (e.g., LV and HV BIL, coe space facto, tuns diection space facto, shot-cicuit facto, ) - Vaiables with default values (e.g., LV and HV taps, guaantee and toleance fields fo load loss, no-load loss and impedance, ) - Cost vaiables (e.g., cost pe weight unit fo LV and HV conducto, magnetic steel, oil, insulating pape, duct stips, cougated panels, ) - Optional vaiables (e.g., vaiables that eithe can be calculated by the pogam o defined by the use) - Vaious paametes (e.g., type of LV and HV conducto, numbe of LV and HV ducts, LV and

HV maximum gadient, maximum ambient tempeatue, maximum winding tempeatue, ) TABLE 2. Toleances accoding to IEC 60076 1 - Vaiables fo conducto coss-section calculations (LV and HV conducto coss-sections can be defined by the use o can be calculated using cuent density, o themal shot-cicuit test) - Solution loop vaiables (e.g., LV tuns, dimensions of coe, magnetic induction, LV and HV cosssection) TABLE 1. Tansfome specifications Specification Desciption IEC 60076-1 Powe tansfomes - geneal IEC 60076-2 Powe tansfomes - tempeatue ise IEC 60076-3 Powe tansfomes - insulation levels and dielectic tests IEC 60076-5 Powe tansfomes - ability to withstand shot-cicuit IEC 60137: 2003 Bushings fo altenating voltages above 1000 V IEC 60354: 1991 Loading guide fo oilimmesed powe tansfomes IEC 60076-11 Dy-type powe tansfomes IEC 60905: 1987 Loading guide fo dy-type powe tansfomes QUANTITY a) Losses a 1 ) Total losses (Fe+Cu) a 2 ) Fe losses (Cu losses) b) Voltage atio b 1 ) Voltage atio on pincipal tapping b 2 ) Voltage atio on othe tappings c) Shot-cicuit impedance (tansfome with two windings) c 1 ) Pincipal tapping TOLERANCE +10% of the guaanteed total losses (Fe+Cu) +15% of Fe losses (Cu losses), povided that the toleance fo total losses is not exceeded The lowe of the following values: a) ±0.5% of guaanteed voltage atio b) ±1/10 of the measued impedance on the pincipal tapping (U k %) To be ageed with the custome ±7.5% of the guaanteed is 10% ±10% of the guaanteed is <10% Using this pogam, and giving enough altenative values to the loop vaiables, enough candidate solutions ae made. Fo each one of the candidate solutions, it is checked if all the specifications (limits) ae satisfied, and if they ae satisfied, the cost is estimated and the solution is chaacteized as acceptable. On the othe hand, the candidate solutions, that violate the specifications ae chaacteized as nonacceptable solutions. Finally, fom the acceptable solutions, the tansfome with the minimum cost is selected which is the optimum technical and economical tansfome. Giving n LV diffeent values fo the tuns of the low voltage coil, n D values fo the coe s dimension D (width of coe leg), n FD ties fo the magnetic flux density, n G diffeent values fo the coe s dimension G (height of coe window), cs LV diffeent values fo the calculation of the coss-section aea of the low voltage coil and cs HV diffeent values fo the calculation of the coss-section of the high voltage coil, the total candidate solutions (loops of the compute pogam), n loops, ae calculated fom the following equation: c 2 ) Any othe tapping d) No-load cuent ±10% of the guaanteed is 10% ±15% of the guaanteed is <10% +30% of the guaanteed no-load cuent The solution algoithm of the technical and economical optimum tansfome is pesented in the followings: fo i:=1 to n LV fo j:=1 to n D fo k:=1 to n FD fo l:=1 to n G n loops = n LV * n D * n FD * n G * cs LV * cs HV (5)

calculate volts pe tun and thickness of coe leg Input Data fo m:=1 to cs LV Fo i=1 to n loops fo n:=1 to cs HV calculate laye insulation calculate coil dimensions calculate coe dimensions and losses i=i+1 Tansfome active pat calculations Examination of technical specifications of Table 2 fo the candidate solution Integation of Finite Element Model calculate shot-cicuit voltage and load losses calculate coil length calculate tank dimensions calculate Cu-oil gadient if tansfome is acceptable then: calculate dimensions of panels calculate dimensions of insulating mateial calculate weight of duct stips Fig. 4. Coppe losses Ion losses Deviation between guaanteed and specified value geate than the toleance of Table 2? YES NO Rejection of candidate solution Acceptance of candidate solution Shot-cicuit impedance Tansfome cooling tank calculations Tansfome cost calculation Integation of finite element model to the existing tansfome study softwae. calculate weight of oil calculate tansfome cost 3.3 Integation of finite element method in the tansfome study softwae The finite element model pesented in Section 2 was incopoated to the tansfome design pocess by integation in the existing study softwae. The model is used fo the calculation of the shot-cicuit impedance of the candidate solutions, in ode to veify whethe the cuent solution satisfies the technical specifications. In this way, a compound study softwae (using analytical fomulas and numeical model) has deived, taking advantage of the accuacy povided by the FEM calculation. The embedding of the finite element model is descibed in the flowchat of Fig. 4.The inteaction between the tansfome study softwae and the finite element model is illustated in Fig. 5. Tansfome Study Softwae Geometical data of cuent iteation (candidate solution) FEM pepocesso Calculation of leakage field by FEM Calculation of shotcicuit impedance Use of pedefined mesh Fig. 5. Inteaction between tansfome study softwae and finite element model.

