Reduction Of Cost And Losses Of Transformer

Reduction of Cost and Losses of Transformers by Using Composite Magnetic Cores Themistoklis D. Kefalas, Member, IEEE, and Antonios G. Kladas, Senior Member, IEEE

Φ Abstract -- 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 composite magnetic core that can be used effectively for manufacturing single–phase and three–phase wound core distribution transformers. The new composite wound core concept is based on experimental evidence concerning the flux density non–uniformity of conventional single–phase and three–phase magnetic wound cores and the losses and magnetization properties of conventional and high permeability Si–Fe grain–oriented steels. A systematic experimental losses and flux distribution analysis of single– phase and three–phase magnetic wound cores is undertaken as well as finite element (FE) analysis considering the bulk anisotropic characteristics of laminated wound cores.

Index Terms–– Finite element methods, magnetic anisotropy, magnetic cores, magnetic field measurement, magnetic losses, power transformers, soft magnetic materials.

I

I.

INTRODUCTION

N order to transmit and distribute electrical energy over large distances economically, it is necessary to minimize Joule losses in the transmission lines by using a high voltage. The required increase and decrease of the voltage is carried out by the electrical transformer which in its simplest form consists of two coils of conductive wire wound around a magnetic core of soft iron. In practice two types of magnetic cores are used, the stack core and the wound core. The wound core in particular is comprised from long continuous strips of sheet steel wound around the coils. The main advantages include reduction of joints and the use of the grain direction of the steel for the flux path. Even though, the transformer remains the most efficient and robust electric machine, a large number of researchers propose transformerless solutions for the electric grid. More specifically, transformerless offshore wind farm appli– cations are studied in [1]–[3] whereas, in [4]–[6] solutions are proposed for photovoltaic plants based on power electronic transformers which include dc–links and multilevel converters. Multilevel applications for grid– connected converters are examined in [7] and converters for renewable energy applications are developed in [8]. Also, researchers study the disadvantages of transformerless solutions in the power grid. In [9], [10] techniques are proposed for magnetic core saturation compensation of grid This work is part of the 03ED45 research project, implemented within the framework of the “Reinforcement Program of Human Research Manpower” (PENED) and cofinanced by National and Community Funds (25% from the Greek Ministry for Development—General Secretariat of Research and Technology and 75% from EU—European Social Fund). T. D. Kefalas is with the School of Electrical and Computer Engineering, National Technical University of Athens, 15780 Athens, Greece (e–mail: [email protected]). A. G. Kladas is with the School of Electrical and Computer Engineering, National Technical University of Athens, 15780 Athens, Greece (e–mail: [email protected]).

connected single–phase power converters, and in [11]–[13] methods for the detection and removal of the DC current component are investigated. The present paper takes into consideration the aforementioned recent trends of eliminating the transformer from the power grid and proposes a novel technique in order to reduce the cost and losses of conventional wound core distribution transformers [14]–[16]. The afore– mentioned technique is called multiple grade lamination wound core and it is based on experimental evidence concerning the non–uniformity of the flux density distribution of the wound core [17]–[19]. By using composite wound cores constructed with a combination of different grades of grain–oriented magnetic steel the total owning cost ( TOC ) of the transformer can be reduced effectively. The multiple grade lamination wound core technique introduces only two design variables, it can be applied after the design optimization of the transformer, or it can be integrated directly in the design optimization scheme, resulting in this way in the generalization of the transformer optimization procedure. If applied after the transformer design optimization a significant reduction of the sum of magnetic steel cost and present value (PV) of future no load loss is achieved. This is very important considering that the PV of future no load loss constitutes more than 60% of the PV of total future losses and of the various materials required to manufacture a wound core transformer the magnetic steel comprises the largest investment [14]. In the case where the multiple grade lamination technique is integrated in the design optimization scheme the resultant optimum transformer designs tend to possess a reduced TOC in comparison with the optimum designs of conventional wound core transformers [16]. In order to evaluate the optimum design variables of a multiple grade lamination wound core, the accurate computation of the peak flux density distribution and no load loss is needed. The specific problem was tackled by developing finite element (FE) models of reduced computational cost. II.

WOUND CORES AND RELATED PATENTS

There have been several patents on wound core topologies and manufacturing. One of the most practical topologies, shown in Fig. 1, was disclosed in 1960 by Treanor [20]. This wound core design is of simple structure and it is constructed by cutting and spirally winding a flat strip of grain–oriented steel into hundreds concentric turn laminations [20]. Cutting of the electrical steel is carried out so that joints are formed in which overlap is gradual, flux transfer is eased, and flux normal to the sheet is minimized. This joint type is known as step–lap joint and its efficiency is determined by the overlap and gap lengths [19].

