Analytical Calculation of Static Leakage Inductances of HF Transformers Using PEEC Formulas

Abstract

Abstract-When the total current going through a transformer window is equal to zero, only a negligible part of the magnetic energy reaches its core. This is shown by finite-element-method simulations carried out on several two-winding transformers having different shapes. Moreover, induction and energy-density values obtained by 3-D simulations and by 2-D approximations are very close to each other. These two key observations justify the use of formulas that give the induction created by straight rectangular cross-sectional wires, as used in the partial-elementequivalent-circuit method, to compute the window field and, thus, to value the leakage inductances. To refine this approach, weak magnetic-core effects are accounted for by introducing the magnetic images of currents that flow in the windings. A comparison between the calculated values and measured ones is provided.

Complete Analytical Calculation of Static Leakage Parameters. Application to HF Transformer Optimization

“…3), the method introduced in [4] is based on exact formulation of potential vector created by a straight rectangular cross section conductor (Fig. 4).…”

“…In our previous paper [4], the double integration which appears in (5) still had to be made numerically. Recently, we find the analytical expression (7) of this integral which is that…”

“…Three years ago we worked on a semi-analytical method based on 2D PEEC formulae [4]. Potential vector was analytically expressed but, in order to reach energy values, a last integration was still carried out numerically.…”

The analysis and comparison of leakage inductance in different winding arrangements for planar transformer

“…In practice, as frequency grows, the leakage inductances slightly decrease. Indeed, relative variation of leakage inductance as the frequency changes is quite small [6]. The leakage inductance for non-interleaving structure can be calculated as follows: , therefore the total energy is sum of the energy stored in each elementary layer which can be expressed by…”

Nonlinear behavior analysis of split-winding dry-type transformer using a new star model and a coupled field-circuit approach

“…Analytical and numerical methods have been introduced for magnetic field calculations [11,[21][22][23][24]; but an accurate method for this purpose is finite element method [11,[24][25][26]. A Coupled field-circuit approach is an accurate, however time-consuming method.…”