Material Consumption Analysis of Three-Dimensional Wound Cores

1) Material Consumption Analysis Under Identical Conditions

Five core structures were selected for horizontal comparison:

• Laminated core (circular cross-section)

• Laminated core (elliptical cross-section)

• Three-dimensional wound core

• Flat wound core

• Four-frame five-column wound core

To facilitate analysis, several uniform conditions were first established:

• Identical effective core cross-sectional area

• Identical coil turn count

• Identical conductor wire size

Once these conditions are set, transformers can be designed based on the five core types. The results yield:

• Identical magnetic flux density in the cores

• Identical total height and thickness of the coils

• Identical window height and width of the cores

Next, weight calculations are carried out for the five core types under these parallel conditions. To aid understanding in the final comparison, structural modifications and mathematical transformations were applied to the core designs and calculations.

Additionally, the perimeter of each core cross-section was calculated. Since the number of turns and the cross-sectional area of the conductor wire are the same, based on the formula for coil weight Gcu = L × N × S, the ratio of perimeters corresponds directly to the material consumption and load losses of the coils.

1) Laminated Core (Circular Cross-Section)

Schematic diagram of circular cross-section laminated iron core

Required Structural Analysis and Transformation:
The two side columns’ corners are cut along the centerline of the upper and lower yokes. These cut corners are then rotated 180° around their midpoint, forming two complete core columns (length = Hw + bm).

Side column transformation

A similar transformation is applied to the upper and lower yokes, resulting in two flat-ended yokes (length = 2M0).
The middle column is cut along the bottom of the upper yoke and the top of the lower yoke, yielding a complete core column (length = Hw).

Lastly, the fusion areas between the columns and the yokes are not yet calculated. In engineering calculations, we typically use the lamination width and step thickness of each layer to determine this. However, for analytical calculations, a more streamlined method is preferred. For instance, integration using only the diameter and fill factor yields reasonably accurate results.

Thus, the weight formula for the laminated core can be transformed as follows:

The weight formula for stacking iron cores

From the formula, we can see that only four parameters—S, Hw, M0, and D—are needed to calculate the weight of the laminated core. For cross-type comparisons among the five core types, these four parameters must be further reduced into a single composite parameter, which will be explained later.

In parallel, the formula for the perimeter of the circular cross-section of a laminated core is also derived:L= πxD。

2) Stacked core (long circular cross-section)

Before calculating the weight of this core type, it’s important to understand its design concept.
This core is evolved from the circular-section laminated core. The transformation process involves multiplying the base circle by a reduction coefficient ks, reducing the diameter and the maximum lamination width, and thickening the maximum lamination layer to maintain the same core cross-sectional area.

This transformation shortens the M0 dimension of the core, thus reducing core weight and no-load losses. However, it increases the perimeter of the core cross-section—because for the same area, a circle has the shortest perimeter.

Illustration of the evolution of the long circular cross-section

Necessary structural analysis and transformation:
By using the same transformation method mentioned above, the weight formula of the laminated core with a long circular cross-section can be obtained:

3) Three-Dimensional Wound Core

A single-frame illustration of a three-dimensional rolled iron core

Required Structural Analysis and Transformation:
By cutting a core frame along the four edges of its core window, we obtain two core columns (length = Hw), two yokes (length = B), and four corner sections. The weight of the four corner parts is calculated using integration, based on diameter and fill factor.

Calculation of the weight of the core of a three-dimensional coil

The weight formula for the three-dimensional wound core can thus be derived as:

4) Flat Wound Core

Required Structural Analysis and Transformation:
Cutting the core frame along the four edges of two core windows yields three core columns (length = Hw), four yokes (length = B), two half-section yokes, and four corner parts of varying sizes.

The principle of calculating the weight of three-dimensional coil cores

The weight formula for the flat wound core can thus be derived as:

5) Four-Frame Five-Column Wound Core

Required Structural Analysis and Transformation:

The weight calculation for the four-frame five-column wound core is relatively straightforward. By multiplying the cross-sectional area of a single frame (S/2) by the total length of the central magnetic path across the four frames, the overall core volume can be obtained.

Thus, the weight formula for the core is:

6) Horizontal Comparison of the Five Core Types

As shown in the table, if parameters such as Hw, M0, and D are converted into a single variable and the corresponding coefficients are substituted, a horizontal comparison of material consumption can then be performed. 

After conducting numerical analysis on a large number of distribution transformer designs with varying performance requirements, three typical sets of Hw, M0, and D relationship values were selected for substitution: 

Note: For ease of comparison, all schemes adopt the same key design parameters. However, in actual design practice, any core structure type can be optimized to achieve the most cost-effective solution.

Future Prospects of the Three-Dimensional Wound Core

The technology behind three-dimensional wound cores has matured significantly, with optimized production processes and standardized equipment and tooling systems now well established. Thanks to its superior performance, cost-efficiency, and long-term energy savings, this design is poised to become the mainstream solution in the transformer industry.

In recent years, national policies have accelerated the adoption of three-dimensional wound core technology, recognizing it as a green, low-carbon, and environmentally friendly transformer solution. It has been included in various promotional catalogs across sectors. As the power industry continues to push for sustainable innovation, this technology is set to lead a transformative shift in transformer design and manufacturing.

About MOOPEC

MOOPEC is a trusted supplier of high-quality electrical steel materials, including grain-oriented silicon steel (CRGO), tailored for transformer applications. With advanced slitting and lamination capabilities, we provide precision-cut core materials that meet the design requirements of both stacked and wound core transformers.

Our facilities support small-batch customization, rapid prototyping, and on-demand production—making us an ideal partner for transformer manufacturers seeking flexibility, speed, and quality. Headquartered in Singapore, MOOPEC serves global clients with end-to-end solutions, from material supply to core processing.

For more information, visit www.moopec.com or contact us directly to discuss how we can support your transformer projects.