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Transformer Harmonics

Transformer Harmonics

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Transformer harmonics refer to the distortion of the electrical waveform caused by non-linear loads connected to a power transformer, resulting in the generation of harmonic frequencies that deviate from the fundamental frequency. This phenomenon can lead to increased losses, overheating, and interference in electrical systems.
lightbulbAbout this topic
Transformer harmonics refer to the distortion of the electrical waveform caused by non-linear loads connected to a power transformer, resulting in the generation of harmonic frequencies that deviate from the fundamental frequency. This phenomenon can lead to increased losses, overheating, and interference in electrical systems.
Determining of Transformers Core Losses Based on Investigation of Core-Sheet Behavior During Power Transformer Test and Operation
by Ahmed Gamil

2024

by identifying the characteristic equation of the specific no-load losses of each iron sheet based on the core configuration, it is possible to reach high accuracy level in detecting the core no-load losses over a wide range of flux... more
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Selection and Rating of the Step-up Transformer for Renewable Energy Application
by Agha Nnachi

2023, Africa research journal

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A Novel De-rating Practice for Distributed Photovoltaic Power (DPVP) Generation Transformers
by Agha Nnachi

2023, Advances in Science, Technology and Engineering Systems Journal

Transformers are habitually designed and manufactured for operation at a fundamental frequency of 50Hz and sinusoidal load current. Transformers are susceptible to non-linear loads. The inception of switching action characterises... more
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A Novel Approach for Evaluating Eddy Current Loss in Wind Turbine Generator Step-Up Transformers
by Agha Nnachi

2023, Advances in Science, Technology and Engineering Systems Journal

South Africa is aiming to achieve a generation capacity of about 11.4GW through wind energy systems, which will contribute nearly 15.1% of the country's energy mix by 2030. Wind energy is one of the principal renewable energy... more
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Application of Polynomial Regression Analysis in Evaluating the Techno-Economic Performance of DSPV Transformers
by Agha Nnachi

2023, Advances in Science, Technology and Engineering Systems Journal

To this extent, the delineation of techno-economic evaluations for transformers becomes more intricate through a lens of Distributed Solar Photovoltaic (DSPV) market in South Africa. Essentially, the transformer price and loss evaluation... more
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Application of Polynomial Regression Analysis in Evaluating the Techno-Economic Performance of DSPV Transformers
by Agha Nnachi

2023, Advances in Science, Technology and Engineering Systems Journal

To this extent, the delineation of techno-economic evaluations for transformers becomes more intricate through a lens of Distributed Solar Photovoltaic (DSPV) market in South Africa. Essentially, the transformer price and loss evaluation... more
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A Novel Approach for Evaluating Eddy Current Loss in Wind Turbine Generator Step-Up Transformers
by Agha Nnachi

2023, Advances in Science, Technology and Engineering Systems Journal

South Africa is aiming to achieve a generation capacity of about 11.4GW through wind energy systems, which will contribute nearly 15.1% of the country's energy mix by 2030. Wind energy is one of the principal renewable energy... more
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Selection and Rating of the Step-up Transformer for Renewable Energy Application
by Agha Nnachi

2023, SAIEE Africa Research Journal

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A Novel De-rating Practice for Distributed Photovoltaic Power (DPVP) Generation Transformers
by Agha Nnachi

2023, Advances in Science, Technology and Engineering Systems Journal

Transformers are habitually designed and manufactured for operation at a fundamental frequency of 50Hz and sinusoidal load current. Transformers are susceptible to non-linear loads. The inception of switching action characterises... more
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Impact of Solar Panel on the Transformer Performance: A Case Study
by JAGANNATH PATRA

2023, Iranian Journal of Science and Technology, Transactions of Electrical Engineering

Transformer is the most important part of any transmission system, so it is necessary to have the transformer in proper working order for uninterrupted power supply in the various locations in around the substations. Renewable energy... more
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Derating method for dry type power transformers based on current distortion parameters
by Johan Rens

2022

Harmonic loads on a transformer cause losses and unwanted heating. This leads to reduced lifetime and unexpected downtime caused by insulation failure. Many publications deal with the life time estimation of transformers. Life time... more
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Defining and Specifying Design Considerations for Distribution Transformers in Large-Scale Solar Photovoltaic Plants
by Pitshou Bokoro

