Electrical Engineering

, Volume 100, Issue 2, pp 1125–1131 | Cite as

Comparison of core loss and magnetic flux distribution in amorphous and silicon steel core transformers

Original Paper


No-load losses are caused by the magnetizing current that needed to energize the transformers core. These losses are constant and occur 24 h a day, regardless of the load. So, the customers should pay the fixed monthly cost for these losses. In recent years, amorphous alloy has been used to improve distribution transformers performance with the decrease in No-load losses and the increase in the efficiency of transformers. This paper outlines the 2605SA1 amorphous core as a new development of the amorphous alloy with a higher saturation induction. This paper presents a comparison between traditional distribution transformers and amorphous distribution transformers. Distribution of flux density in two different transformers with amorphous core and M5-type silicon steel core has been simulated using 3-D finite element modelling. The simulation and modelling results have been compared with the tests results of 630 kVA, 34.5/0.4 kV prototypes manufactured in the TEK TRANSFORMER factory in Turkey. A good agreement has been obtained between the simulation and experimental results. The simulation and test results show that amorphous core considerably (about 63%) reduces the no-load power losses as well as efficiency of transformers.


Distribution transformers No-load losses Amorphous core Finite element method Magnetic materials 

1 Introduction

Table 1

Specifications of M5 silicon steel and amorphous cores



Amorphous metal

M5 steel





Specific resistance




Typical core loss (50 Hz, 1.4 Tesla)






\(25\,\upmu \)m

0.30 mm

Space factor








Available form


Ribbon foil (142.2,172.2 and 213.4 mm)

Sheet roll

Annealing temperature




Annealing atmosphere


Inert gas

Inert gas

Special annealing requirement


Magnetic field annealing

Transformers are one of the crucial component in distribution and transmission systems, and also they often represent a large investment for power companies. Therefore, transformers should be designed to provide as low power loss as possible. To build the traditional transformers core, ordinarily thin sheets or grain-oriented silicon steel has been used. The thickness of the steel layers is between 0.1 and 0.3 mm, which usually contains up to 3% of silicone to provide the higher electric resistivity for the material. Developments made in distribution transformer core materials had a significant impact on worldwide energy-savings efforts and on environmental improvement. Amorphous core considerably reduces the energy loss as well as decreases the impact on the global environment. This high level of energy savings leads to reducing \(\hbox {CO}_{2}\) emissions. The amorphous alloy was produced at the end of 1950 [1]. But utilization of this materials was investigated much later [2]. At the present time, METGLAS factory manufactured two kinds of amorphous alloys with different specifications. The saturation induction of 2605SA1 amorphous alloys is 1.56 tesla, and for the 2605HB1M amorphous alloys this value is 1.63 tesla. These low-loss, high-permeability alloys have excellent performance for single- and three-phase commercial, industrial and distribution transformer applications. In the amorphous core, the no-load losses of transformer are reduced by 60–70% compared to standard grain-oriented silicon steel (GOSS) transformers [3]. In [4], the dynamic magnetic characteristics including magnetic induction intensity, core loss and magnetic permeability under different operating temperature in the annealed \(\hbox {Fe}_{78}\hbox {Si}_{13}\hbox {B}_{9}\) amorphous alloy cores are systematically investigated. The complex permeability analysis reveals that high \(\upmu \prime \) and low \(\upmu ''\) values are observed at low frequencies. High Fe content \(\hbox {Fe}_{83}\hbox {C}_{1}(\hbox {Si,B,P})_{16}\) amorphous alloys with excellent magnetic properties and high AFA were successfully developed by introducing new amorphous-forming elements and adjusting composition in [5]. In [6], a method presents to reduce the acoustic noises due to the vibration of electromagnetic cores. The effect of high magnetic field on the crystallization of \(\hbox {Fe}_{83}\hbox {B}_{10}\hbox {C}_{6}\hbox {Cu}_{1}\) alloys has been investigated in [7]. The high magnetic field improves both the nucleation rate and the growth rate of \(\alpha \)-Fe crystals. New high-permeability amorphous alloy Co\(_{64}\) Fe\(_4\) Ni\(_1\) Si\(_{15}\) B\(_{14}\) has been used in [8] as a current transformer for monitoring of a leakage current in surge arresters. HB1 amorphous material applied in [9] to reduce the noise and vibration in fluxgate core. In [10], a shell-type power transformer with amorphous alloy cores is used to investigate the withstanding ability and also noise level of this type of transformer under short circuit condition. The results of this reference show that the proposed prototype improved the withstanding ability of transformer under short circuit conditions. In [12], the effects of the joints where the yokes and limbs meet have been investigated. In these regions, the flux may deviate from the rolling direction of the steel or become distorted so that local areas of high loss are produced.

