EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia 3D Finite Element Analysis of a Three Phase Power Transformer Dorinel Constantin, Petre-Marian Nicolae, Cristina-Maria Nitu Electric, Energetic and Aero-spatiale Engineering Department, University of Craiova Romania, Craiova, Blvd. Decebal, st. 107 1 3 [email protected] [email protected] SC INAS SA Romania, Craiova, Blvd. Romanescu, st. 37C 2 [email protected] Abstract—The purpose of this study was to validate a designed three phase power transformer with modern software that use finite element method, by analyze it from two points of view: magnetic and thermal. For that, on the analysis it will be used two modules from ANSYS software, ANSYS Maxwell 3D and ANSYS Mechanical, both coupled in the same environment, ANSYS Workbench. It has used the latest versions from ANSYS, Workbench 14.5 and Maxwell 3D 16.  On the same time, it can be seen the 3D magnetic nonlinear behavior of this three phase power transformer and thermal effects for the ferromagnetic core. Also it can be found the magnitude of B field, the regions with problems and the value of the total core losses for the same transformer but at 3 types of voltages: 330 kV, 400 kV and 430 kV. Keywords: ANSYS Maxwell 3D, ANSYS Mechanical, B field, Finite Element Analysis, three phase power transformer, nonlinear behavior. I. INTRODUCTION Many years on the past, power transformer designers had done their job using only the pencil, the paper and their guide of designing transformers. With time, it seems that those things are not enough.  Soon appeared analytical software’s that are doing multiples calculation on the same time and comes with an optimized transformer, minimum of materials, minimum of cost and short time of calculation. A second problem was how to see this new transformer working connected at the network without constructing a prototype. And this problem has found the answer: finite element or volume analysis using dedicated software. The most used software for almost all domains is ANSYS, a powerful tool for engineers. One of the new acquisitions for ANSYS was Maxwell, a high-performance interactive software package, accurate and powerful tool that uses finite element analysis (FEA) to solve transient, AC electromagnetic, magnetostatic, electrostatic, eddy current and electrotransient problems solving the force, torque, capacitance, inductance, resistance and impedance, as well as generate state-space models. Maxwell solves the electromagnetic field problems by solving Maxwell's equations in a finite region of space with appropriate boundary conditions and – when necessary – with user- 978-1-4673-2232-4/13/$31.00 ©2013 IEEE specified initial conditions in order to obtain a solution with guaranteed uniqueness. Starting with future versions of ANSYS from 14, Maxwell is fully integrated on the environment called Workbench. On ANSYS Workbench, the user can connect very simple and easy more then one type of analyze (magnetic with thermal or thermal with mechanic, etc.). About this transformer must be said that it comes already designed, but not yet validated with a finite element software, like ANSYS Maxwell 3D from an electromagnetic point of view, for three types of voltages: 330 kV, 400 kV and 430 kV. For that it must solve a transient problem and find the B field magnitude for each case, the pick for total core losses and also the highest value of the temperature on the core. II. ANSYS MAXWELL 3D Some of applications for ANSYS Maxwell are: motor and generator, linear or rotational actuators, relays, MEMS, sensors, coils, permanent magnets, transformers, converters, bus bars, IGBTs and similar devices, etc. This module of ANSYS software are using for solving all the problems, Maxwell's equations: • Faraday's Law of induction: z *E= B6 (1) • Gauss's Law of magnetism: (2) z·B=0 • Ampere's Law for current: 6 z *H J D (3) • Gauss's Law of electricity: (4) z·D= From those general equations, after the user select type of problem for solving, then it will automatically change in the behind of the software. For spatial discretization, Maxwell 3D are using tetrahedrons, working the best for the 2nd order quadratic interpolation between nodes. 