Transformer 4 Research Papers

Reduction of Power Grid Losses by Using Energy Efficient Distribution Transformers

2014, Journal of Materials Science Forum, vol. 721, pp. 269-274

The importance of distribution transformer no-load loss on the operation of modern electrical grids is often underestimated. Internationally, distribution transformer no-load loss constitutes nearly 25% of the transmission and... more

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Experimental and Theoretical Analysis of Iron Losses of Electrical Steels Subjected to Distorted Supply Voltage Waveform Conditions

by Themistoklis D. Kefalas

2014, Journal of Materials Science Forum, vol. 721, pp. 171-176

Iron losses of grain-oriented electrical steels, is sensitive to the distortion of the supply voltage waveform of the excitation winding. As a result, magnetic cores of electrical machines and transformers manufactured of grain-oriented... more

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Advanced computational tools for wound core distribution transformer no-load analysis

by Themistoklis D. Kefalas

2014, COMPEL, vol. 31, no. 2, pp. 682-691

Purpose – This paper aims to present an accurate representation of laminated wound cores with a low computational cost using 2D and 3D finite element (FE) method. Design/methodology/approach – The authors developed an anisotropy model in... more

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Normal flux distribution at step-lap joints of Si-Fe wound cores

by Themistoklis D. Kefalas

2014, Journal of Materials Science Forum, vol. 670, pp. 284-290

Even though, the flux distribution at joints of stacked type transformer cores has been investigated thoroughly many issues remain unclear in the case of wound transformer cores. The paper addresses this lack of information by... more

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FEM package for iron loss evaluation and minimization of two grade lamination wound cores

by Themistoklis D. Kefalas

2014, Journal of Optoelectronics and Advanced Materials, vol. 10, no. 5, pp. 1197-1202

The iron loss and manufacturing cost of a strip-wound core can be reduced by constructing the wound core with combination of average and high magnetization grade steel. The present paper introduces a two-dimensional finite element (2D... more

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Unification of anisotropy and FEM-BE models for distribution transformer optimization

by Themistoklis D. Kefalas

2014, Journal of Optoelectronics and Advanced Materials, vol. 10, no. 5, pp. 1143-1148

The paper presents a three-dimensional finite element (3D FEM) anisotropy model, based on a particular scalar potential formulation, for the no load loss evaluation of wound core shell type distribution transformers. The specific 3D FEM... more

Fig. 4. Perspective view of the geometry and the flux density vector plot of a one-phase wound core (B = 1.57 T). Fig. 4 illustrates a perspective view of the geometry, and the flux density vector plot of a wound core, obtained by the 3D FEM anisotropy model. The core is built of high permeability magnetic steel, and the mean flux density used for the FE analysis is 1.57 T. Figs. 5 and 6 display the flux density vector, and nodal plot respectively, of the upper front part of the same wound core, for a mean flux density of 1.66 T.

Fig. 1. Geometry of the FEM-BE model. The use of the hybrid FEM-BE technique results in the accurate evaluation of the magnetic field in the transformer’s active part and in the air region surrounding it, with low computational effort comparing with the FE method. Fig. 1 depicts the 3D one-phase model of the three-phase wound core distribution transformer, consisting of the LV and HV windings and the iron cores. The hybrid FEM-BE model is divided in two subdomains, the transformer’s active part, FEM subdomain, represented by a tetrahedral FE mesh, and the subdomain between the active part and the transformer’s tank walls, BE subdomain, represented by a triangular mesh of its boundaries. 5. Experimental verification of the 3D FEM models

Fig. 3. Detail of the wound core, the excitation coil, and the search coils. Fig. 2. Experimental setup.

Fig. 9. Flux density magnitude distribution along line AB.

Fig. 7. Flux density magnitude distribution along line AB. The computed results, shown in Figs. 7 to 10, verify that the flux density distribution along lines AB and CD is different. Nevertheless, due to the fact that the FE analysis does not take into consideration the stress induced by manufacturing processes, the error of the computed flux density is greater in the inner sheets than in the outer sheets, especially along line AB as can be seen from Figs. 7 and 9.