Fig. 3. Conventional wound core transformer (a) 1–phase core type, (b) 1– phase shell type, (c) 3–phase five–legged. Fig. 1. Treanor’s wound core, extracted from patent U.S. 2 960 756, 1960.

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. III. COMPOSITE WOUND CORES AND RELATED PATENTS The concept of composite magnetic cores was disclosed in 1929 by Johannesen [24]. 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 [25]. The inner part of the core, is constructed of high permeability grain–oriented steel, having low loss but high cost unit, and the outer part of the core, is constructed of conventional grain–oriented steel, having higher loss but low cost unit [25]. Since then, a number of researchers have investigated different topologies of composite cores for various applications [26]–[29].

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

IV. WOUND CORE DISTRIBUTION TRANSFORMERS Typical oil–immersed, distribution transformers are constructed of one or more conventional wound cores assembled about preformed windings as shown in Fig. 3. Ratings range from a few kVA to a few MVA. Topologies of distribution transformers assembled of composite magnetic cores remain the same, as in Fig. 3, and the conventional wound cores are replaced by composite cores. Fig. 4 shows the parts of single–phase and three– phase transformers assembled of composite cores. The inner and outer part of the composite core is made of conventional grain–oriented steel and the middle part is made of high magnetization grain–oriented steel. V.

DESCRIPTION OF THE EXPERIMENTAL SETUP

In this Section a systematic experimental analysis is carried out in order to determine the flux density distribution of conventional single–phase and three–phase wound magnetic cores and also the flux distribution of mixed three–phase wound magnetic cores. The experimental findings presented herein are important in understanding the concept of the novel composite wound core proposed in Section VI.

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. 9. Experimental setup for three–phase transformers cores.

Fig. 7. DAQ setup, current, and active differential voltage probes.

The experimental setup for single–phase wound core measurements is shown in Figs. 5–7. The single–phase wound cores were magnetized from 1.0 T to 1.74 T by a twenty turn excitation coil supplied with a sinusoidal voltage waveform, 50 Hz, from a programmable ac and dc power supply (California Instruments MX30) [30]. In the three–phase experimental setup shown in Figs 8, 9, three twenty turns excitation coils in delta connection were supplied with a balanced three–phase, 50 Hz, sinusoidal voltage waveform, from the programmable power supply MX30 in order to magnetize the three–phase transformer cores to the same induction levels. Four one– turn search coils (SCs), were wound around the total width of the upper yoke of each core as shown in Fig. 8.

The voltage across the excitation coil terminals was captured using active differential voltage probes. Current probes based on the Hall Effect were used for capturing the magnetizing currents. The output of the probes and the SCs was connected to a noise rejecting BNC connector block via passive probes. A noise rejecting cable connects the data acquisition (DAQ) device directly to the BNC connector block. Four virtual instruments (VI) were created with the use of LabVIEW software. The first two were used for capturing the voltage and magnetizing current waveforms. The last two were used for manipulating the acquired voltage and current data in order to compute, losses, flux waveforms, and their harmonic content [31], [32]. A. Single–phase magnetic core losses and flux distribution Fig. 10 shows the specific iron losses of six conventional wound cores as a function of the induction level. For 1.5 T the mean loss of the high magnetization (HiB) and conventional magnetization (M4) cores is 0.715 W / Kg and 0.81 W / Kg. For 1.7 T the respective mean loss is 0.97 W / Kg and 1.235 W / Kg.

Fig. 10. Single–phase transformer cores specific iron losses.

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

Fig. 13. Three–phase and single–phase specific iron loss increase percentage. Fig. 11. Peak flux density distribution across the limb of a wound core.

Fig. 11 shows the peak flux density distribution across the limb of a conventional wound core, for different magnetization levels. The flux density distribution non–uniformity is due to the step–lap joint, the difference in magnetic path length of the steel sheets, harmful stresses induced in the inner steel sheets during manufacturing processes, and flux leakage in the inner and outer steel sheets. B. Three–phase magnetic core losses and flux distribution 1) Three–phase magnetic core losses: Fig. 12 shows the specific iron losses of the typical and the mixed three–phase transformer cores as a function of the induction level. Also, it shows for comparison the sum of the single–phase losses of the HiB and mixed wound cores. For 1.5 T and 1.7 T the loss of the typical and the mixed three–phase transformer cores is 1.02 W / Kg, 1.05 W / Kg and 1.43 W / Kg, 1.56 W / Kg respectively. The building factor at 1.5 T for the typical and mixed three–phase transformer cores is 1.45, [30]. For 1.7 T the building factor is 1.49 and 1.51 respectively. Fig. 13 shows the specific iron loss increase percentage of the three–phase and single–phase transformer cores, as a function of the induction level. In both cases the increase in losses is exponential. The increase in losses of the mixed three–phase transformer core is limited to less than 5.4% up to 1.6 T. For 1.7 T the respective increase percentage is 9.4%. This suggests that a critical induction level exists, where after that the increase in loss is unacceptable. 2) Peak flux density harmonics content: Fig. 14 shows the peak flux density harmonics contents of the typical and mixed three–phase transformer cores for 1.2 T and 1.6 T. The peak amplitude of the 1st harmonic component is larger than the induction level due to the phase angle of the higher harmonic components relative to the fundamental. Also, the