2 2 (5) A z x,y =a 0 +a 1 x+a 2 y+a3 x +a 4 xy+a 5 y III. TECHNICAL DATA OF THE TRANSFORMER This transformer is a three phase power transformer, fivelegs magnetic core, laminated steel, having 31 steps, 5 steps of 1548 Authorized licensed use limited to: Universidad de Concepcion. Downloaded on September 14,2021 at 00:28:50 UTC from IEEE Xplore. Restrictions apply. EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia TABLE 1. GENERAL PARAMETERS FOR THE TRANSFORMER 325 MVA Transformer HV winding LV winding 1 Type of connection YNd11 2 Rated power 195 / 260 / 325 MVA 3 Cooling system 4 Rated voltage 400 kV 17.5 kV 5 Voltage variation 330 kV – 430 kV 17.5 kV +/- 10% 6 Rated frequency 50 Hz Number of turns 90 turns (Tap winding) 7 ONAN / ONAF / ONAF 690 turns 55 turns Fig. 2, dimensions that were analytical calculated, without an optimization software. Another observation is that regulation is doing on the HV winding. Fig. 1. BH and BP curves for the transformer core  upgraded insulation and 2 cooling ducts on a side plus another one on the core centre. The transformer has 3 windings: LV winding, HV winding and 2 coils for Tap winding. HV winding has a 690 turns, LV winding has 55 turns and the Tap winding has 10 disks and 45 turns on each coil. The type of connection for this transformer is YNd11 and the transformer frequency is 50 Hz. One other particularity for the transformer are the cuts at the superior and inferior yoke for each step, aiming to reduce the core quantity of metal and implicit the core losses and making it easier to transport. To find the total core losses and electromagnetic behavior for 3D transformer modeling, it can use a simplified geometry of physical model, eliminating the tie rods, the box and other parts. Of course, and other metallic parts are come with their contribution at losses. For transformer construction was used copped for the windings, upgraded paper for the insulation and laminated steel with the characteristics presented below to Fig. 1 from manufacturer. As for designing characteristics, you can see them on the IV. THE PHYSIC MODEL DRAW IN MAXWELL 3D AND COUPLING WITH ANSYS MECHANICAL For 3D analyze of the transformer, there must done some simplification from the designed model. There will take account the magnetic core with insulation and the spacing between the steps and also the windings arrangement. For all 3D model was used two types of geometrical figures, box and cylinder and also the Maxwell subtract function. First must said that all the simulations are done in time domain (Transient). For each winding (LV and HV) or disk (Tap winding) was created sections to apply excitations. As excitations was chosen Terminal Coil and putted on the fields the turns number (see Table 1). Also was set core losses only to core geometry and negligible the eddy current effect to the windings. After this operation, all the terminals was assign to the two windings (LV and HV winding), Tap winding been introduced to HV winding. The excitation for windings was Voltage and selected the Stranded type for the turns and a calculated resistance. ·l Χ R= (6) s 2 Χ·mm with 15 0 . 0214 m TABLE 2. RESISTANCES VALUES FOR THE WINDINGS Resistances HV winding 330 kV 400 kV Fig. 2. Core design and windings arrangement for 325 MVA transformer (red – LV winding; blue – HV winding; green – Tap winding; gray – core) 978-1-4673-2232-4/13/$31.00 ©2013 IEEE 430 kV 0 . 4822 HV 0 . 51 R HV R + R = HV tap 0. 5504 R LV winding Voltage sources HV and LV winding 0.002306 7; 8; 9 0.002306 7; 8; 9 0.002306 7; 8; 9 1549 Authorized licensed use limited to: Universidad de Concepcion. Downloaded on September 14,2021 at 00:28:50 UTC from IEEE Xplore. Restrictions apply. EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia Vpeak· 1e ·cos 2··50·time V 50·time ·cos 2··50·time+ 23·time Vpeak· 1e 50·time ·cos 2··50·time+ 43·time Vpeak· 1e 50·time V (8) V (9) *Vpeak is modify once for HV winding and once for each case (330, 400 and 430 kV). For LV winding is always the same because in secondary the voltage remains approximately constant, 17.5 kV.  