Fig. 8. Flux density magnitude distribution along line CD.

Fig. 6. Nodal plot of the wound core flux density distribution during no load test (B = 1.66 T). Fig. 5. Vector plot of the wound core flux density distribution during no load test (B = 1.66 T).

Table 2. Three-phase wound core distribution transformer parameters and solution output. 7. Conclusion A 3D FEM anisotropy model for the no load loss evaluation of one-phase and three-phase wound core transformers was developed, based on a computationally efficient scalar potential formulation. The accuracy of the The specific optimization problem presents multiple optima and it was tackled by stochastic optimization algorithms. In [2] the geometric programming was applied, whereas in [5] a heuristic solution was chosen. In the present paper two well known stochastic algorithms were tested the genetic algorithm (GA) and the simulated annealing (SA). Table 2 summarizes the transformer’s parameters and the solution obtained by the SA algorithm, i.e. the most effective of the algorithms tested. The GA was proven to be more computationally expensive as it required a greater number of objective function evaluations, and also the final TOC value was 0.51 % higher than that obtained by the SA algorithm.

Table I. Comparison of the computed and measured no load loss values, of three-phase wound core distribution transformers of various apparent power and working induction ratings. The results obtained by the hybrid FEM-BE technique were validated for a number of three-phase distribution transformers through local leakage field measurements by a Hall Effect probe during the short-circuit test. Also the difference between the measured and the computed short circuit impedance is in most cases less than 2.7 %. Further details on the experimental verification of the hybrid FEM-BE technique may be sought in [3] and [6].

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Robust numerical analysis of wound core distribution transformers

by Themistoklis D. Kefalas

2014, Proceedings of the 18th International Conference on Electrical Machines ICEM 2008, Vilamoura, Portugal

In this paper a robust three-dimensional (3D) finite element (FE) anisotropy model is introduced based on a particular scalar potential formulation. The specific 3D FE model is suitable for the accurate evaluation of the peak flux density... more

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Analysis of Transformers Working Under Heavily Saturated Conditions in Grid-Connected Renewable-Energy Systems

by Themistoklis D. Kefalas

2014, IEEE Transactions on Industrial Electronics, vol. 59, no. 5, pp. 2342-2350

In recent years, researchers have proposed transformerless solutions for connecting renewable-energy power plants to the grid. Apart from lack of efficiency and increased cost and weight of the transformer, one of the reasons is the dc... more

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Mixed Si-Fe Wound Cores Five Legged Transformer: Losses and Flux Distribution Analysis

by Themistoklis D. Kefalas

2014, EEE Transactions on Magnetics, vol. 48, no. 4, pp. 1609-1612

This paper proposes a three-phase five legged wound transformer core constructed of two high permeability Si-Fe wound cores and two conventional Si-Fe wound cores. The two large internal wound cores are manufactured of high permeability,... more

Fig. 1. Simplified schematic of wound core and its geometrical parameters.

Fig. 2. (a) Typical and (b) mixed, three-phase wound transformer cores.

Fig. 3. Experimental setup for single-phase transformer core measurements.

wound around the total width of the upper yoke of each core as shown in Fig. 4.

Fig. 4. Experimental setup for three-phase transformer core measurements.

Fig. 5. Single-phase transformer cores specific iron losses

Fig. 6. Comparison of typical three-phase, mixed three-phase, and the respec- tive single-phase, transformer cores specific iron losses.

Fig. 8. Flux waveforms of (a) typical 1.2 T, (b) mixed 1.2 T, (c) typical 1.6 T, and (d) mixed 1.6 T, three-phase transformer cores. Fig. 7. Three-phase and single-phase specific iron loss increase percentage.

