January 8, 2015

Magnetic component design

Abstract AC currents in multiple layers in the transformer window can increase copper losses significantly due to the proximity effect. Traditionally used Dowell’s curves show...

---

Abstract

AC currents in multiple layers in the transformer window can increase copper losses significantly due to the proximity effect. Traditionally used Dowell’s curves show that the phenomenon starts at copper thickness as low as 1/5 of the skin depth which is just 1.7 mm at 60 Hz. Many designs deviate from assumptions beyond Dowell’s solution, which leads to suboptimal design. Finite Element Analysis software allows accurate modelling of high frequency phenomenon but is still considered too tedious to use and requires expert operators for accurate results. New generation products like EMS from EMWorks combine powerful simulation capabilities with easy to use interface appropriate for hands-on engineers in everyday use.

Keywords: Finite Element Analysis, AC copper losses, skin effect, proximity effect

1. Introduction

Finite Element Analysis (FEA) software has been used by electrical engineers for several decades. It is a great tool for simulating electromagnetic fields in chokes and transformers allowing accurate computation of the spatial distribution of the current, flux density, associated losses and resulting temperature rise as well as the impact on efficiency of the whole magnetic component. By manipulating dimensions and geometrical arrangements we can yield the most compact, efficient and lowest-cost structure. Unfortunately, commercial 3D FEA software gained reputation as expensive, tedious and requiring highly skilled and specialised operator to yield sufficiently accurate and reliable results. In this situation many practicing designers were forced to resort to simplified methods with results left to chances. FEA vendors have been busy for years trying to improve the ease of use, accuracy, stability and versatility of their tools with slow but systematic progress. Some of them became truly practical design tools not only for a PhD working on a science project but also for hands-on designers with general knowledge of magnetic components. Examples for this article were generated using EMS from EMWorks.

2. AC copper losses due to the skin and proximity effect

The nature of AC copper loss challenge in power transformer design is well known. AC currents in windings induce eddy currents. These currents create an uneven current distribution leading to thermal problems and the necessity to redesign the transformer. In general, currents tend to alter their distribution in a way, which minimises the overall amount of energy extracted from the source, both real and reactive. Reduction of the reactive component associated with the energy stored in the magnetic field inside the wire pushes the current towards the surface of the conductor.

Figure 1: The mechanism for AC current crowding towards the surface of a conductor and resulting current density distribution for a single wire.

Because the conduction losses are proportional to the square of the current density, this uneven current distribution leads to an increase of total losses. Resulting current crowding in a single conductor is most conveniently characterised by skin depth which is defined as a depth below the surface at which the current density has fallen to 1/e. Effective resistance of a wire with AC current is equal to that with DC current uniformly distributed across the skin depth. See Fig. 1.

Subscribe to Transformers Magazine