Transformer Harmonics Research Papers

Harmonic Impact on Distribution Transformer No-Load Loss

2010, 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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Analysis of Transformers Working Under Heavily Saturated Conditions in Grid-Connected Renewable-Energy Systems

by Themistoklis D. Kefalas

2012, 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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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

2008, 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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Artificial Intelligence Combined with Hybrid FEM-BE Techniques for Global Transformer Optimization

by Themistoklis D. Kefalas

2007, 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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Flux Distribution Analysis in Three-Phase Si-Fe Wound Transformer Cores

by Themistoklis D. Kefalas

2010, IEEE Transactions on Magnetics, vol. 46, no. 2, pp. 594-597

This paper shows experimental results of longitudinal flux density and its harmonics at the limb, the yoke and the corner of a three phase, Si-Fe, five-legged wound transformer core. Results show that the flux density is nonuniform in the... more

Fig. 1. Measurements setup of the five-legged wound core transformer. This paper shows experimental results of longitudinal flux density and its harmonics at the limb, the yoke and the corner of a three- phase, Si-Fe, five-legged wound transformer core. Results show that the flux density is nonuniform in the cores and there is high level of third harmonic component. Moreover, the lower flux values in the outer cores have been assessed and the simultaneous time variation of the flux in both outer cores has been demonstrated by measurements while the peak magnetic flux density values have been compared to FEM analysis. These findings enable a better understanding of the magnetic behavior of five-legged wound transformer cores and their consideration is expected to achieve respective improvement of the design with respect to core losses and magnetostriction noise.

Fig. 2. Geometry of the wound core and mesh adopted for the FEM analysis. (a) Dimensions of the core (not to scale). (b) Triangular mesh involving 6000 nodes.

Fig. 3. Flux density waveforms obtained from search coils wound around the top yoke of the cores at 1.1 T/50 Hz.

Fig. 7. Simulated field distribution in the transformer by FEM at 1.7 T/50 Hz Fig. 6. Flux density waveforms obtained from search coils wound around the 9th and 48th sheet of the cores at 1.7 T/50 Hz.

Fig. 4. Flux density waveforms obtained from search coils wound around the top yoke of the cores at 1.5 T/50 Hz.

Fig. 5. Flux density waveforms obtained from search coils wound around the top yoke of the cores at 1.7 T/50 Hz.

Fig. 8. Comparison of measured and simulated flux density distribution in the transformer by FEM at 1.7 T/S0 Hz. (a) Core B limb. (b) Core A yoke. (c) Core E corner; -: flux density distribution simulated by the FEM model; 0 0 o: flux density measurements.

PEAK FLUX DENSITY DISTRIBUTION of the yoke. Distortion levels increased with increasing flux den- sity as it was expected. single phase transformer [6]. It can also be seen that the flux concentrates at the inner layers at the corners of the cores. It can be observed that the flux density value of the 3rd layer at the corner is higher than its respective value at the limb by 0.02 to 0.16 T depending on the core. This has been reported in stacked transformer cores but is now shown in wound transformer cores. A difference of the order of 0.08 T can be observed when com- paring cores A and D. The reason for this could probably be a statistical variation due to the material properties and the con- struction of the cores. The FEM results, shown in Fig. 8(a)-(c), provide a good estimation of the global core flux density but fail to accurately represent the small local field variations revealed by the search coils. The greater discrepancy between simulated and measured flux densities in these figures is observed at the 3rd layer, which can be explained by the difficulty of the perme- ability tensor to represent accurately iron laminations situated in the vicinity of iron-air boundary.

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Reduction of cost and losses of transformers by using composite magnetic cores

by Themistoklis D. Kefalas

2014, Proceedings of the 21st International Conference on Electrical Machines ICEM 2014, Berlin, Germany

Even though, the transformer is the most efficient of electrical machines, with efficiencies typically in the high 90s, it is possible to reduce transformer costs and losses by using composite magnetic cores. This paper presents a new... more

Fig. 9. Experimental setup for three-phase transformers cores.