Fig. 10. Line excitation rms currents of typical and mixed three-phase trans former cores. Fig. 9. Peak flux density harmonics contents of typical and mixed three-phase transformer cores (a) 1.2 T and (b) 1.6 T.

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Flux distribution in single phase, Si–Fe, wound transformer cores

by Themistoklis D. Kefalas

2014, ournal of Magnetism and Magnetic Materials, vol. 320, pp. 874-877

This paper shows experimental results of longitudinal flux density and its harmonics at the limb, the yoke and the corner as well as normal flux in the step lap joint of a single phase, Si–Fe, wound transformer core. Results show that... more

Fig. 8. Ratio of normal to longitudinal flux as a function of reference core flux density.

Maximum flux values in the step lap joint of the wound core under test

Fig. 4. Flux density distribution across the corner of the core.

Fig. 2. Flux density distribution across the limb of the core.

Fig. 3. Flux density distribution across the yoke of the core.

Fig. 5. Harmonics components of the localized flux density when the core is magnetized at 1.7, 1.6 and 1.5T.

Fig. 6. Harmonics components of the localized flux density when the core is magnetized at 1.4, 1.3 and 1.0T.

Fig. 7. Detail of a wound core section showing the locations of search coils used for normal flux density measurements (figure not in scale).

Fig. 1. Wound core modeled (dimensions in mm).

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Power Transformer No Load Loss Optimization considering Manufacturing Process Effects

by Themistoklis D. Kefalas

2014, Proceedings of the 12th Biennial IEEE Conference on Electromagnetic Field Computation CEFC 2006, pp. 370, Miami FL, USA

Transformer no load loss optimization is crucial for transformer manufacturers as well as for electric utilities, since it results to significant economic benefits. In this article, the three-dimensional finite element analysis is applied... more

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Development of Distribution Transformers Assembled of Composite Wound Cores

by Themistoklis D. Kefalas

2014, IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 775-778

This paper proposes the manufacturing of distribution transformers using a novel type of magnetic core which is called composite wound core. A composite wound core is constructed of a combination of conventional and high magnetization... more

Fig. 2. Composite wound cores comprising (a) 1-phase core type, (b) 1-phase shell type, and (c) 3-phase five-legged transformers.

Fig. 3. Design variables of a two-grade composite wound core.

Fig. 1. Conventional wound core transformer (a) 1-phase core type, (b) 1-phase shell type, (c) 3-phase five-legged.

Fig. 4. Regions comprising the FE model of a composite wound core. anisotropy model is used due to the wound core topology. The specific model is based on the assumption that H has an elliptic trajectory for the modulus of B constant. The magnetic perme- ability is considered as a tensor quantity and the component par- allel to the lamination rolling direction ji), is given by (7) where /tq is the permeability component transverse to the lamination rolling direction, and r is the ratio of the ellipse semi-axes. The third component jz,, normal to the lamination plane has little influence on the 3D FE analysis and it is taken to be equa to the component along the rolling direction 4. Fig. 4 shows the regions comprising the FE model of a composite wound core. For regions Al to A5, and All to A15, the conventiona grain-oriented steel is assigned, and for regions A6 to A10 the high magnetization grain-oriented steel is assigned. Due to the wound core geometry the permeability tensor yz must be rotated to a different coordinate system in some of the regions of the 3D FE model. All iron loss components, including anomalous losses, are represented by the experimentally determined loca specific iron loss characteristic, expressed as a function of the peak flux density and approximated by cubic splines. Wound core transformer no-load loss is evaluated by a post-processing algorithm that combines the experimentally determined specific iron losses with the FE calculated peak flux density distribution.

