Single-phase transformer

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Single-phase transformer

Electrical power transformer is a static device which transforms electrical energy from one circuit to another without any direct electrical connection and with the help of mutual induction between two windings. It transforms power from one circuit to another without changing its frequency but may be in different voltage level.

A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning the transformer relies on a voltage cycle that operates in a unified time phase. 

It consists of two coils of electrical wire called inner and outer windings. The primary is usually known to have the higher amount of voltage. Both coils are wrapped around a common closed magnetic iron circuit which is referred to as the core. The core is made up of several layers of iron, laminated together to decrease losses. Being linked at the common core allows power to be transferred from one coil to the other without an electrical connection. When current passes through the primary coil, a magnetic field is created which induces a voltage in the secondary coil. Usually, the primary coil is where the high voltage comes in and then is transformed to create a magnetic field. The job of the secondary coil is to transform the alternating magnetic field into electric power, supplying the required voltage output.

Solid works model of a Single-phase transformer

The Solid works model of a single-phase transformer consists of a Core, an inner coil and an outer coil, as shown in Figure 1.
3D model of a single phase transformer
Figure 1 - 3D model of a single phase transformer

EMS Simulation of a Single-phase transformer

In EMS, a single-phase transformer is analyzed using AC Magnetic study coupled with thermal analysis to calculate the core loss, magnetic flux density and temperatures.

The frequency of operation of this transformer is 60 Hz.

Coupling to Thermal Analysis

Thermal analysis calculates the temperature distribution in a body due to conduction in the solids. A convection boundary condition is allowed to define what happens to the heat flux in the extremities of the model.

In EMS, Thermal analysis automatically follow an electromagnetic analysis so that the heat sources in the model are automatically pre-computed.


The simulated model composed of a laminated steel Core, an inner coil, an outer coil and Air. The properties of the materials are summarized in Table 1.
The core loss curve is shown in Figure 2.

Table 1 - Materials used in the EMS simulation
Component Material Relative permeability Electrical Conductivity (S/m) Thermal Conductivity (W*m-1  * k-1)
Core laminated steel (M36 at 0.47mm; Mass density: 7700 kg/m^3) 1616 2.32558 e+006 43
Inner Coil/ Outer Coil Copper 0.99991 5.7e+007 401
Coils Air, Inner Air, Outer Air Air 1 0 0.024
Core loss curve
Figure 2 - Core loss curve


In this simulation, the inner and outer coils are modeled as wound coils. They operate at 60 Hz with the inner coil passing 150 A-turns (300 turns, RMS current magnitude 500 mA, Current Phase 0 deg), while the outer coil passes 60 A-turns (600 turns, RMS current magnitude 100 mA, Current Phase 0 deg). This scenario captures one operating condition of the transformer at a particular load. The wire diameter of the wound conductors is 0.91168568 mm.

Thermal Inputs

Convection is the heat transfer mode in which heat transfers between a solid face and an adjacent moving fluid (or gas). In EMS, all air bodies (Outer Air, Inner Air and Coils Air) are applied a convection boundary condition.
Convection coefficient was set to be   10 W/ (m2 *k), and the Bulk ambient temperature was set to be 300 Kelvin.


Meshing is a very crucial step in the simulation. EMS estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry and dimensions of the model, element size, mesh tolerance, and mesh control. In the early stages of your design where approximate results may suffice, you may specify a larger element size for a faster solution. For a more accurate solution, a smaller element size may be required.

To achieve a good accuracy without increasing the total number of mesh elements, it is recommended to apply a mesh control to the regions where a large variation is expected. Four locals mesh control are applied to the two coils, the Core, the inner Air and the Coils Air as shown in Table 2. Figure 3 shows the resulting mesh.

Table 2 - Mesh control
Name Mesh size Components /Bodies
Mesh control 1        25.40 mm Inner Coil, Outer Coil
Mesh control 2        25.40 mm Coils Air
Mesh control 3        50.80 mm Inner Air
Mesh control 4        50.80 mm Core

Figure 3 - Meshed model


The Eddy loss, the Hysteresis loss, the Excess loss and the Core loss in the Core of the transformer, computed by EMS, are shown in Figure 4. These constitute the total core loss.

Core losses computed by EMS
Figure 4 - Core losses computed by EMS

3D plots generated by EMS

In AC Magnetic study coupled to thermal analysis, EMS generates 3D plots of Magnetic Flux Density as shown in Figures 5, Eddy current distribution as shown in Figure 6, Core Loss in the Core body as shown in Figure 7 and Temperature  in the solids as shown in Figure 8.

Magnetic flux density in the transformer
Figure 5 - Magnetic flux density in the transformer
Eddy Current distribution
Figure 6 - Eddy Current distribution
Core loss

Figure 7 - Core loss
Figure 8 - Temperature


Using EMS, the AC Magnetic study coupled with thermal analysis of a single phase transformer gives the different core losses in the Core body, the magnetic flux density, the magnetic flux intensity, the current density and the Temperature. Users can do various scenarios like No Load test, Short circuit test and operating condition test to study the performance of the transformer. 



Core Loss and Transformers

Core Loss and Transformers