The mesh was treated for each type of geometry part and inside of the parts, setting a length based and having the number of tetrahedrons presented in Table 3. TABLE 3 MESH CHARACTERISTICS 1 Core 60 363 tetrahedrons 2 HV winding 26 536 tetrahedrons 3 LV winding 24 638 tetrahedrons 4 Tap winding 14 037 tetrahedrons 5 Insulation 5 425 tetrahedrons V. RESULTS FROM ANSYS MAXWELL 3D AND MECHANICAL (7) First case: U HVwinding330kV For this case, HV winding has only 690 turns, without regulation interfering. For the LV winding, the number of turns remains for each case the same, 55 turns. Also is modifying the voltage peak and the resistance. (see Table 1 and Table 2). After the simulation, it can be seen from the B field graphic the nonlinear behavior of the transformer, with a minimum of 1.26 T and a maximum of 1.63 T, for 330 kV case. The total core losses for the transformer are maximum at the end of the simulation, gradually increasing from 0 until 56.83 kW. For the interval 0.08 ÷ 0.1, the average of the total core losses are 49.15 kW.  As for the Setup Analysis, the time is set from 0s to 0.1s (this interval was chosen because if the end value are greater, the voltage pick is approx. constant and the simulation will take longer), with a step of 0.0005s. The recording time was from 0.08s to 0.1s because this is the most important period were the voltage reached the pick and with a nonlinear 6 . residual of 10 Using ANSYS Workbench, after the simulations are done, it will connect Maxwell 3D with a problem Steady State from ANSYS Mechanical (see Fig. 3). From the Engineering Data, it will create 3 materials: Copper, Core and Insulation. For Copper, the material for the windings is chosen a density 3 of 8933kg m , an isotropic thermal conductivity of 2 2 400 W m ·°C and a specific heat of 385 J kg ·°C . 3 For Core, is chosen a density of 7650kgm and an 2 isotropic thermal conductivity of 5W m ·°C . For Insulation, is chosen an isotropic thermal conductivity of 2 4 . 5W m ·°C . Fig. 3. ANSYS Workbench, the environment were are coupled a problem from Maxwell 3D to ANSYS Mechanical 978-1-4673-2232-4/13/$31.00 ©2013 IEEE Fig. 4. B field on the core for 330 kV Fig. 5. Core losses for the three phase transformer for 330 kV 1550 Authorized licensed use limited to: Universidad de Concepcion. Downloaded on September 14,2021 at 00:28:50 UTC from IEEE Xplore. Restrictions apply. EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia Fig. 8. B field on the core Fig. 6. B field on the core for 400 kV The total core losses for the transformer are maximum at the end of the simulation, gradually increasing from 0 until 66.55 kW. For the interval 0.08 ÷ 0.1, the average of the total core losses are 55.94 kW.  Fig. 7. Core losses for the three phase transformer for 400 kV Second case: U HVwinding 400kV HV winding has 690 turns plus 16 turns from Tap winding, and a higher voltage, 400 kV and also different value for the HV winding resistance.  On the Fig. 5 it can be seen that the minimum B field is 1.29 T and a maximum is 1.64 T, for 330 kV case. The total core losses for the transformer are maximum at the end of the simulation, gradually increasing from 0 until 62.86 kW. For the interval 0.08 ÷ 0.1, the average of the total core are 53.41 kW. ANSYS software has a great working environment that offers to the users the possibility of combining more than one module, easy and at a click distance. This environment is called Workbench. The thermal analyze has been done for ONAN type of ventilation and without the oil, only with air, to see if the transformer can be work with this type of cooling system and that is the contribution of it, on the measuring stand in the future. The thermal simulation was done only for the highest B field value, so for the last case of voltage, and to Mechanical was imported only Heat Generation as parameter. The maximum temperature of the core is 94.76 °C (for the zone were there are those points at the corners for the central windows).   The simulation was reduced to 2D for a sheet from the biggest step of the ferromagnetic core. The value obtain after the simulation are smaller that the value of 98 °C that are on the IEC standards for this type of insulation paper.  