2022, Energies

In the new era of the renewable energy market in South Africa, there is a knowledge gap in the technical standards relating to distribution transformers, which are exclusively intended to serve in large-scale solar photovoltaic (PV)... more
Figure 1. Comparison of the winding Eddy loss correction functions.
Figure 2. Developed 2D FEM model: 40 MVA 88/11 kV. The assessment of the winding Eddy losses using 3D FEM would yield unerring results; however, the computational complexity would widen. Fortunately, in many instances, an alleviation of 2D is feasible without appreciable imprecision. The 2D FEM technique is the most prevalent in the computation of the Eddy losses. By taking into consideration transformer symmetry, one-half of the transformer can be modelled in contrast to the entire unit. The ability of higher-order elements to capture complex data representation is employed to enhance the accuracy of the field solution. The case studies presented herein have been simulated using plane axisymmetric solutions. The main components of the developed FEM model are demonstrated in Figure 2.
Figure 3. 40 MVA, 88/11 kV transformer field solution. In Figure 3, a field solution of a 40 MVA, 88/11 kV transformer is presented. It is observed that the magnetic flux leakage between the LV and HV projects upwards and curves radially across the windings. The magnetic flux leakage is further more concentrated at the interface between the windings and then declines observed to be o diverge away from the winding interspace. As a result of the high magnetic core permeance, the inner LV winding has a significant inclination to draw the magnetic flux leakage. On the HV winding, the magnetic flux leakage is segregated among the tank walls, flitch plate, core clamping structure, and other metallic structures.
Figure 4. No-load loss test arrangement drawing. The no-load and loss measurements at the manufacturer’s premises were performe in accordance with the IEC 60076-7 standard [20-23] to attain the copper losses and th no-load losses at a fundamental frequency (50 Hz) and current. The arrangement drawin, of the no-load and load loss test is illustrated in Figures 4 and 5, respectively.
Figure 5. Load loss test arrangement drawing.
Figure 6. Harmonic current profile.
Figure 7. Harmonic loss factor comparison (conductor dimension of 6.4 mm). Figure 7 presents a graphical comparison of the different correction factor methods. The figure demonstrates the significance of the proposed winding Eddy loss factor where the factors are presented with respect to the harmonic order for the compared methods.
Table 1. Material properties.
Table 2. Estimated losses per disc (W/m) on the LV winding—Case 1
Table 3. Losses in metallic structures—Case 1.
Table 4. Measured rated losses (kW)—Case 1. The developed 2D FEM model can further be employed to compute the hotspot factor of the windings. This factor can be estimated as the density of the maximum winding loss that triggers the hotspot temperature to the average winding loss. The estimation of the HSF for the LV winding can then be estimated as shown below in Equation (22).
Table 5. Estimated losses per disc (W/m) on the LV winding—Case 2 Table 6. Losses in metallic structures—Case 2.
Table 7. Measured rated losses (kW)—Case 2.
It can be observed that the supplied harmonic profile has a significant third and fifth 1armonic content. If a new transformer is designed to facilitate a solar PV application with | significant harmonic content, it must be specified with a harmonic current profile, as neasured at the point of common coupling. The electrical designer cannot estimate nor an the IPP require the designer to apply standard harmonic current distribution tables. n case the harmonic profile of the load to be supplied by a transformer is unknown, hen the IPP and the electrical designer are likely to suffer from short unit service life ind premature failure. Subsequently, adequate measures must be undertaken in order to ruarantee a conservative design for solar PV plant application. Guiding principles on how his information can be applied to establish adequate unit sizing are also detailed in the ubsequent section.