This paper outlines the 2605SA1 amorphous core as a new development of the amorphous alloy with a higher saturation induction. The prototypes of this kind of transformer have been manufactured in the TEK TRANSFORMER factory in Turkey. The simulations result based on 3-D and 2-D time stepping finite element method were verified by tests on the 630 kVA, 34.5/0.4 kV distribution transformer prototypes. The results show that the 2605SA1 amorphous core provided a significantly lower core loss in comparison with the traditional grain-oriented silicon steel such as M5-type steel which is widely used in transformer factories.

2 Distribution transformer analysis with amorphous core and M5-type silicon steel using finite element method

Finite element method (FEM) is a numerical technique to solve the differential and integral equations such as electromagnetic, magneto static, thermal conductivity, solid and structural mechanics, and fluid dynamics. The basic idea of FEM is subdividing physical problems with complicated differential equations into a number of subproblems and dissolving these equations in the linear systems. The computer simulation based on the finite element method that improved in Ansoft—Maxwell has been used. Maxwell includes very powerful library for the electromagnetic analysis as well as the calculation of load and no-load losses of transformer and electrical machines. In this study, MAXWELL software version 15 has been used. In this paper, two kinds of 630 kVA, Dyn11, 34.5/0.4-kV, distribution transformer with amorphous as well as M5-type silicon steel cores are studied. The comparison between the performances of these transformers has been done based on the finite element method. Table 1 briefly illustrates the technical characteristics of amorphous and M5-type silicon steel cores used in this study. Three-dimensional FEM solves the following Poisson in order to determine the magnetic flux distribution [11]:
$$\begin{aligned} \frac{\partial }{\partial X}\left( {R\frac{\partial A}{\partial X}} \right) +\frac{\partial }{\partial Y}\left( {R\frac{\partial A}{\partial Y}} \right) +\frac{\partial }{\partial Z}\left( {R\frac{\partial A}{\partial Z}} \right) =\frac{-ni}{S_\mathrm{c} } \end{aligned}$$
In this equation, A is the magnetic potential vector, R is the core sheet reluctivity, n is the number of winding turns, i is the current and \({S}_{\mathrm{c}}\) is the cross section of the conductors. There are two methods of analysing the transformer based on FEM: static and dynamic analyses. If we have a static analysis, the magnetizing current in Eq. (1) is known. However, to calculate the current from inrush current (startup) to the steady state condition, dynamic analysis of the transformer is required. So, it is necessary to model the voltage source as input. Figure 1 shows the circuit elements of the external circuit between the voltage source and the region under FEM analysis.
In this figure, input voltage is presented as follows:
$$\begin{aligned} V_\mathrm{s} =R_\mathrm{s} i+L_\mathrm{s} \frac{\mathrm{d}i}{\mathrm{d}t} \end{aligned}$$
where \(V_\mathrm{s} \) is the input voltage of the transformer, \(R_\mathrm{s}\) is the resistance of the supply added by the resistance of primary coils, and \(L_\mathrm{s} \) is the inductance of the supply. When current flows into the windings of the transformer, the governing equation of the magnetic field is as follows [11]:
$$\begin{aligned} \nabla ^{2}A-\mu \sigma \frac{\partial A}{\partial t}+\mu J_0 =0 \end{aligned}$$
In this equation, \(\mu \) is the magnetic permeability, \(\sigma \) is the electrical conductivity, and \({J}_{0}\) is the applied current density.
$$\begin{aligned} \frac{\partial A}{\partial t}=jwA \end{aligned}$$
Having obtained A from (3), the distribution of flux density can be calculated in the core as follows:
$$\begin{aligned} B=\nabla \times A \end{aligned}$$
As can be seen in Table 1, M5-type silicon alloy steel plates with 0.30 mm thickness and amorphous metal with 25 \(\upmu \)m are used for laminations of the transformer core. Figure 2a indicates the half cycle the B–H curve of the amorphous metal (from the ENPAY factory). It can be seen in this figure that saturation flux density is approximately 1.42 T. Figure 2b shows mesh operation of the active part of studied amorphous core transformer. Mesh operation has been done in 8 passes in which the increasing rate of meshing has been considered as 5% per pass. Based on this procedure, the total number of mesh elements is 224310. In the three-dimensional modelling, all the shapes of meshes are tetrahedral.
Fig. 1