Fig. 1. Treanor’s wound core, extracted from patent U.S. 2 960 756, 1960.

Fig. 3. Conventional wound core transformer (a) 1—phase core type, (b) 1— phase shell type, (c) 3—phase five—legged. Fig. 4. Composite wound cores comprising (a) 1—phase core type, (b) 1— phase shell type, and (c) 3—phase five—legged transformers.

Fig. 2. Composite wound core, extracted from patent U.S. 4 205 288, 1980. Despite the fact that the transformer is the most efficient of all electrical machines, present energy costs are forcing transformer manufacturers and _ utilities to reduce transformer life-cycle costs while maintaining the manufacturing cost within acceptable limits. A number of new transformer cores [21], core joint types [22], and improved amorphous and grain—oriented magnetic steels [23], have been developed recently in order to reduce the manufacturing and operational cost of transformers. Nevertheless, there exists an alternative technique with which it is possible to improve transformer characteristics without the need to revolutionize transformer design or magnetic materials. By using composite magnetic cores constructed with a combination of different grades of grain— oriented magnetic steels the transformer designer can effectively reduce cost and losses.

Fig. 5. Block diagram of experimental setup for single-phase transformer core measurements.

Fig. 8. Block diagram of the experimental setup for three-phase transformer core measurements.

Fig. 6. Experimental setup for single-phase transformer cores. Fig. 7. DAQ setup, current, and active differential voltage probes.

Fig. 12. Comparison of typical three-phase, mixed three-phase, and the respective single-phase, transformer cores specific iron losses.

Fig. 14. Peak flux density harmonics contents of typical and mixed three— phase transformer cores (a) 1.2 T and (b) 1.6 T. Fig. 13. Three-phase and single-phase specific iron loss increase percentage.

Fig. 10. Single-phase transformer cores specific iron losses. Fig. 11. Peak flux density distribution across the limb of a wound core.

Fig. 15. Concept and design variables of a two-grade composite wounc core.

Fig. 16. Regions comprising the FE model of a composite wound core.

Fig. 18. Peak flux density distribution along line AB for B = 1.4 T and x =Smm, x, = 10mm.

Fig. 17. Peak flux density nodal plot of a multiple grade lamination wound core(B =1.5T, x, =5mm, x, = 10mm).

Fig. 19. Peak flux density distribution along line AB for B = 1.5 T and x, =3Smm, x, = 10mm.

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

by Themistoklis D. Kefalas

2008, 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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Development of Distribution Transformers Assembled of Composite Wound Cores

by Themistoklis D. Kefalas

2012, 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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Generalized representation of transformer electrical steels working under heavily saturated conditions

by Themistoklis D. Kefalas

2010, 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

2011, 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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Mixed Si-Fe Wound Cores Five Legged Transformer: Losses and Flux Distribution Analysis

by Themistoklis D. Kefalas

2012, 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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Advanced computational tools for wound core distribution transformer no-load analysis

by Themistoklis D. Kefalas

2012, 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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Unification of anisotropy and FEM-BE models for distribution transformer optimization

by Themistoklis D. Kefalas

2008, 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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Grid voltage harmonics effect on distribution transformer operation

by Themistoklis D. Kefalas

2010, Proceedings of the 7th Mediterranean Conference and Exhibition on Power Generation, Transmission and Distribution MedPower 2010, Agia Napa, Cyprus

Distribution transformer operation is sensitive to the distortion of the supply voltage waveform. According to Strategies for development and diffusion of Energy Efficient Distribution Transformers (SEEDT), reactive power and harmonic... more

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Power Transformer No Load Loss Optimization considering Manufacturing Process Effects

by Themistoklis D. Kefalas

2006, 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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Energy conservation by low loss distribution transformers adapted to load characteristics

by Themistoklis D. Kefalas

2010, Proceedings of the 5th International Conference on Deregulated Electricity Market issues in South-Eastern Europe DEMSEE 2010, Sitia, Greece