Table 8. Computation of the harmonic loss factor (IEEE Std. C57.110-2018). In Table 8, the computation of the harmonic loss factors based on the IEEE Std. C57.110- 2018 are presented by contemplating the supplied harmonic spectrum in Figure 6. For an existing unit, this method presumes that the winding currents are measured at the rated currents of the unit in-service.
Table 9. Computation of the harmonic loss factor. In order to calculate the total increased losses on account of the supplied harmonic profile, a 40 MVA, 88/11 kV transformer, presented as Case study 1 in the previous section, are examined and tabulated. This transformer has a full load current of 2099A on the LV winding and the winding Eddy loss at the region of peak loss ratio is 11% of the local copper loss. To calculate the load losses in Table 9 under the supplied harmonic current profile, the rated loss components are carried out as follows in Equation (24).
Table 10. Computation of the harmonic loss factor (Emanuel et al.). It follows that the effective winding Eddy loss is the ratio of column 6 and column 3 above, yielding 8.426. The total particular standardized losses are 2.378. The value of the maximum harmonic load current producing this loss as a sinusoidal current is 0.759 and the maximum permissible per-unit harmonic load current provided the supplied harmonic current is 1593 A. Consequently, with the supplied harmonic current profile, the studied transformer capability is estimated at 75.8% of the rated full-load current capability, or 1593 :.A.
Table 11. Computation of the harmonic loss factor (Thango et al. method). It follows that the effective winding Eddy loss is the ratio of column 6 and column 3 above, yielding 6.948. The total particular standardised load loss is 2.178 and the value of the maximum harmonic load current producing this loss as sinusoidal current is 0.793, calculated using Equations (22) and (23). The maximum permissible per-unit harmonic load current provided the supplied harmonic current i is 1665 A. pan ai a ae tif . po” rf
Table 12. Harmonic loss factor comparison.
Table 13. Computation of the K-Factor. Provided with the harmonic current profile, the initial step is to calculate the r.m.s load current on a per-unit basis, which is 1.234 in this instance. Subsequently, the squares of the proportional values for individual harmonic currents are evaluated, carrying out the K-Factor. Based on the K-Factor value of 8.144 and the range of rating, the studied unit can be specified as a K-9 rating transformer. The maximum permissible p.u harmonic load current with the given harmonic profile is 1890 A. The amount of derating necessary for the studied unit to handle the supply of the considered harmonic current profile is calculated in Table 14.
Table 14. Computation of the Factor-K. The initial step to determine the Factor-K is to ascertain the value of e, which is the ratio of the winding Eddy loss to the load losses at a fundamental frequency of 50 Hz. The electrical designer should be able to supply this value; alternatively, the value ranges from 0.05 to 0.1. In this case study, a value of 0.01 is applied. The empirical exponent q. is heavily reliant on the transformer design and is generally obtainable from the manufacturer. This value ranges from 1.5 to 1.7, and a value of 1.7 is considered in this case study. Finally, the transformer would need to be de-rated to 85. 52% (1/1.17) of the nominal power rating, which is 34. 21 MVA when supplying this spectrum.
Table 15. Derating factor comparison. The amount of derating by the methods above yields an error of estimate of 11% and 17.6%, respectively, on the adequate power rating supply for the supplied harmonic current profile. The maximum permissible harmonic load current increases by 30.45% and 11%, respectively.
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Application of Polynomial Regression Analysis in Evaluating the Techno-Economic Performance of DSPV Transformers
by Bonginkosi Thango