Third case: U HVwinding 430kV HV winding has 690 turns plus 20 turns from Tap winding, but at maximum voltage. After the simulation, it can be seen from the B field graphic the nonlinear behavior of the transformer, with a minimum of 1.31 T and a maximum of 1.66 T, for 430 kV case. 978-1-4673-2232-4/13/$31.00 ©2013 IEEE Fig. 9. Core losses for the three phase transformer for 430 kV 1551 Authorized licensed use limited to: Universidad de Concepcion. Downloaded on September 14,2021 at 00:28:50 UTC from IEEE Xplore. Restrictions apply. EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia z The highest value of the temperature from the ferromagnetic core was 94.76 °C. V. CONCLUSION A first conclusion is that the highest B field is recorded for 430 kV at the corners of the 2 central windows and the pick of the core losses is recorded for 430 kV. The simulation time is quite long, but if is used a HPC license and an advanced computer, can be reduce it. The highest temperature of the core are found on the same places were the B field is maximum and were the designers can come with different solutions to decrease or increase the distance between core and windings. After those 2 studies, magnetic and thermal with ANSYS Maxwell 3D and ANSYS Mechanical, the results can be very easy sent to other modules from ANSYS for a structural and fluid dynamic analysis, to see if the designed transformer resist and what are the effects of the cooling system. This study and the results obtained validate the designed product and it can be sent to production. Fig. 10. The heat generation on the core for 430 kV case REFERENCES Fig. 11. The thermal distribution on the core for 430 kV case All the simulations were done using ANSYS Workbench 14.5, and the last version of Maxwell, 16 and a personal computer with the following characteristics: − CPU: Intel Pentium 4, Dual Core 3.2 GHz/core; − RAM: 4 GB; − Video: 128 MB; 1280×1024. z z z z VI. RESULTS Number of tetrahedrons after creating the mesh was 130 999 elements; Solution time for the simulations was approx. 393.44 min; The maximum B field for 330 kV was 1.63 T; the maximum B field for 400 kV was 1.64 T and the maximum B field for 430 kV was 1.66 T; The core losses pick for 330 kV was 56.83 kW; the core losses pick for 400 kV was 62.86 kW and the core losses pick for 430 kV was 66.55 kW; 978-1-4673-2232-4/13/$31.00 ©2013 IEEE  www.ansys.com; User's guide Maxwell 3D 637-667.  D. Lin, P. Zhou, W.N. Fu, Z. Badies and Z.J. Cendes, “A dynamic core loss model for soft ferromagnetic and ferrite materials in transient finite element analysis”, IEEE Transactions on Magnetics, vol. 40, no. 2, March 2004.  E. Schmidt and S. Ojak, “3D MSC/EMAS simulation of a three phase transformer by means of anisotropic material properties”, Vienna, Austria, In Proceedings of the 1996 MSC World Users Conference, Newport Beach (CA, USA),1996.  M. Jamali, M. Mirzaie and S. Asghar Gholamian, “Calculation and analysis of transformer Inrush current based on parameters of transformer and operating conditions”, Electronics and Electrical Engineering – Kaunas: Technologija, no. 3 (109). 2011, pp. 17-20.  R. Rahnavard, M. Valizadelu, A.A.B. Sharifian and S.H. Hosseini, “Analytical analysis of transformer inrush current and some new techniques for its reduction”, In Proc. of Int. Conference on Power Systems and Transients, 2005, pp. 1-5.  M. H. Amrollahi and S. Hassani, “Determination losses and estimate life of distribution transformers with three computational, measurement and simulation methods, despite harmonic loads”, 2010, pp. 1-4.  Pavlos S. Georgilakis, Spotlight on modern transformer, Springer, 2009, 18-23, 33, 263-325.  D. Constantin, P.M. Nicolae, “Analiza comparativa privind utilizarea unor programe de specialitate pentru validarea proiectarii unor transformatoare de putere”, SNET 2012 Symposium, Bucharest, Romania, 2012  D. Ebehard and E. Voges, “Digital single sideband detection for interferometric sensors”, In Proc. of the 2nd Int. Conf. Optical Fiber Sensors, Stuttgart, Germany, 1984  D. Susa, “Dynamic thermal modeling of power transformers”, Ph.D. dissertation, Dept. of Electrical and Communications Eng., Helsinki Univ. of Technology, 2005  IEC Guide for Power and Distribution Transformers, IEC 60076-1 to 10.1 1552 Authorized licensed use limited to: Universidad de Concepcion. Downloaded on September 14,2021 at 00:28:50 UTC from IEEE Xplore. Restrictions apply.