Fig. 5. FE-BE model of the 3-phase wound core distribution transformer. The evaluation of the short-circuit impedance using conven- tional FE techniques requires a dense discretization of the air surrounding the transformer active part. We have addressed this problem by developing a hybrid FE-BE technique. The 3D model shown in Fig. 5, is partitioned in two subdomains, the FE subdomain of the transformer active part represented by a tetrahedral mesh, and the BE subdomain between the active part and the transformer tank walls, represented by a triangular mesh of its boundaries. The solution domain was reduced to one eighth of the transformer active part. The symmetries of the problem were taken into consideration by imposing a Dirichlet boundary condition (6 = 0) at the bottom facet of the model and a Neumann boundary condition (O®/On = 0) at the back and left facets of the model as shown in Fig. 5. The boundary integral equation corresponding to Laplace equation is given by (8) where gs is the observation point, s’ is the boundary I’ coordinate, n/ is the unit normal, and G is the fundamental solution of Laplace equation in free space. The use of the hybrid FE-BE technique results in the accurate evaluation of the magnetic field in the transformer active part and in the air region, with low computational effort comparing with the FE method.

Fig. 7. Flux density distribution of 3-phase five-legged transformer assembled of composite wound cores (7, = 0 mm, x2 = 20 mm). Fig. 6. Flux density distribution of 1-phase shell type transformer assembled of (a) conventional wound cores, and (b) composite wound cores.

TRANSFORMER PARAMETERS AND OPTIMIZATION SOLUTION TABLE I

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Artificial Intelligence Combined with Hybrid FEM-BE Techniques for Global Transformer Optimization

by Themistoklis D. Kefalas

2014, IEEE Transactions on Magnetics, vol. 43, no. 4, pp. 1633-1636

The aim of the transformer design optimization is to define the dimensions of all the parts of the transformer, based on the given specification, using available materials economically in order to achieve lower cost, lower weight, reduced... more

Fig. 1. Perspective view of the transformer FEM—BE model.

Fig. 2. DT for selection of winding material in power transformers.

Fig. 3. Best five results (according to the highest CSR on TS) of each case are presented using as input neurons the 13 attributes of Table I and two different cases regarding the sizes of LS and TS. (a) One hidden layer with 50% LS-50% TS. (b) One hidden layer with 70% LS-30% TS. (c) Two hidden layers with 50% LS-50% TS. (d) Two hidden layers with 70% LS-30% TS. Elapsed ATNN training times (in seconds) are given in parentheses.

Fig.4. Best five results (according to the CSR on TS) of each case are presented using as input neurons the six attributes selected by the DT and two different cases regarding the sizes of LS and TS. (a) One hidden layer with 50% LS-50% TS. (b) One hidden layer with 70% LS-30% TS. (c) Two hidden layers with 50% LS-50% TS. (d) Two hidden layers with 70% LS-30% TS. Elapsed ATNN training times (in seconds) are given in parentheses.

CLASSIFICATION SUCCESS RATE ON THE TEST SET FOR THE DT

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Multiple Grade Lamination Wound Core: A Novel Technique for Transformer Iron Loss Minimization Using Simulated Annealing With Restarts and an Anisotropy Model

by Themistoklis D. Kefalas

2014, IEEE Transactions on Magnetics, vol. 44, no. 6, pp. 1082-1085

This paper introduces a novel technique for iron loss minimization of wound core transformers. The proposed technique involves the evaluation of appropriate design variables of wound cores constructed by a combination of standard and high... more

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Harmonic Impact on Distribution Transformer No-Load Loss

by Themistoklis D. Kefalas

2014, IEEE Transactions on Industrial Electronics, vol. 57, no. 1, pp. 193-200

The losses in European Union distribution transformers are estimated at about 33 TW · h/year, whereas reactive power and harmonic losses add a further 5 TW · h/year. The reduction of distribution transformer no-load loss is particularly... more

Fig. 7. Phase-angle plot of deformed line-to-line and line-to-neutral suppl voltages.

Fig. 11. Wound-core simulated and experimental current waveforms under deformed line-to-neutral voltage excitation.