2022, Advances in Science, Technology and Engineering Systems Journal

A R T I C L E I N F O A B S T R A C T Article history: Received: 22 December, 2020 Accepted: 08 February, 2021 Online: 17 March, 2021 To this extent, the delineation of techno-economic evaluations for transformers becomes more intricate... more
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A Novel De-rating Practice for Distributed Photovoltaic Power (DPVP) Generation Transformers
by Bonginkosi Thango

2021, Advances in Science, Technology and Engineering Systems Journal

Transformers are habitually designed and manufactured for operation at a fundamental frequency of 50Hz and sinusoidal load current. Transformers are susceptible to non-linear loads. The inception of switching action characterises... more
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Peculiar Stray Gassing Occurrences in Solar Photovoltaic Transformers during Service
by Bonginkosi Thango

2021, Advances in Science, Technology and Engineering Systems Journal

Distributed Solar Photovoltaic (DSP) Plants are one of the fastest growing renewable energy systems in South Africa. The primary components forming an integral part of the point of common coupling (PCC) are, the inverter used to convert... more
The no-load losses and stray losses in windings and structural parts evaluated at nominal tap position are tabulated in Table 1. In order to compute these losses to account for the presence of harmonics it is necessary to obtain the values of the harmonic loss factors using the IEC 519-2014 [19] standard. Generally, from a manufactures perspective, the case of considering the harmonic spectrum proposed by this standard for a transformer intended to operate in a DSP plant is when there is no full harmonic spectrum supplied by the IPP. The harmonic spectrum recommended by IEC is shown in Figure 2. Figure 2: IEC 519-2014 Harmonic spectrum [2]
Figure 1: 2D geometry of the DSP plant transformer are detailed by the authors in [17] and [18]. The advancement of computational power has enabled the development of tools capable of simulating complex geometries, mapping of electromagnetic fields and accurate evaluation of these transformer losses. A software tool embedding analytical methods with Finite Element Method (FEM) is used to estimate the transformer losses. The tool is automated to simulate complete transformer model geometries, magnetic field quantities and computation of eddy current losses in tank walls, flitch plate, core clamps, bus-bar’s and windings. Figure 1 shows the complete model of the transformer 2-D geometry with the main parts that are susceptible to the leakage flux.
data. Notably, this high harmonic order exceeds the recommended IEEE spectrum presented in the last section. Figure 3: Simulated transformer harmonic spectrum at the PCC
At tender stage, the transformer technical specifications supplied by IPP’s to the manufacture generally include information about the permissible top oil, mean winding and HS flemperatures. Electrical designers are then challenged to optimize transformer designs such that they adhere to the IEC 60076-2 [22] and IEEE C57.91-1995 [23] standards and to design the thermal and cooling requirements at an ambient temperature. During the manufacturing stage, as part of the Factory Acceptance Tests (FAT’s) for newly manufactured transformers, the temperature rise test is conducted with the intent to demonstrate these temperatures, at full load and specified ambient temperature. The loading capability of the transformer is predominantly regulated by the HS temperature. In accordance with the IEC, the HS lemperature is described as the mean winding temperature rise over the mean oil temperature multiply by a HS factor [22] and [23].
the provision of a full harmonic study from the IPP, and judging from the results, the indication is that it was under-designed for the environment it was intended to operate, which would explain the reported high temperature rise and oil gassing patterns. Subsequently, this knowledge gap led to insufficient design of the winding conductor sizes and cooling system for this application. Figure 4: Loss comparison (IEC vs. Simulated Harmonic Spectrum)
Table 1: Tabulated loss computation under a harmonic spectrum From both the fundamental and harmonic losses above, it can be noticed that the loss percentage error is higher for winding stray losses. Additionally, the core losses are observed to be constant, indicating that the no-load losses are independent of the harmonic currents. The minimum winding stray losses as a result of axial and radial leakage fields are computed by optimizing the selection of conductor dimensions while maintaining the permissible flux and current density of the winding [20] and [21]. The transformer winding subject to harmonic distortion is designed using continuously transposed cable epoxy (CTCE) with minimum axial and radial dimensions of each conductor to reduce the eddy losses [20] and [21]. The tank is designed using mild steel which hold a nonlinear permeability. The quantity of the magnetic field in the tank walls is evaluated by eliminating the impact of nonlinearity. Thereafter, the losses in the LV and HV tank walls are computed taking into account the effect of nonlinearity through repetitive estimation. The flitch plates are also mild steel type and contain slots at the upper and lower positions. While their loss quantity is low compared to winding eddies and tank losses under harmonic effects, the magnetic field quantity is high which results in the flitch plate being more susceptible to HS temperature.
To analyse the complete transformer harmonic response (THR), Figure 4 shows the results of the predicted transformer losses by IEC harmonic spectrum and compares them with the simulated harmonic spectrum the transformer is subjected to while in service. The transformer under inspection was designed without Table 2: Transformer losses based on actual DSP plant harmonic spectrum
Table 3: DGA oil sample results (ppm) The adverse effect for under-designing this transformer for requirements such as suitable conductor choice and size, and cooling system can be observed from the gas concentration exceeding the permissible IEC limits as shown in red in Table 3. Due to the excessive nature and production rates of hydrogen, a possible solution would be to replace the oil in all the affected units in case there were contaminants in the oil that resulted in the production of the abnormal gassing patterns. If the observed gassing patterns persist after the oil replacement, then a redesign of the transformer units might be needed. A proper harmonic study of the DSP plant as well as the loading conditions should be conducted in order to design for the DSP conditions. For the above
Table 4: DGA oil sample results after oil replacement (ppm) Air and moisture are generally the main determinants of gas pressure in the transformer oil. The progression of these components are determined by the transformer tank design and loading profile. The above irregular gas bubbling patterns are observed at hot spot temperature [22] far beyond the maximum permissible temperature of 78°C by the IEC. These patterns instigate rapid ageing of oil and cellulose insulation.
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Contemplation of Harmonic Currents Loading on Large-Scale Photovoltaic Transformers
by Bonginkosi Thango