External \(\Delta \)/Y connected of three-phase transformers

Fig. 2

a First quadrant of the B–H curve of the new amorphous metal b mesh operation of studied amorphous core transformer

Fig. 3

z-type unicore arrangement

The transformer core joints are one of the important factors that affect the efficiency of transformer. In other words, air gaps at the joints of laminations lead to the variations of flux density in transformer core. To design the amorphous core transformer, we used Unicore technology (Fig. 3). These technologies improve the internal flux distribution compared to the C- and E-type core that are generally used in M5-type transformer core. Figure 4a and b, respectively, shows the prototypes of M5 and amorphous core transformer that manufactured in the TEK TRANSFORMER factory in Turkey. As can be seen in Fig. 4b, I-type laminations have been used to manufacture the 630 kVA ((34.5/0.4 kV), Po:1100 W, Pt(+70\({^{\circ }}\)C):5200 W) M5-type transformer core.
Fig. 4

Manufacture prototype transformer with a Amorphous core b M5 silicon steel

The core joint of transformer is shown with red circle. Created air gap at this point is the important factor that contributes to the increase in no-load loss in distribution transformers. Therefore, to optimize design of transformer the z-type unicore arrangement of core laminations in amorphous core transformer has been used. This arrangement for the 630 kVA ((34.5/0.4 kV), Po:401 W, Pt (+70\({^{\circ }}\)C) : 5180 W) prototype shown in Fig. 4a with red circle. Based on z-type unicore, the amount of flux that deviates from the rolling direction at the corners of transformer cores significantly decreases. By reducing the effective corner area of the core, a reduction in the total power loss can be achieved since stacked transformer cores exhibit higher power loss at the corner regions. This reduction is a combination of the restriction of the sideways movement of flux, due to the narrower laminations, and more importantly, the reduction of the effective corner area of the core and, thus, the reduction of the transverse component of flux as are illustrated in Figs. 7 and 8.

Figure 5a and b, respectively, indicates the transformer core loss and exciting power for the typical amorphous core based on 2605SA1 material at different operating temperatures. These data were taken on the cores referred to in Fig 2b as well as Fig. 4a. This feature reflects that the exciting power starts to rapidly increase after the 1.3 tesla. These features caused by the lower coercivity and relatively faster rate of magnetization saturation in the 2605SA1 material. Utilizing this property, the performance of amorphous core transformers will further increase.
Fig. 5

a Core loss taken in SA1 at 50 Hz b exciting power at 50 Hz as a function of operating induction

In the next section, 3-D and 2-D finite element methods have been used to compare the distribution of flux density of 3-phase, 630 kVA distribution transformer based on amorphous SA1 core materials and a typical M5 silicon steel. As mentioned above, for current computation from start up to steady state, the dynamic analysis of the transformer has been used in this study. The electrical circuit in Fig. 1 is used to connect each winding to a voltage terminal. The peak value of voltage sources is 34.5 kV and they have 120-degree phase difference and the frequency is 50 Hz. Figure 6 shows the primary current of the given transformer, which changes with time. It can be observed in this Fig. 6 that inrush current after about 500 ms reduced to the normal value.
Fig. 6

Primary current of the studied transformer

Fig. 7

3-D Magnetic flux density inside the a M5-type silicon steel core b amorphous core

FEM with utilize magnetic parameters and geometrical dimensions of the transformer applied to compute the magnetic field distribution inside the transformer. The time step has been chosen about 0.5 ms, for all simulations of this paper. Figures 7a and 8a display the 3-D and 2-D magnetic flux density in the transformer with M5-type silicon steel, and Figs. 7b and 8b show the flux density in amorphous core, respectively. Distribution of magnetic flux density is one of the most important parameters for the accurate comparison between different material and topologies of transformer core. As can be seen in this figures, in the transformer with silicon steel, yoke and legs are mounted from laminated sheets and connections between them are usually arranged as 45 degree mitred joint. Accordingly, most of the core loss occurs in this section of transformer core. In amorphous core transformer, there are no mitred corners since the amorphous core is prepared as the ring core. This is one of the reasons (but not the main one) of reduced core loss as compared to the case of silicon steel.
Fig. 8

2-D Magnetic flux density inside the a M5-type silicon steel core b amorphous core

Table 2

Prototype design parameters


Prototype liquid-filled hermetically amorphous core transformer



Rated power



Primary voltage



Secondary voltage






Number of phases



Vector group



Ambient temperature max.