The importance of distribution transformer noload 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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A new technique for reducing the total owning cost of wound core distribution transformers

by Themistoklis D. Kefalas

2008, Proceedings of the 6th Mediterranean Conference and Exhibition on Power Generation, Transmission and Distribution MedPower 2008, Thessaloniki, Greece

The total owning cost of a wound core distribution transformer can be reduced by constructing the wound core with a combination of conventional and high permeability grain-oriented magnetic steel. The proposed technique can be applied... more

Table 1: Comparison between measured and computed no load loss

Fig. 5. Peak flux. density distribution of a multiple grade laminatior wound core, (a) x; = 0 mm, x2 =10 mm (b) x; = 5 mm, x. =10 mm. x,, x, configurations is illustrated in Fig. 6. These distributions show clearly that the flux density is considerably higher in the high permeability steel than the conventional steel. Also the peak flux density decreases almost linearly both in the standard and high magnetisation steel regions until the outer steel sheets.

Fig. 6. Peak flux density distribution along line AB for B = 1.5 T and two x1, X2 configurations. Table 1 presents a comparison between the calculated no load loss with the FEM models of Section HI and the respective experimental values for a number of x,, x, configurations. The wound core geometry parameters are the same as before and the mean flux density is 1.7 T in all cases. As can be seen from Table 1, the computed results are in good agreement with the measured ones and the erro is less than 5% in all cases. Also the difference between the computed no load loss with the 2D and 3D FEM models is insignificant and is less than 1.1%.

Fig. 1. Peak flux density distribution across the limb of a strip wound core. The multiple grade lamination wound core technique is based on experimental evidence concerning the flux density distribution non-uniformity of strip wound cores. According to [4] and [5] the peak flux density is low in the core’s inner steel sheets, then it increases to a value higher than the core mean flux density, and finally it decreases until the outer sheets. Fig. 1 depicts experimental curves of the peak flux density distribution, across the limb of a wound core consisting of 90 steel sheets, for different levels of magnetisation [5]. The flux density distribution non-uniformity is attributed to a number of factors like the wound core’s step-lap joints, the difference in magnetic path length, harmful stresses induced in the inner steel sheets during core formation, and flux leakage. No load loss is a function of the peak flux density and as a result the specific core loss of the inner and outer part of the wound core is reduced in comparison with the rest part of the core.

Fig. 4. Representation of the multiple grade lamination wound core geometry and variables. Fig. 3. Specific core loss curves of conventional, M4 0.27 mm, and high permeability, M-OH 0.27 mm, grain-oriented steels.

Fig. 2. Normal magnetisation curves of conventional, M4 0.27 mm, and high permeability, M-OH 0.27 mm, grain-oriented steels. multiple grade lamination wound core technique.

Fig. 7. Detail of the peak flux density vector plot of the multiple grade lamination wound core with optimum design variables x), x2. B. Application of the new technique to a single-phase wound core distribution transformer

Table 2: Comparison between optimum designs of conventional and multiple grade laminations wound core transformers and Ag = 1.93% respectively, of the sum of magnetic steel cost, winding material cost, and PV of total future losses, compared to the cases where the transformer is manufactured using only conventional (M4) and high permeability (M-OH) grade. As a result, by integrating the multiple grade lamination technique in a typical design optimisation procedure, the transformer designer can effectively control not only the magnetic steel cost and the no load loss, but also the winding material cost, the load loss, and other design and operational parameters, in contrast with the method given in Section IV.A. A novel method that reduces the sum of first cost and PV of future losses of wound core distribution transformers is introduced in this paper. It consists in the evaluation of specific design variables of multiple grade laminations wound cores by minimising properly defined objective functions. The proposed methodology can be used after the design optimisation of the transformer or it can be directly integrated into a typical optimisation procedure. The minimisation of the objective function is based on a formulation that combines FEM anisotropy models of low computational cost with stochastic optimisation algorithms.

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Transformer Harmonics

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