2021, 2020 6th IEEE International Energy Conference (ENERGYCon)

A surge in harmonics and distortion in the South Africa's electric power system has come to the fore in the early phases of integrating renewable energy resources to the national electric grid. Having said that, in this day and age a... more
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Effects of Current Harmonics on Maximum Loading Capability for Solar Power Plant Transformers
by Bonginkosi Thango

2021, 2020 International SAUPEC/RobMech/PRASA Conference

Distribution transformers are commonly designed and manufactured to operate at fundamental frequency and to facilitate sinusoidal loads. The operation of loads that draw distorted currents culminate in higher losses, hotspot temperatures,... more
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EA SA EASA AR200 G U I D E FOR THE REPAIR OF POWER AND DISTRIBUTION TRANSFORMERS (Revised 2011
by Hồ Văn Học

2019

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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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Grid voltage harmonics effect on distribution transformer operation
by Themistoklis D. Kefalas

2014, 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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Energy conservation by low loss distribution transformers adapted to load characteristics
by Themistoklis D. Kefalas

2014, 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

2014, 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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Reduction of Power Grid Losses by Using Energy Efficient Distribution Transformers
by Themistoklis D. Kefalas

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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Transformers Made of Composite Magnetic Cores: An Innovative Design Approach
by Themistoklis D. Kefalas

2014, Journal of Recent Patents on Electrical Engineering, vol. 2, no. 1, pp. 1-12,