\(^{\circ }\)C


Max. average temp. rise (oil/winding)

\(^{\circ }\)C




IEC 60076

Impedance at nominal voltage



No-load losses



Load loss at 75 c


Below standard

Sound power level






Pri/sec. winding conductor material


Cu (copper)

3 Experimental model verification

Although ideal transformers have zero power loss and would be 100% efficient, practically, power transformer when energized will have some losses that occur in its constituent parts. No-load power loss or core losses value of transformer is constant; and its depends on the material that is used in the core. Voltage and frequency are the important factors of no-load losses, accordingly under operational conditions they vary only slightly with system variations. The following equations can be used to calculate the transformer no-load losses.
$$\begin{aligned} P_0= & {} P_\mathrm{hys} +P_\mathrm{eddy} +P_\mathrm{ano} \end{aligned}$$
$$\begin{aligned} P_0= & {} \left( {k_\mathrm{h} \times f\times B_\mathrm{m}^\mathrm{n} } \right) {+}\left( {k_\mathrm{g} \times f^{2}\times B_\mathrm{m}^2 } \right) \nonumber \\&+\,\left( {k_\mathrm{a} \times f^{1.5}\times B_\mathrm{m}^{1.5} } \right) \end{aligned}$$
In this equation, \({P}_{\mathrm{hys}}\) is the hysteresis losses, \(P_{\mathrm{edy}}\) isthe eddy-current losses and \(\hbox {p}_{\mathrm{ano}}\) represents anomalous losses. Generally, hysteresis losses are responsible for 60–70 % of total no-load losses.
Fig. 9

Manufactured prototype amorphous core transformers

Table 3

Reducing the no-load loss in 630 kVA using the amorphous core


Core type

Voltage kV

Frequency Hz

Capacity kVA

No-load loss (w) simulation result

No-load loss (w) experimental result


Amorphous core







M5 steel core






Nowadays, eddy-current losses account for 30–50% of total no-load losses. In order to optimize design as well as improving the efficiency of transformer, the biggest progress has been achieved in mitigation of these losses. This improvement of grain-oriented silicon steel over the years to decrease the no-load losses will be relatively modest. In this study, SA1 amorphous metal has been used to design the 630 kVA Prototype amorphous transformer.

Amorphous metal reduces no-load loss to as low as one-third of that in grain-oriented electrical steel. The design parameters of these kind of transformers are given in Table 2. Figure 9 shows the active parts of manufactured prototype transformers. To verify the simulation results based on finite element method, the experimental measurements are needed. In the comparison between the M5 and amorphous core transformer, no-load loss shall be measured based on IEEE Standard C57.12.00.2006. The transformer was supplied from its LV side, and the HV terminals were open-circuited. Table 3 summarizes the comparing experimental and simulation results between two types of transformers.

It can be observed in this table that transformer core loss about 63.5% reduced using the amorphous core in comparison with M5 silicon steel. Figure 10 shows the comparison of efficiency between the amorphous and M5-type silicon steel 630 kVA transformers. Efficiency of transformer is characterized as the ratio of the output power to the input power. Between electrical machines, distribution transformers are very high efficiency. For having the maximum efficiency of transformer, the load losses should be equal to the no-load losses. It can be seen in this figure that efficiency for amorphous transformers is considerably higher than that of the conventional transformer.
Fig. 10

Comparison efficiency of transformer with amorphous and silicon steel cores

4 Result

This paper proposed an optimized distribution transformer based on the amorphous material. The results obtained based on 3-D finite element method confirmed the measured ones. The 3-phase amorphous core transformer and with M5-type silicon steel under the same rated power (630 kVA) have been compared. The simulation and experimental results show that core losses in amorphous one are about 2.7 times lower than those of the traditional one. As can be seen based on 2-D and 3-D simulation results, the most of the core loss occurs in the core joint of traditional transformer core. In this study, amorphous core is prepared as z-type unicore arrangement. So, these technologies improve the internal flux distribution. The results show that based on this arrangement the core joint effects considerably decreased.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringOndokuz Mayis UniversitySamsunTurkey
  2. 2.Department of Electrical and Electronic EngineeringGazi UniversityAnkaraTurkey

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