(a)

(b) Fig. 14. Peak flux density harmonics contents of typical and mixed three– phase transformer cores (a) 1.2 T and (b) 1.6 T.

peak flux density of the two inner cores of the typical three– phase transformer core is lower than the two inner cores of the mixed three–phase transformer core. This is because the inner cores of the mixed transformer core conduct more flux due to the low permeability of the outer cores. For 1.6 T and in both cases, the peak flux density of the outer cores reaches that of the internal cores due to the saturation of the HiB grain–oriented steel of the internal cores. The mixed transformer core has larger 3rd and 5th harmonic components. The outer M4 cores have larger 3rd and 5th harmonic components than HiB cores. This explains the increased losses of the mixed three–phase transformer core.

its future losses, given by (2). CHM , CSM , and C Cu are the high magnetization steel, conventional steel, and winding material unit cost ($/Kg), M Cu is the mass of the winding material (Kg), SM is the sales margin, and PNLL ,

PLL are the no–load loss and load loss (W). The A factor and B factor ($/W) are the PV of 1 W of no–load loss and load loss respectively, over the life of the transformer. In the case of the 3–phase five–legged transformer, the mass of the high magnetization and conventional steels M HM and

M SM , are calculated by (3) and (4), where d ms is the steel density (Kg/m3), and c sf is the wound core stacking factor. The minimization of (2) is subject to the three inequality constraints of (5) according to IEC 60076–1, where U k is

Fig. 15. Concept and design variables of a two–grade composite wound core.

VI. MULTIPLE GRADE LAMINATION WOUND CORE TECHNIQUE The operating principle of the proposed composite wound core is based on experimental findings presented on Section V concerning the local flux density distribution non–uniformity of conventional wound cores. According to Fig. 11, the flux density is low in the inner steel sheets, then it increases linearly up to a value higher than the core magnetization level, and finally it decreases until the outer sheets. As a result, by using conventional grain–oriented steel for the inner and outer part of the wound core, and high magnetization grain–oriented steel for the rest part of the core, transformer manufacturers may reach an optimum arrangement between the manufacturing cost and the cost of no load losses. The specific composite wound core exhibits comparable core losses with a core constructed of the high cost, high permeability grain–oriented steel even when the high permeability material represents only a fraction of the total weight of the wound core with the rest part of the core being low cost conventional grain–oriented steel [25]. This is attributed to the flux density non–uniformity of the wound core and the fact that the core loss is a function of the flux density. The concept of the proposed composite wound core is shown in Fig. 15. The generalized design procedure of wound core distribution transformers is obtained by considering the composite wound core design variables x1 , x2 , Fig. 15. They represent respectively, the position and amount of the high magnetization grain–oriented steel, and are subject to the constraints of (1). The design of a transformer constructed of the conventional (high magnetization) steel is a special case of the generalized design process and it is obtained by setting x 2 = 0 ( x1 = 0), and x1 = x3 ( x 2 = x3 ).

spec spec the short circuit impedance (%), PNLL , PLL , and U kspec are the specified, by international technical standards, no– load loss, load loss, and short circuit impedance. TOC is also subject to the apparent power constraint, the induced voltage constraint, the temperature rise constraint and the magnetizing current constraint. The thermal calculation of the transformer is realized through the number of the windings cooling ducts, and the calculation of the cross– sectional area of the conductors is implemented from the current density. The independent variables chosen for the solution of the specific optimization problem are the design variables x1 , x2 , x5 , x6 , the magnetization level B p , the

number of turns of the low voltage winding N p , and the cross–sectional area of the low and high voltage windings, csLV and csHV respectively.

TOC = (CHM M HM + CSM M SM + CCu M Cu ) / SM + A factor PNLL + B factor PLL

{

}

(2)

M HM = 4d ms csf πx22 x6 + x2 x6 (2πx1 + 3 x4 + 2 x5 )

(3)

(

(4)

)

⎫⎪ ⎧⎪πx x 2 − x22 − 2 x1x2 M SM = 4d ms csf ⎨ 6 3 ⎬ ⎪⎩+ x6 ( x3 − x2 )(3x4 + 2 x5 )⎪⎭ spec spec PNLL < 1.15 PNLL , PLL < 1.15 PLL ,

VII.