Nowadays, transformers are made of conventional magnetic cores which are constructed of a single grainoriented or amorphous, magnetic steel. Even though, the transformer is the most efficient of electrical machines, with efficiencies... more
Fig. (1). Treanor’s wound core, extracted from patent US2960756, 1960.
In 1980 Lin, Ellis, and Burkhardt disclosed a composite wound core having two parallel magnetic circuits of unequal mean lengths as shown in Fig. (2) [42]. The short magnetic circuit, i.e. inner part of the core, is constructed of a high permeability grain-oriented steel, having low loss but high cost unit, and the long magnetic circuit, i.e. outer part of the core, is constructed of a conventional grain-oriented steel, having higher loss but low cost unit [42]. Fig. (2). Composite wound core, extracted from patent US4205288 1980.
Fig. (5). Specific core loss curves of conventional, M4 0.27 mm, and high permeability, M-OH 0.27 mm, grain-oriented steels. Fig. (4). Normal magnetization curves of conventional, M4 0.27 mm, and high permeability, M-OH 0.27 mm, grain-oriented steels.
Fig. (3). Peak flux density distribution across the limb of a strip wound core.
High permeability grain-oriented steels present improved magnetization and specific core loss characteristics in comparison with the conventional grain-oriented steel as illustrated in Fig. (4 & 5). On the other hand the cost unit of high permeability steel is higher than that of conventional grain-oriented steel. Thus, by using conventional grain- oriented steel for the inner and outer part of the wound core and high permeability grain- oriented steel for the rest part of the core, the transformer manufacturer may achieve an optimum tradeoff between first cost and PV of future no load loss.
Fig. (6). Representation of the multiple grade lamination wound core geometry and variables.
Fig. (9). Current probe and differential voltage probe.
Figure 10 illustrates a detail of the wound core, the excitation coil, and the search coils. The wire used for the search coils is a solderable enameled copper wire 0.1 mm in diameter. A total of 30 search coils were inserted in the wound core for the experimental evaluation of its peak flux density distribution along the limb, yoke and comer. The overall loss of the core did not change noticeably after the coils were wound in position. Therefore, it was assumed that the flux distribution did not change much due to the search coils being introduced. Fig. (10). Detail of the wound core, the excitation coil and the search coils.
Fig. (8). Experimental setup. The experimental setup used for the local flux density and no load loss measurements of wound cores is illustrated in Fig. (8). It consists of a PC and a National Instruments (NI) 6143 data acquisition (DAQ) card (8 voltage differential inputs, 16 bit, 250 ksamples / s). The excitation coil terminals are connected to the input of the DAQ card via an active differential voltage probe (3 dB frequency of 18 MHz) and a current probe based on the Hall Effect (1 dB frequency of 150 kHz) is used for capturing the no load current. Both probes are depicted in Fig. (9). For the magnetization of the wound cores, a 23 turn excitation coil is supplied by a one- phase 230 V, 50 Hz source through a variable transformer. The no load loss was evaluated by the acquired voltage and current data with appropriate virtual instruments (VI) created with the use of LabVIEW.
Fig. (12). Contours of the magnetic vector potential of a conven- tional wound core.
Fig. (14). Peak flux density nodal plot of a multiple grade lamination wound core(B =1.5T, x, =0 mm, x, =10 mm). Fig. (13). Peak flux density nodal plot of a conventional wound core(B =1.5T).
Fig. (11). Areas comprising the 2D model of a conventional wound core.
Fig. (19). Peak flux density distribution along line AB for B =1.5 T and x, =5 mm, x, =10mm. Fig. (18). Peak flux density distribution along line AB for B =1.4 T and x, =5mm, x, =10mm.
Fig. (15). Peak flux density nodal plot of a multiple grade lamination wound core(B =1.5T, x, =5 mm, x, =10 mm).
Fig. (17). Peak flux density distribution along line AB for B =1.5 T and x, =Omm, x, =10mm.
Fig. (16). Peak flux density distribution along line AB for B =1.4 T and x, =Omm, x, =10mm. Table 1 presents a comparison between the calculated no load loss with the FEM models of Section 4 and the respective experimental values for a number of x,, x, configurations. The considered wound core parameters are X, =24.3 mm, x, =57 mm, x, =183 mm, x, =190 mm, and the mean flux density is B =1.7 T. As can be seen from Table 1, the computed results are in good agreement with the measured ones and the error 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% in all cases.
Fig. (21). Detail of the peak flux density vector plot of the multiple grade lamination wound core with optimum design variables x,,
Fig. (20). Variation of the objective function with respect to SAR iterations. During the minimization of (18) a number of local minimums with values very close to the global minimum were identified. Due to this fact the number of successes of the GA was lower than that of the SA and SAR algorithm, as the GA was trapped most of the times in local minima. The optimum distribution of the design parameters as calculated by the SA and SAR algorithms correspond to an objective function value of f «) = 677.5 $, ie. a 3.2% reduction of the sum of magnetic steel cost and PV of future no load loss as it was pre-evaluated by the industrial optimization scheme [48]. Furthermore, the SAR algorithm exhibits a 20% reduction in objective function calls comparing to the classic SA algorithm. Figure 20 depicts the variation of the objective function with respect to the SAR iterations and Fig. (21) illustrates a detail of the computed flux density distribution with the 3D FEM model of the multiple grade lamination wound core with the optimum variables.
Table 1. Comparison Between Measured and Computed no Load Loss (x, = 24.3 mm) optimization with a heuristic methodology which is already used by the transformer industry [48]. The parameters of the wound cores under consideration are x, =51.3 mm, x, =57
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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
Fig. 1. Typical wound core.
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
SIMULATED VERSUS EXPERIMENTAL RESULTS
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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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Flux Distribution Analysis in Three-Phase Si-Fe Wound Transformer Cores
by Themistoklis D. Kefalas

2014, 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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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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