Fig. 2. Wound-core transformer. (a) One-phase core type. (b) One-phase shell type. (c) Three-phase shell type. the stack core and the wound core. A typical wound core, shown in Fig. 1, is composed of hundreds of long continuous strips of sheet steel. The main advantages include reduction of joints and the use of the grain direction of the steel for the flux path. Wound cores are commonly used for distribution transformers with ratings that range from a few kVA to a few MVA. One- and three-phase wound-core distribution transformers are con- structed by using one or more wound cores assembled about a preformed electrical winding coil, as shown in Fig 2. Il. FE ANALYSIS FOR NO-LOAD LOSS EVALUATION The FE method has been used extensively by many re- searchers for the accurate field analysis of electromagnetic de- vices. A 2-D FE analysis approach used for the analysis of 3-D magnetic components was developed in [19], an FE analysis to validate a new winding design for planar integrated magnetics has been carried out in [20], and a coupled electrothermal

The experimental setup used for evaluating the harmonic impact on wound-core no-load loss is shown in Fig. 3. The block diagram of the experimental setup is shown in Fig. 4. A 23-turn excitation coil was supplied from a single- and three-phase supply via a variable transformer (Regulac, type RQ 25-M, input: 240 V 50/60 Hz, output: 0-275 V, 25 A and Regulac, type RK8-G3M, input: 415 V 50/60 Hz, output: 0-476 V, 8 A) in order to magnetize the wound cores with a distorted supply-voltage waveform. A programmable ac and dc power supply (California Instruments MX30) was used so as to magnetize the wound cores with a sinusoidal waveform.

Fig. 6. Percentage of higher voltage harmonics plot of deformed line-to-line and line-to-neutral supply voltages.

Fig. 8. Wound-core geometry and flux-density vector plot (wound-core width: 190 mm, electrical steel: M-OH 0.27 mm). Fig. 9. Wound-core simulated and experimental current waveforms under sinusoidal voltage excitation.

Fig. 15. Phase-angle plot of experimental and simulated no-load currents under deformed line-to-line supply-voltage excitation.

Fig. 10. Wound-core simulated and experimental current waveforms under deformed line-to-line voltage excitation.

Fig. 17. Phase-angle plot of experimental and simulated no-load currents under deformed line-to-neutral supply-voltage excitation. Fig. 16. Amplitude plot of experimental and simulated no-load currents under deformed line-to-neutral supply-voltage excitation.

Fig. 12. Amplitude plot of experimental and simulated no-load currents under sinusoidal supply-voltage excitation.

Fig. 13. Phase-angle plot of experimental and simulated no-load currents under sinusoidal supply-voltage excitation.

Fig. 14. Amplitude plot of experimental and simulated no-load currents under deformed line-to-line supply-voltage excitation.

By using (12) and the 2-D vector potential, the second left- hand term of (11) is given by Also, the relationship between the differentials of magneti- zation and flux density can be expressed by means of a tensor [16], [17]. Using the Euler scheme to represent the differentials yields

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Generalized representation of transformer electrical steels working under heavily saturated conditions

by Themistoklis D. Kefalas

2014, Proceedings of the 19th International Conference on Electrical Machines ICEM 2010, Rome, Italy

A generalized macroscopic representation of electrical steels used in transformer manufacturing industry is developed. The proposed representation is specifically formulated for integration in the finite element method. Usage of the... more

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Transformer joints FE analysis using pseudo-source technique

by Themistoklis D. Kefalas

2014, Proceedings of the 14th Biennial IEEE Conference on Electromagnetic Field Computation CEFC 2010, Chicago IL, USA

The paper introduces a finite element methodology for the magnetic field analysis of transformer joints. The proposed technique consists in the application of certain boundary conditions for the excitation of the joints region. The main... more

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Transformer Joints FE Analysis Using Pseudo-Source Technique

by Themistoklis D. Kefalas

2014, IEEE Transactions on Magnetics, vol. 47, no. 5, pp. 1058-1061

Distribution transformers losses are equal to almost 2% of the electricity generated worldwide and only in the European Union are estimated at about 33 TWh/year. Approximately 75% of the total losses are due to core losses as a result of... more

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