4. BENEFITS FROM THE INCORPORATION OF FEM TO THE TRANSFORMER DESIGN PROCESS The benefits fom the incopoation of the finite element model to the existing manufactue design pocess affect many aspects of the manufactuing cycle: 1. Incease in the accuacy of the leakage field and shot-cicuit impedance calculation, especially in cases of tansfomes that do not fit into lage scale standadized constuctions. In these cases, expeiential ways of pedicting the tansfome leakage field (based on coection coefficients and simplifications of the eal geomety) pesent significant deviations fom the actual values, as they concen paticula geometies. On the othe hand, 3D FEM enables the detailed epesentation of the tansfome geomety, which is cucial fo the acquisition of eliable esults. 2. Reduction of the tansfome industial cycle, as the accuate pediction of the opeational chaacteistics eliminates the need fo constuction of tansfome pototype (to confim the accuacy of tansfome design) as well as fo shot-cicuit tests unde nominal voltage (which ae vey laboious and expensive). 3. Reduction of the tansfome constuction cost, by ovecoming the need to ovesize the tansfome in ode to emain within the design magins. 4. Impovement of the design methodology, by poviding a pope analysis and optimization tool. With this tool, the designe is no longe obliged to ely on empiical fomulas and intuition, thus avoiding possible inadequacies leading to penalties involving equipment weight, efficiency and othe pefomances. 5. CONCLUSIONS The pesent pape pesented the development of a costeffective 3D FEM model fo the computation of the leakage field and shot-cicuit impedance of theephase, wound coe, distibution tansfomes. The method has been embedded to the automated design pocess of a tansfome manufactuing industy, enabling the accuate pediction of the pefomance chaacteistics. This numeical model, along with the optimal solution seach algoithm of the study softwae, enable the techno-economical optimization of the tansfome design, esulting to significant benefits fo the manufactuing industy. industial cycle, Poc. IEE MEDPOWER 98, Nicosia, Cypus, Nov. 1998. 2. P. Geogilakis, N. Hatziagyiou, D. Papaigas, AI Helps Reduce Tansfome Ion Losses, IEEE Compute Applications in Powe, Vol. 12, N. 4, pp. 41-46, 1999. 3. C. Lin, C. Xiang, Z. Yanlu, C. Zhingwang, Z. Guoqiang, Z. Yinhan, "Losses calculation in tansfome tie plate using the finite element method," IEEE Tans. Magn., Vol. 34, N. 5, 1998, pp. 3644-3647. 4. S. Salon, B. LaMattina, K. Sivasubamaniam, Compaison of Assumptions in Calculation of Shot-cicuit Foces in Tansfomes, IEEE Tans. Magn., Vol. 36, N. 5, pp. 3521-3523, Sept. 2000. 5. H. De Gesem and K. Hameye, A Finite Element Model fo Foil Winding Simulation, IEEE Tans. Magn., Vol. 37, N. 5, pp. 3427-3432, Sept. 2001. 6. C. Xiang, Y. Jinsha, Z. Guoquiang, Z. Yuanlu, H. Qifan, Analysis of Leakage Magnetic Poblems in Shell-Fom Powe Tansfome, IEEE Tans. on Magn., Vol. 33, N. 2, pp. 2049-2051, Mach 1997. 7. A.G. Kladas, M.P. Papadopoulos, J.A. Tegopoulos,"Leakage Flux and Foce Calculation on Powe Tansfome Windings unde shotcicuit: 2D and 3D Models Based on the Theoy of Images and the Finite Element Method Compaed to Measuements," IEEE Tans. Magn., Vol. 30, N. 5/2, Sept. 1994, pp. 3487-3490. 8. K. Zakzewski, M. Kukaniszyn, Theedimensional model of one- and thee-phase tansfome fo leakage field calculation, IEEE Tans. Magn., Vol. 28, N. 2, Mach 1992, pp. 1344-1347. 9. A. Kladas, J. Tegopoulos, "A new scala potential fomulation fo 3D magnetostatics necessitating no souce field calculation," IEEE Tans. Magn., vol. 28, pp. 1103-1106, 1992. 6. REFERENCES 1. P. S. Geogilakis, N. D. Hatziagyiou, S. S. Elefsiniotis, D. G. Papaigas, J. A. Bakopoulos, Ceation of an efficient compute-based envionment fo the eduction of tansfome