U k < 1.1U kspec (5)

DEVELOPMENT OF FE WOUND CORE MODEL

A 2D FE model considering the laminated wound core was developed for the flux density distribution and no–load loss evaluation. In 2D FEM analysis the Poisson’s equation is solved which is a function of the magnetic vector potential and the reluctivity

∇ ⋅ v∇Az = − J z

(6)

(1)

where v is the reluctivity tensor and it is represented as a function of the flux density, Az is the z –th component of

The transformer design procedure consists in the minimization of the total owning cost of the transformer [33] i.e., the sum of the first cost and the present value (PV) of

the magnetic vector potential, and J z is the z –th component of the current density. The representation of the

0 ≤ x1 ≤ x3 , 0 ≤ x2 ≤ x3 , 0 ≤ x1 + x2 ≤ x3

Fig. 18. Peak flux density distribution along line AB for B = 1.4 T and x1 = 5 mm, x2 = 10 mm. Fig. 16. Regions comprising the FE model of a composite wound core.

Fig. 19. Peak flux density distribution along line AB for B = 1.5 T and x1 = 5 mm, x2 = 10 mm. Fig. 17. Peak flux density nodal plot of a multiple grade lamination wound core ( B = 1.5 T, x1 = 5 mm, x2 = 10 mm).

nonlinear characteristics of the core materials is achieved by cubic splines interpolation of the v(B ) characteristic and a Newton–Raphson iterative scheme is used for the solution of the particular nonlinear problem. The elliptic anisotropy model, for the 2D FE analysis, is based on the assumption that the flux density B has an elliptic trajectory for the modulus of magnetic field intensity constant. Therefore, if v p is the reluctivity tangential to the lamination rolling direction, vq is the reluctivity normal to the lamination rolling direction, and r is the ratio of the ellipse semi–axes then vq = rv p , r > 1.

(7)

The areas comprising the 2D FE model of a conventional wound core are depicted in Fig. 16. One half of the geometry is modeled due to symmetry and a Dirichlet boundary condition ( Az = 0 ) is imposed on the outer boundaries of the 2D model. 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. 17 shows the peak flux density nodal plot of a two grade lamination wound core for x1 = 5 mm, x2 = 10 mm. The computed peak flux density distribution across the limb of the core for the aforementioned configuration and for two different magnetization levels is shown in Figs. 18, 19. VIII.

CONCLUSION

Conventional transformers will continue to be the dominant component for transmitting and distributing electrical energy for a long time despite the advent of transformerless solutions. This is due to the robustness, reliability, and efficiency of the conventional transformer. Nevertheless, present energy and material costs are driving utilities and manufacturers to improve transformer characteristics. A simple and effective way to achieve this is the composite magnetic core technique with which the manufacturer can achieve an optimum arrangement between manufacturing and operating cost. Even though patents related to composite magnetic cores can be traced back to at least 1929, the specific technique remains a challenging and innovative design approach and it has not been used extensively due to inherent difficulties in determining the optimum configuration of the composite magnetic core design variables.

The present paper introduces the concept of a novel composite wound core and the definition of its respective design variables in a manner suitable for integration to a transformer design optimization procedure. IX. REFERENCES [1]

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X.

BIOGRAPHIES

Themistoklis D. Kefalas (M’09) was born in Greece in 1977. He received the Electrical Engineering Educator degree from the School of Pedagogical and Technological Education, Athens, Greece, in 1999 and the Diploma and the Ph.D. degree in electrical engineering from the National Technical University of Athens, Athens, Greece, in 2005 and 2008, respectively. Since 2010, he has been an Adjunct Assistant Professor with the laboratory of electric machines, School of Pedagogical and Technological Education. Since 2008, he has been an Adjunct Lecturer and Research Associate with the School of Electrical and Computer Engineering, National Technical University of Athens. His research interests include electric machine and transformer design, modeling, and optimization. Dr. Kefalas is a member of the Technical Chamber of Greece. Antonios G. Kladas (S’80–A’99–M’02–SM’10) was born in Greece in 1959. He received the Diploma in electrical engineering from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1982 and the D.E.A. and Ph.D. degrees from Pierre and Marie Curie University (Paris 6), Paris, France, in 1983 and 1987, respectively. From 1984 to 1989, he was an Associate Assistant with Pierre and Marie Curie University. From 1991 to 1996, he was with Public Power Corporation S.A., Athens, Greece, where he was engaged in the System Studies Department. Since 1996, he has been with the School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece, where he is currently a Professor. His research interests include transformer and electric machine modeling and design, as well as the analysis of generating units by renewable energy sources and industrial drives. Dr. Kladas is a member of the Technical Chamber of Greece.